Are Champion fighters better now that we have Crusher/Piercer/Slasher?

[Greywander]

Champions get both the most attacks and the highest crit chances, allowing them to maximize the odds of proccing the crit effects of these feats. You could also dual-wield bludgeoning and slashing weapons so that you can use both feats on the same turn (if the party focus fires one enemy, you only need to crit once with Crusher, so subsequent crits could be made with Slasher and spread out among multiple enemies if you get lucky). (Piercer is generally the least interesting of the three, but there might be some builds that make good use of it, especially archer builds, though a slinger Crusher or hand axe thrower Slasher build could be interesting.) Or, you could use PAM with a slashing polearm, since the BA attack deals bludgeoning damage.

Also, aside from a Genielock dip, is there any way to deal two or more types of BPS damage on the same weapon attack?

Furthermore, what would a typical critfish Champion build look like? Elven Accuracy makes sense to get (though it limits you to finesse/ranged weapons), but if you already have a way to consistently get advantage then perhaps the Crusher benefit isn't really needed? Some methods for getting advantage, such as using obscurement and the Blind Fighting style, would also impose disadvantage on the enemy, making the Slasher crit effect not really do anything.

Mainly the idea I'm playing with here is leveraging the crit effects of Crusher and Slasher, along with their once-per-turn effects, in order to try and build a more tactical fighter. By using Slasher to give enemies disadvantage, that could be a form of tanking. Giving advantage to my allies with Crusher increases the damage of the entire party, even if my own damage is mediocre. Using the knockback and speed reduction allows some measure of control to be used, moving enemies where I want them and keeping them from moving away, and could synergize well with the abilities of other party members.

[Kane0]

Short answer is yes, these feats improve champions.
*How much* they improve the champion compared to other feats is a matter of some contention. I would say they are decent and help give you some fun widgets to help flesh out your combat routine but they arent incredibly strong.
That said, if you take them and it helps you have more fun I consider that a well chosen feat.

[stoutstien]

It makes the champion dip stronger but a sammy, BM, or EK are still probably stronger as crit focused fighter subclasses if looking past 3 levels.

[Maan]

Also, I think the other problem with Champion Fighter is it's pretty boring to play: it doesn't give you a lot of options, really.

[zinycor]

Personally I never thought that champion was bad, just pretty boring.

[Schwann145]

Gonna just repeat what's essentially already been said: Champions are not, and have never been, *bad.* They're boring. They offer zero tools for exploration or social encounters, and nothing but mathematical bonuses for combat encounters.

They are quite strong and very very dull.

[Greywander]

It makes the champion dip stronger but a sammy, BM, or EK are still probably stronger as crit focused fighter subclasses if looking past 3 levels.
This confuses me, as Champions are the ones that specifically get a bonus to crits. I understand Samurai can generate advantage whenever and turn one of their attacks with advantage into two attacks without. I'm not super familiar with Battle Master maneuvers, but I'm sure they have things that help. EKs can get spells that can help you get advantage (e.g. Fog Cloud/Darkness + Blind Fighting). I can also see how something like a Champion 3/barbarian 17 would do a lot more damage, but if we're specifically looking to get as many crits as possible in order to get the most from Crusher/Slasher, wouldn't a straight Champion perform better than anyone?

Edit:

Gonna just repeat what's essentially already been said: Champions are not, and have never been, *bad.* They're boring. They offer zero tools for exploration or social encounters, and nothing but mathematical bonuses for combat encounters.

They are quite strong and very very dull.
There are ways of dealing with this, though. Fighters get more feats than anyone, making it easier to grab things like Ritual Caster or Actor or Linguist. Champions also get Remarkable Athlete, allowing you to ignore STR and DEX skills, instead picking other skills. It might not outright give you stuff for non-combat, but it frees you up to spend your other build resources on such things.

[stoutstien]

This confuses me, as Champions are the ones that specifically get a bonus to crits. I understand Samurai can generate advantage whenever and turn one of their attacks with advantage into two attacks without. I'm not super familiar with Battle Master maneuvers, but I'm sure they have things that help. EKs can get spells that can help you get advantage (e.g. Fog Cloud/Darkness + Blind Fighting). I can also see how something like a Champion 3/barbarian 17 would do a lot more damage, but if we're specifically looking to get as many crits as possible in order to get the most from Crusher/Slasher, wouldn't a straight Champion perform better than anyone?
Mostly the there subclasses are getting stuff past criticals but let's just look at that part alone.
make it an easy comparison. Champ get 2/20 per attack rolled to get a critical hit at level 3. A flat 10% critical chance Is nice but advantage is actually better because it also protects against low rolls while doubling the number of D20s per attack is almost as good as the extended crit range. *If* the champion has an ally supplying advantage they could leverage it but in a straight up 1 for 1 comparison the extended crit range is lacking even in the area of crits. By the time champion gets the 18-20 range It only has a slightly higher crit rate than the bog standard cursed samurai.

For someone looking to roll crits as often as possible anything past 3 lvs of champion is a hard sell. Maybe a champion 11/beast barbarian 8/genie lock 1.

[bid]

Fighters get more feats than anyone, making it easier to grab things like Ritual Caster or Actor or Linguist.
BM, EK, and sammy also get the same tools. You need to wait for level 10-11 until champions are finally no more "boring" that the other fighters.


Mainly the idea I'm playing with here is leveraging the crit effects of Crusher and Slasher, along with their once-per-turn effects, in order to try and build a more tactical fighter.
Napkin maths...
I think we already evaluated critical range needs to be 17+ to match with BM extra damage at level 5.

So you'd need more 2 crits every time you roll 19 to match that damage... Assuming your party is all champions, you get 2/20 extra crits per attack, so 20 attacks overall... or about 10 extra champions.
{compared to all BM which goes from 1/20 to 2/20 = +1/10 extra crits per attack.}

So no, you'd do that for the RP concept and not for any "optimal" result.

[Man_Over_Game]

Napkin maths...
I think we already evaluated improved critical needed to be 17+ to match with BM extra damage at level 5.

So you'd need more 2 crits every time you roll 19 to match that damage... Assuming you're all champions, you get 2/20 extra crits per attack, so 20 attacks overall... or about 10 extra champions.

So no, you'd do that for the RP concept and not for any "optimal" result.


I'd be down for Champion to change to treat any 1 or 2 on any STR, DEX, or CON roll to be changed to a 20.

Better tank, better athlete, more consistent damage dealer.

[bid]

I'd be down for Champion to change to treat any 1 or 2 on any STR, DEX, or CON roll to be changed to a 20.
The +2 hit you're giving them makes a big difference in damage, even before adding the crit dice.

Once per turn, or it might add too much damage with 4 attacks. Champion is kinda ok at level 20, it's before level 11 that they're terribad.

[heavyfuel]

@OP: Better? Yeah. Good enough to be competitive with other Fighter sublcasses? Nah.

@People saying the champion isn't bad: How are they not terrible? With a Greatsword (the best weapon for pure crit damage), Improved Critical is adding an average of 0.35 points of damage per attack (or about 0.65 if you have advantage, which isn't exactly a granted for a Fighter). I once gave a Champion Fighter the Superior Critical ability at level 3 and it still underperformed significantly compared to a Battlemaster in the same party. I can see how, by level 20, with 4 attacks, the Champion is actually pretty decent, but before then, it just sucks.

[DwarfFighter]

What is your math for that average? The reason I ask is that, well, when you MISS you tend to do zero damage...

[JNAProductions]

@OP: Better? Yeah. Good enough to be competitive with other Fighter sublcasses? Nah.

@People saying the champion isn't bad: How are they not terrible? With a Greatsword (the best weapon for pure crit damage), Improved Critical is adding an average of 0.35 points of damage per attack (or about 0.65 if you have advantage, which isn't exactly a granted for a Fighter). I once gave a Champion Fighter the Superior Critical ability at level 3 and it still underperformed significantly compared to a Battlemaster in the same party. I can see how, by level 20, with 4 attacks, the Champion is actually pretty decent, but before then, it just sucks.

Because the Champion is a Fighter.

A Fighter without a subclass is still good. So the Champion, despite not adding a ton, is still a strong and competent PC.

[x3n0n]

I don't see much point in pursuing Piercer as a crit-fisher in specific. There are probably better ways to get that damage.

The most valuable thing we could add for crit-fishing is a source of advantage, and I think the least expensive in build resource is to choose Blind Fighting and assume someone can provide heavy obscurement.

A couple of build sketches for level 6ish:

Vhuman PAM (quarterstaff), Fighter, Blind Fighting, Champ, Crusher.

(Wood?) Elf (whip and/or dual scimitar), Fighter, Blind Fighting, Champ, Slasher, Elven Accuracy.

Each advantaged Champ attack is 19% likely to crit, or 27% with Elven Accuracy.

With 3 advantaged attacks (Extra and PAM), the Crusher will crit on 47% of turns; the Elven Slasher with 2 advantaged attacks will crit at the same rate, and 61% of turns with 3 attacks (Extra and dual scimitar).

[heavyfuel]

Because the Champion is a Fighter.

A Fighter without a subclass is still good. So the Champion, despite not adding a ton, is still a strong and competent PC.

I don't buy it. You could say the same thing about literally every class in the game (except maybe the Monk and the Ranger in Tier 2+)

The fact that the Champion adds practically nothing makes it a trap option, and trap options are bad game design.

[JNAProductions]

I don't buy it. You could say the same thing about literally every class in the game (except maybe the Monk and the Ranger in Tier 2+)

The fact that the Champion adds practically nothing makes it a trap option, and trap options are bad game design.

No? Rangers rely a LOT MORE on their subclasses than a Fighter does. Different classes get more or less from their subclasses.

And it doesn't add nothing, it just doesn't add quite as much as another subclass. I wouldn't consider something a trap option unless it either makes you actually WORSE than picking nothing, or is so much worse than the others that you shouldn't play at the same table as someone who picked a more balanced option.

Neither is true for Champion-you can play a Champion Fighter in pretty much any normal party, and you won't be failing to contribute. Sure, if you're level 17 and the Wizard is doing Wish-Sim chaining, you'll feel useless, but so will literally everything but that one trick.

I feel like we might be talking past each other, so just in case, can you define what you mean by "trap option"?

[heavyfuel]

I wouldn't consider something a trap option unless it either makes you actually WORSE than picking nothing [snip]

I guess this is where our view diverge. I consider something a trap option based on the opportunity cost of of something rather than the straight value added.

For example, take a look the Dual Wielder feat. Is it a bad feat, by itself? No, of course not. It gives you +2 damage, +1 AC, and the unique - if situational - ability to draw two weapons at once. All of these things definitely make your character stronger than it was before you picked the feat.

However, when you look at the opportunity cost of the feat, it's far less attractive. Getting a Dex ASI instead of the feat gives +2 damage and +1 AC just like the feat, but it also gives +1 to attack, +1 to Dex saves, +1 to Initiative, and +1 to all other Dex checks (including skills).

It's no surprise a lot of people (myself included) thing the Dual Wielder feat is a trap option. In order to get the benefits of the feat, you have to let go of the benefit of an ASI, which is a superior benefit.

Is the Champion bad, by itself? No, of course not. But when your options are either the Champion's +0.35 extra damage per attack, or the Battlemaster's 12/day +4.5 extra damage with riders, I think the Champion is a pretty clear trap.

It takes over 150 attacks in an adventuring day for the Champion match the BM's damage, and the utility of the BM (both in and out of combat) also far exceeds the Champion's.

[JNAProductions]

I guess this is where our view diverge. I consider something a trap option based on the opportunity cost of of something rather than the straight value added.

For example, take a look the Dual Wielder feat. Is it a bad feat, by itself? No, of course not. It gives you +2 damage, +1 AC, and the unique - if situational - ability to draw two weapons at once. All of these things definitely make your character stronger than it was before you picked the feat.

However, when you look at the opportunity cost of the feat, it's far less attractive. Getting a Dex ASI instead of the feat gives +2 damage, +1 AC just like the feat, but it also gives +1 to attack, +1 to Dex saves, +1 to Initiative, and +1 to all other Dex checks (including skills).

It's no surprise a lot of people (myself included) thing the Dual Wielder feat is a trap option. In order to get the benefits of the feat, you have to let go of the benefit of an ASI, which is a superior benefit.

Is the Champion bad, by itself? No, of course not. But when your options are either the Champion's +0.35 extra damage per attack, or the Battlemaster's 12/day +4.5 extra damage with riders, I think the Champion is a pretty clear trap.

It takes over 150 attacks in an adventuring day for the Champion match the BM's damage, and the utility of the BM (both in and out of combat) also far exceeds the Champion's.

What out of combat utility does the BM have?

And I do agree that opportunity cost can make something a trap-Toughness, in 3.5, is a trap despite inarguably being a bonus. It's just that, as I said earlier, a Fighter with literally no subclass is still a good party member-the subclass is just gravy.

It'd be neat if the game was 100% perfectly balanced, but that's not the case, and it will never be the case. Some stuff will be better than others-which that is will depend on the DM and campaign, though I'm perfectly fine saying that Champion is generally the weakest of the Fighter subclasses. (Maybe PDK is worse? I never looked at that much.) But it's a perfectly fine subclass, especially for people who are just starting the game.

[heavyfuel]

What out of combat utility does the BM have?

And I do agree that opportunity cost can make something a trap-Toughness, in 3.5, is a trap despite inarguably being a bonus. It's just that, as I said earlier, a Fighter with literally no subclass is still a good party member-the subclass is just gravy.

It's not much OOC utility, but the "skill maneuvers" like Ambush and Commanding Presence help the BM in Social and Exploration encounters. At least help more than Improved Critical.

The fact that the character is still competent despite the trap option doesn't mean the chosen option isn't a trap. You can have both cases in a single character.

In your 3.5 analogy, a Cleric (widely considered the best class in 3.5) that picks Toughness is both a strong character AND the chooser of a trap option. A Fighter that picks Champion is both a good combatant (despite the Champion) AND the chooser of a trap option (the Champion subclass).

One doesn't negate the other.

[Greywander]

But when your options are either the Champion's +0.35 extra damage per attack,
Where is this number coming from? I'm looking at a damage calculator and the champion is getting ~8 extra damage, or 2 damage per attack. This does include a bonus for being a half-orc; the damage increase is a bit less without that, but still about 1 damage per attack (whether or not you have GWM also affects damage added).

Part of the appeal of the Champion is also the lack of resources to manage, making you great at endurance fighting. BMs and EKs need to manage their resources, and can find themselves making tough decisions whether or not to spend those resources. Sure, they can create much more potent effects by doing so, but they're limited in how often they can do this, and once those resources expire they're almost a fighter without a subclass. Ideally, you should be resting enough that this isn't a problem, but that won't stop you from agonizing over whether to spend a resource or wishing you had a resource you spent earlier.

In any case, I still feel like an elf (for Elven Accuracy) or half-orc (for bonus crit damage) Champion with either/both Crusher and Slasher can provide a lot for a party. The argument that the Champion adds very little damage per attack doesn't really mean much here, as raw damage isn't the main thing we're going for (and on a half-orc the extra damage is higher anyway), it's more the effects of Slasher and/or Crusher, both the once per turn and the crit effects. I'm sure the BM or EK or Samurai are "stronger", but I'm not convinced the Champion is weak or that this isn't a viable build.

[bid]

Where is this number coming from? I'm looking at a damage calculator and the champion is getting ~8 extra damage, or 2 damage per attack.
With ONE extra crit every 20 rolls, that would mean every crit adds 40 damage...

That's so far out that even Selene maths won't cover it.



Compare to 7 extra crit damage when you crit, every 20 rolls. Which turns out to be .35 in normal human maths.

[JNAProductions]

With ONE extra crit every 20 hits, that would mean every crit adds 40 damage...

That's so far out that even Selene maths won't cover it.

That would only be true if you hit on a 1.

You get one extra crit every 13 hits, if you hit on an 8+.

[heavyfuel]

Where is this number coming from? I'm looking at a damage calculator and the champion is getting ~8 extra damage, or 2 damage per attack. This does include a bonus for being a half-orc; the damage increase is a bit less without that, but still about 1 damage per attack (whether or not you have GWM also affects damage added).

Part of the appeal of the Champion is also the lack of resources to manage

I could ask you the same thing :smallbiggrin:

I'm using Ludic's DPR Calculator, and a character dealing 2d6+3 damage with +5 to hit vs AC 13 has a DPR of 6.85 (9.4575 with advantage). Increasing the crit range to 19 gives me 7.2 average damage (10.105 with advantage)

If your weapon deals an extra of 7 damage (2d6) on a crit, and you crit on a 19 (everybody crits on a 20, so that doesn't affect the calculation), you're dealing an extra 7 damage 5% of the time (the number of times you'd roll a 19). 5% of 7 is 0.35, so - on average - you're dealing an extra 0.35 damage per attack.

If you have advantage, you're almost twice as likely to roll a 19 so the extra average damage is almost double, hence the 0.65 I mentioned.

Lack of resource management is always the reason people say the Champion isn't bad, but the fact remains that the BM outdamages the Champion unless you're making over 150 attacks in a day, and I find such a scenario very unlikely, especially since you do have at least one major resource to manage, HP.

[Greywander]

I was setting the crit range to 18-20 in the calculator, as if for a 20th level character. Someone else said that Champion is okay at 20 but does poorly between 5 and 11, so perhaps those are the ranges I should have been checking in.

[heavyfuel]

I was setting the crit range to 18-20 in the calculator, as if for a 20th level character. Someone else said that Champion is okay at 20 but does poorly between 5 and 11, so perhaps those are the ranges I should have been checking in.

I said that :smallbiggrin:

Though now that I've calculated that the levels 3~7 Champion requires 154 attacks to match a levels 3~7 BM in terms of damage, I no longer think the Champion compares even at level 20.

With two short rests in a day, a lv20 BM deals an average of 142.5 damage from maneuvers alone (6d12*3 (+1d12 from Relentless)). A lv20 Champion with a Flametongue Greatsword would need to crit 14 times to beat that. With a 10% chance to crit due to Superior Critical (18-19 on the d20), that's still 140 attacks!

[Kane0]

What out of combat utility does the BM have?


Tashas has maneuvers that add to checks like Insight, and they get a tool prof and the ability to discern some stats of people they talk to.

[JNAProductions]

Tashas has maneuvers that add to checks like Insight, and they get a tool prof and the ability to discern some stats of people they talk to.

I knew the latter, just never saw much use.

The former, though... neat!

[strangebloke]

With ONE extra crit every 20 rolls, that would mean every crit adds 40 damage...

That's so far out that even Selene maths won't cover it.

Compare to 7 extra crit damage when you crit, every 20 rolls. Which turns out to be .35 in normal human maths.

If you're consistently generating advantage (which is a reasonable goal for any fighter) you can get one extra crit every ten attacks. If you're playing as a half-orc its pretty easy to get +14.6 damage from a crit (+2d12 with GWF) meaning you end up with ~1.5 per attack. If you look at the level 17 feature it doubles to ~2.9 per attack.

1.5 per attack makes it about a third as much damage as an extremely naive usage of superiority die, so you assume two short rests, 12 superiority dice, and 36 attacks in an adventuring day, they end up breaking even. If you have more attacks (which isn't hard) the champion does better.

Naturally BM is better than this and more flexible. With cleverness you can turn pretty much every SD into an extra attack, which becomes insane with GWM. But suffice to say that even as subclasses they're on the same order of magnitude.

And Fighters don't get most of their power from their subclass anyway.

[RogueJK]

Tashas has maneuvers that add to checks like Insight

Yep, Battlemasters can now learn maneuvers that let them add Superiority dice to Persuasion, Intimidation, and Performance (Commanding Presence) or Investigation, History, and Insight (Tactical Assessment).

The Rally maneuver can also be used out of combat, potentially expending leftover Superiority Dice to generate Temp HP for teammates before/during a rest. (Not as efficient as Inspiring Leader, but it's a similar roleplaying angle - the inspiring group leader giving a Short Rest Pep Talk.)

[Frogreaver]

With ONE extra crit every 20 rolls, that would mean every crit adds 40 damage...

That's so far out that even Selene maths won't cover it.



Compare to 7 extra crit damage when you crit, every 20 rolls. Which turns out to be .35 in normal human maths.

+.35 per greatsword attack with the ability to crit on 19's. Multiple that by number of attacks to get the DPR value. For 2 attacks it's +0.7 DPR. For 3 it's 1.05. For 4 it's 1.4. Then double this again for criting on an 18. Then double it again for a flametongue (assuming you acquire one).

That said it seems some buffs help the champion more. GWM Feat. Advantage. Flametongues - although that may be debatable with some battlemaster maneuvers.

By the end of your career with a good magic weapon you could be looking at something like +5.6 DPR due to the crit ability. Presumably gaining advantage would about double this again. So it's theoretically possible to get +11 DPR (and more) due to the crit ability at max level.

[HPisBS]

If you're consistently generating advantage (which is a reasonable goal for any fighter) you can get one extra crit every ten attacks. If you're playing as a half-orc its pretty easy to get +14.6 damage from a crit (+2d12 with GWF) meaning you end up with ~1.5 per attack. If you look at the level 17 feature it doubles to ~2.9 per attack.

1.5 per attack makes it about a third as much damage as an extremely naive usage of superiority die, so you assume two short rests, 12 superiority dice, and 36 attacks in an adventuring day, they end up breaking even. If you have more attacks (which isn't hard) the champion does better.

Naturally BM is better than this and more flexible. With cleverness you can turn pretty much every SD into an extra attack, which becomes insane with GWM. But suffice to say that even as subclasses they're on the same order of magnitude.

And Fighters don't get most of their power from their subclass anyway.

Bottom line is that expanded crit range needs consistent elven super-advantage to be particularly relevant. Or, better yet, consistent (super-) advantage while Smiting or Sneak Attacking. Which, of course, means only dipping Champion.

[J-H]

To really crit-fish, I think I'd go with an elven dex champion dual-wielding light hammers and using the Crusher feat. Each time he crits, all successive attacks have advantage, which becomes elven triple advantage.

[Ertwin]

Also, I think the other problem with Champion Fighter is it's pretty boring to play: it doesn't give you a lot of options, really.

I prefer passive skills, so champion is ideal for me. No worries about combos or resources. I know what I can do every battle. It allows me to dedicate more time to throwing monkey wrenches at the dm.

[x3n0n]

To really crit-fish, I think I'd go with an elven dex champion dual-wielding light hammers and using the Crusher feat. Each time he crits, all successive attacks have advantage, which becomes elven triple advantage.

Light hammers can't be Dex-wielded (without a level of Monk), unfortunately. (Slings are ranged, but can't be TWFed.)

[HPisBS]

Light hammers can't be Dex-wielded (without a level of Monk), unfortunately. (Slings are ranged, but can't be TWFed.)

Yep. Daggers only. So you'd need that Bracer of Flying Daggers from Waterdeep to keep it going.

[strangebloke]

Bottom line is that expanded crit range needs consistent elven super-advantage to be particularly relevant. Or, better yet, consistent (super-) advantage while Smiting or Sneak Attacking. Which, of course, means only dipping Champion.

Well, I think the assumption for champion is that you'll be getting access to weapons like flametongue or frostbrand in t2 and t3 that will allow you to get more mileage out of improved critical. A half-orc champion with a flaming greataxe that deals 3d12 + 4d6 + STR + 10 on a crit won't really be missing SA or smite in that moment. Besides which, improved critical is just one features. At higher levels you'll get access to +1 AC from the extra fighting style, the jack-of-all-trades effect that boosts physical abilities (including initiative.). IMO these abilities are at least comparable to the higher level abilities of other fighter classes.

There's no arguing against the idea that Battlemaster and Samurai are better overall but the only reason they're a lot better is because magic items are ignored and feats (notably GWM and SS) are assumed.

[Jerrykhor]

Its 2021, and some people are still denying the fact that Champions suck?

[strangebloke]

Its 2021, and some people are still denying the fact that Champions suck?

lmao they're pretty bad, they're just not that bad. You're still a fighter, and IA does improve your damage output, about as much as a +1 to attack would under most circumstances.

[Frogreaver]

Well, I think the assumption for champion is that you'll be getting access to weapons like flametongue or frostbrand in t2 and t3 that will allow you to get more mileage out of improved critical. A half-orc champion with a flaming greataxe that deals 3d12 + 4d6 + STR + 10 on a crit won't really be missing SA or smite in that moment. Besides which, improved critical is just one features. At higher levels you'll get access to +1 AC from the extra fighting style, the jack-of-all-trades effect that boosts physical abilities (including initiative.). IMO these abilities are at least comparable to the higher level abilities of other fighter classes.

There's no arguing against the idea that Battlemaster and Samurai are better overall but the only reason they're a lot better is because magic items are ignored and feats (notably GWM and SS) are assumed.

Maybe. I'd need to do the math on that because it's possible that battlemasters due to their ability to increase accuracy or gain more attacks may actually benefit more from such weapons than the champion - growing the gap wider instead of shrinking it.

[strangebloke]

Maybe. I'd need to do the math on that because it's possible that battlemasters due to their ability to increase accuracy or gain more attacks may actually benefit more from such weapons than the champion - growing the gap wider instead of shrinking it.

Possibly, though this isn't really the sort of thing that matches up well with math because the power of the battlemaster is going to be contingent on:

how long the adventuring day is
how many attacks you're really getting from superiority die


My quick math would be that if you assume 2 short rests, you get 12 SD, and if you use every single one of those on a successful riposte/precision strike you effectively get 12 more attacks. Now its important to note here: you have to actually hit with these 'extra' attacks, so even with 12 extra attacks you only end up with 6-9 extra hits. Since each hit 'doubles' the increased damage gained by having a flaming/freezing weapon, its roughly the same as getting a crit off improved critical, which happens every 20 d20 roles, on average. So 7 attacks with super advantage or 10 attacks with normal advantage or 20 attacks without.

If you assume EA, the champion needs 42-63 attacks over the course of the day to get more of a bonus out of a magic weapon. For a t3 champion on a two-rest day (so 3 actions surges) that's 11-18 rounds of combat. With regular advantage it'd be 60-90 attacks or 17-27 rounds of combat (less with GWM). Then with no advantage its 37-77 rounds.

Pretty doable with EA up even half the time imo (particularly on action surge rounds), but you might argue that's unrealistic, or you might point out how crits tend to come when you least need them. I could bring up too that turning every SD into an extra attack is also going to lead to some waste, particularly with riposte.

Not really dying on the hill that magic weapons close the gap, just saying that newbies shouldn't be told "Don't pick champion, its a trap" because you still end up dealing really good damage and it is a lot less work.

[Kane0]

I knew the latter, just never saw much use.

The former, though... neat!

Mostly true, however i’ve seen know thy enemy to have fun ribbon uses.
Posturing noble threatening to challenge you to a duel? You know he’s all talk and no bite.
Retired guy running the inn always going on about those mounted heads ok the wall? He certainly could have killed them all himself.
Selling off your loot to a fence that’s is starting to get lippy? You know you can take him.
Tax collector enquiring on your income from the last adventure the kinr sent you on? You know you CANT take him.

[Frogreaver]

Possibly, though this isn't really the sort of thing that matches up well with math because the power of the battlemaster is going to be contingent on:

how long the adventuring day is
how many attacks you're really getting from superiority die


My quick math would be that if you assume 2 short rests, you get 12 SD, and if you use every single one of those on a successful riposte/precision strike you effectively get 12 more attacks. Now its important to note here: you have to actually hit with these 'extra' attacks, so even with 12 extra attacks you only end up with 6-9 extra hits. Since each hit 'doubles' the increased damage gained by having a flaming/freezing weapon, its roughly the same as getting a crit off improved critical, which happens every 20 d20 roles, on average. So 7 attacks with super advantage or 10 attacks with normal advantage or 20 attacks without.

If you assume EA, the champion needs 42-63 attacks over the course of the day to get more of a bonus out of a magic weapon. For a t3 champion on a two-rest day (so 3 actions surges) that's 11-18 rounds of combat. With regular advantage it'd be 60-90 attacks or 17-27 rounds of combat (less with GWM). Then with no advantage its 37-77 rounds.

Pretty doable with EA up even half the time imo (particularly on action surge rounds), but you might argue that's unrealistic, or you might point out how crits tend to come when you least need them. I could bring up too that turning every SD into an extra attack is also going to lead to some waste.

Not really dying on the hill that magic weapons close the gap, just saying that newbies shouldn't be told "Don't pick champion, its a trap" because you still end up dealing really good damage and it is a lot less work.

Sure, the other thing the magic weapon does is greatly lessen the gap between attacking normally and power attacking with GWM - that alone puts the champion on much more equal footing with the battlemaster - as the battlemaster's accuracy boosting abilities (trip attack and precision) both make using the -5/+10 much better.

I'm with you that in practice the champion is quite a bit better than it's perception (at least at high levels). Maybe I should do an analysis on battlemaster with flametongue vs champion with flametongue at various levels and with various options to see the exact difference. I think it's an interesting thought experiment that doesn't traditionally get accounted for.

[Kane0]

How does the Champ’s crit math work out if you let them double ALL damage from a crit and not just the dice?

[Frogreaver]

How does the Champ’s crit math work out if you let them double ALL damage from a crit and not just the dice?

Assuming you mean everyone doubles all damage from a crit then the DPR effect of the crit would be the same as an additional 10% accuracy over the battlemaster for all cases except where you already had an 85% or higher chance to hit.

*Advantage changes these results significantly

[bid]

My quick math would be that if you assume 2 short rests, you get 12 SD, and if you use every single one of those on a successful riposte/precision strike you effectively get 12 more attacks. Now its important to note here: you have to actually hit with these 'extra' attacks, so even with 12 extra attacks you only end up with 6-9 extra hits.

For a t3 champion on a two-rest day (so 3 actions surges) that's 11-18 rounds of combat.
For a t3 BM, it's 5d10 SD per short rest. Even with an off-by-3 precision strike, you get 4 hits. It's closer to 8-12 hits overall.

But of course, at level 11, BM and champion are close enough once they're out of HP resource and must take a rest. So the only issue left to champion is the randomness of its extra damage. Nothing can beat spending SD on turn 1 to remove a target.

[strangebloke]

How does the Champ’s crit math work out if you let them double ALL damage from a crit and not just the dice?

My hot take would be that because your crits add twice as much damage as a normal character's, AND you crit twice as often, you overall get four times as much crit damage as a normal character, or twice as much as a champion.

In twenty attacks a fighter with dueling and a rapier would get

one crit if they're a battlemaster, adding 1d8=4.5
two crits if they're a champion adding 2d8=9
two crits if they're an improved champion, adding 2d8 + 10 = 19


Not a gamechanger but a solid buff. Gets a little crazy with SS/GWM but those feats are just crazy by default.

[heavyfuel]

lmao they're pretty bad, they're just not that bad. You're still a fighter, and IA does improve your damage output, about as much as a +1 to attack would under most circumstances.

Not really. If you hit due to the +1 to attack, you're hitting for Weapon Damage + Ability mod. If you crit due to Improved Critical, you're only dealing Weapon Damage.

The best case scenario is a low level champion with a Greatsword hitting for 2d6+3, in which case IC is worth about 0.7 points to attack. By the time you have +5 Str, IC is only worth about 0.6 points to attack. If you use a weapon with lower damage dice, it's worth even less. If you have a +X magic weapon, even less still.

[x3n0n]

Not really. If you hit due to the +1 to attack, you're hitting for Weapon Damage + Ability mod. If you crit due to Improved Critical, you're only dealing Weapon Damage.

The best case scenario is a low level champion with a Greatsword hitting for 2d6+3, in which case IC is worth about 0.7 points to attack. By the time you have +5 Str, IC is only worth about 0.6 points to attack. If you use a weapon with lower damage dice, it's worth even less. If you have a +X magic weapon, even less still.

So the best cases for Improved/Superior Critical are:

effects that generate extra to-hit attack dice (especially advantage and Elven Accuracy)
weapons and effects that generate or benefit from many and/or large damage dice (e.g. Greatsword/Axe, Flame Tongue, Half-Orc/Piercer, GWF style, Hex)
other valuable effects that trigger specifically on a critical hit (e.g. Crusher, Slasher)


Unfortunately, there are tradeoffs among those: the weapons with the most damage dice aren't eligible for PAM or TWF or Elven Accuracy, and Champion doesn't have any built-in sources of advantage.

And, as you said, there are lots of other valuable things that Fighters would benefit from in general that do *not* interact with Improved Critical, raising the opportunity cost of pursuing the things that benefit disproportionately from crits.

[Kurt Kurageous]

Its 2021, and some people are still denying the fact that Champions suck?

I'm not denying that you have an opinion!

I notice no one mentioned half orc for brutal critical. My favorite casual build is GWM half orc champion. Every chance to attack is a pull on the slot machine, and the damage is pretty solid. Sure, not mathematically but potentially over the good run of luck.

[strangebloke]

Not really. If you hit due to the +1 to attack, you're hitting for Weapon Damage + Ability mod. If you crit due to Improved Critical, you're only dealing Weapon Damage.

The best case scenario is a low level champion with a Greatsword hitting for 2d6+3, in which case IC is worth about 0.7 points to attack. By the time you have +5 Str, IC is only worth about 0.6 points to attack. If you use a weapon with lower damage dice, it's worth even less. If you have a +X magic weapon, even less still.

It's not exactly +1, hence why I said "like." But if we're truly nitpicking the greatsword is more like .75 since GWF adds .65 to each damage die.

But yeah, obviously you're going with a heavy weapon as a champion, that's assumed. I'd not consider than an opportunity cost since two-handed weapons are generally considered one of the better options anyway. Improved Critical also has great synergy with Half-Orc (already a really good fighter race) and has synergy with GWM (already a great fighter feat) and now has synergy with slasher and crusher which are also pretty good feats.

And while things are worse with a +X weapon, they're better with a +xd6 weapon.

[Zhorn]

Wanting to dig into the math a bit for comparing DPR outputs of the Champion vs Battle Master.
What base assumptions should we take as standard?

I'm taking it from the post so far that 2d6 maul/greatsword with GWM+GWF is the go-to, locking in our mod as STR and baring Elven Accuracy from the comparison.

What of AC ranges? is there a sweet-spot value idea for DPR comparisons?

Same goes for character level, should I run numbers for level 20, or stick to the more realistic levels of 7 and/or 11?
Assuming 20(+5) mod is a given, though if directed to a lower level range maybe should leave that as 16(+3) or 18(+4)?

Will be ignoring magic items as that's not a thing within the player's control.

[Frogreaver]

Wanting to dig into the math a bit for comparing DPR outputs of the Champion vs Battle Master.
What base assumptions should we take as standard?

I'm taking it from the post so far that 2d6 maul/greatsword with GWM+GWF is the go-to, locking in our mod as STR and baring Elven Accuracy from the comparison.

What of AC ranges? is there a sweet-spot value idea for DPR comparisons?

Same goes for character level, should I run numbers for level 20, or stick to the more realistic levels of 7 and/or 11?
Assuming 20(+5) mod is a given, though if directed to a lower level range maybe should leave that as 16(+3) or 18(+4)?

Will be ignoring magic items as that's not a thing within the player's control.

There’s no perfect set of assumptions. Just pick some reasonable ones and calculate. If others think one of your assumptions are really bad they’ll state so and can calculate based on the new assumptions.

I would also calculate at a few different levels. I’d also consider that the best weapon for a champion may not be the best weapon for a battlemaster. So you may want to compare a few different weapon configs as well. Oh and pick a few ACs as well to compare.

[Man_Over_Game]

Rough math shows that GWM on a normal attack adds about 1.5-2 damage per swing, but with Advantage it jumps up to 4.5, assuming you need like a 7 or an 8 to hit.

sauce (https://rpg.stackexchange.com/a/76656)

Essentially, if your average damage per hit is 10 or less, and you need less than a 11 to hit, GWM is almost always worth it (in a strictly average-damage viewpoint, why waste a big miss on a weak enemy?). For every 2 points less than 11, add +1 damage, and double that value if you have Advantage (so a 7 to hit with Advantage is about +4 damage).

[stoutstien]

Wanting to dig into the math a bit for comparing DPR outputs of the Champion vs Battle Master.
What base assumptions should we take as standard?

I'm taking it from the post so far that 2d6 maul/greatsword with GWM+GWF is the go-to, locking in our mod as STR and baring Elven Accuracy from the comparison.

What of AC ranges? is there a sweet-spot value idea for DPR comparisons?

Same goes for character level, should I run numbers for level 20, or stick to the more realistic levels of 7 and/or 11?
Assuming 20(+5) mod is a given, though if directed to a lower level range maybe should leave that as 16(+3) or 18(+4)?

Will be ignoring magic items as that's not a thing within the player's control.
GWF is probably not worth it even with expanded crits unless damage is needed at any cost. Defense or interception are probably better returns.

Precision is a pain to calculate and depending on how often a DM uses similar NPC blocks AC could be just a know factor to prevent any waste. Then you have a hit or added damage on crit factor on top of that. It's a fun problem but be prepared for about 15 if/then statements to works with.

[Man_Over_Game]

GWF is probably not worth it even with expanded crits unless damage is needed at any cost. Defense or interception are probably better returns.

Precision is a pain to calculate and depending on how often a DM uses similar NPC blocks AC could be just a know factor to prevent any waste. Then you have a hit or added damage on crit factor on top of that. It's a fun problem but be prepared for about 15 if/then statements to works with.

On a tangent, we made it so that GWF allowed you to reroll a single die from your damage roll and keep the higher of the rolls. This not only buffed GWF slightly but also made the 1d12 preferable to the 2d6, so now we have a reason for both.

[stoutstien]

On a tangent, we made it so that GWF allowed you to reroll a single die from your damage roll and keep the higher of the rolls. This not only buffed GWF slightly but also made the 1d12 preferable to the 2d6, so now we have a reason for both.

I like it. I ended up with adding 1d4 to GWF in place of the reroll. I just don't like rerolls for anything less impactful than attack and saves. Damage rerolls are so grating on game flow IMO.

[Delnatha]

There is actually one item that breaks the champion fighter:

Once upon a time, I jumped in with a group that contained the "Kobold Krew"; a set of three high level kobold martials who would jump enemies and use pact tactics to get advantage on all attacks. The problem was that the kobold champion fighter was wielding Wave from white plume mountain.

"If you score a critical hit with it, the target takes extra necrotic damage equal to half its hit point maximum."

That, combined with a champion fighters extra attacks, expanded crit range, and advantage on every attack meant that there were a lot of crits and two crits would kill literally anything.

[LudicSavant]

Wanting to dig into the math a bit for comparing DPR outputs of the Champion vs Battle Master.
What base assumptions should we take as standard?

First thing is that a Battle Master should be using an optimal or at least near-optimal decision tree. This means that they only use Precision Attack if they miss within a certain range, use smite-like manuevers with the efficiency a critfishing Paladin would in practice, etc.

The fact that they can react to whatever their attack roll is after the fact is mathematically important so we can’t just skip that variable.




I'm taking it from the post so far that 2d6 maul/greatsword with GWM+GWF is the go-to, locking in our mod as STR and baring Elven Accuracy from the comparison.

What of AC ranges? is there a sweet-spot value idea for DPR comparisons?

Same goes for character level, should I run numbers for level 20, or stick to the more realistic levels of 7 and/or 11?
Assuming 20(+5) mod is a given, though if directed to a lower level range maybe should leave that as 16(+3) or 18(+4)?

Will be ignoring magic items as that's not a thing within the player's control.

I say use whatever levels you want — there’s no “perfect level” to compare at and any level provides extra data so long as the math is accurate. There’s not going to be some perfect set of assumptions, so just try to identify where (if anywhere) the Champion can come out equal or ahead, even if these circumstances are limited. Just be clear about what the circumstances are.

As for attributes and builds, I strongly suggest *using a real build* instead of some assumed “standard” strength score. And then just pick the very strongest Champion build you can come up with.

A while ago I did some mathing out for someone’s “Is this Piercer Champion as good as a Battle Master” post and wasn’t impressed with the results, but perhaps other Champ builds will fare better.

[Frogreaver]

So I just compared a Crusher + GWM + Maul on a level 20 battlemaster and on a level 20 Champion
***I used a reasonable estimate for precision attacks impact instead of an exact calculation - estimation is that it provides effectively a +1.5 to hit for a battlemaster at level 20. It's effect is quite more pronounced at lower levels - due to making relatively less attacks compared to the number of superiority dice you get.

Anyways, I get the champion will do slightly more damage than the Battlemaster in this scenario against AC values from 11-20.

I need to compare to Battlemaster with Glaive + GWM + PAM but I'm not convinced that's going to have a greater impact on DPR than crusher even for the battlemaster.

Would love to hear if anyone else gets similar results. Calculations are rather involved but I'm open to posting them later if anyone would like to see.

EDIT:
Wanted to add why I chose level 20 even though I typically dislike comparing level 20 builds. Level 20 was chosen because in relative terms its the point I believe it is at it's strongest vs the battlemaster. I actually expected the Battlemaster to hands down beat the Champion and thus this be enough to validate the claim that the champion is too far behind even with crusher, but the level 20 comparison is much closer than I imagined.

[x3n0n]

So I just compared a Crusher + GWM + Maul on a level 20 battlemaster and on a level 20 Champion
***I used a reasonable estimate for precision attacks impact instead of an exact calculation - estimation is that it provides effectively a +1.5 to hit for a battlemaster at level 20. It's effect is quite more pronounced at lower levels - due to making relatively less attacks compared to the number of superiority dice you get.

Anyways, I get the champion will do slightly more damage than the Battlemaster in this scenario against AC values from 11-20.

I need to compare to Battlemaster with Glaive + GWM + PAM but I'm not convinced that's going to have a greater impact on DPR than crusher even for the battlemaster.

Would love to hear if anyone else gets similar results. Calculations are rather involved but I'm open to posting them later if anyone would like to see.

EDIT:
Wanted to add why I chose level 20 even though I typically dislike comparing level 20 builds. Level 20 was chosen because in relative terms its the point I believe it is at it's strongest vs the battlemaster. I actually expected the Battlemaster to hands down beat the Champion and thus this be enough to validate the claim that the champion is too far behind even with crusher, but the level 20 comparison is much closer than I imagined.

Thanks for doing that; you've piqued my interest. :)

Does you calculation assume that this is single-target damage? If so, how much difference did it seem to make that the first Crusher crit on a turn gives advantage for the rest of the attacks on that turn (including the GWM BA)?

Are both Fighters risky-striking vs all ACs or only for low ones?

[Zhorn]

Ok, so trying out this damage comparison .
(math done on spreadsheet, rounding to three decimal places)

Both Champion and Battle Master will be compared using the same setup.

Weapon: Two Handed 2d6 (Greatsword or Maul seems the standard for fighter DPR discussions)
Feat: Great Weapon Master (Both subclasses interact favourably and we're already using a 2H)
Fighting Style: Great Weapon Fighting (non-damaging Fighting Styles might be more appealing, but when comparing DPR we should use something that is reliably interacting with the DPR)
Race: None (not concerned with niche flavour builds and optimized picks)
Magic items: None (not reliably in player's control)

Lv1 Base: Starting STR score 15 from standard array, and GWF
Lv4 ASI: GWM
Lv6 ASI: STR +2, STR 15 -> 17
Lv8 ASI: STR +2, STR 17 -> 19
Lv12 ASI: STR +1 (& +1 to another non concerning stat or half-feat), STR 19 -> 20
Lv14/16/19: ASI's not used for this

Calculating as lv20; Prof = +6, Superiority dice as d12's, Superior Critical range of 18-20

Enemy AC: 15 (high enough to not be outclassed by a high +hit modifier, but low enough to be reasonably expected AC to encounter regularly)

Damage of a standard hit
2d6+mod = 2(3.5)+5 = 12
With GWF+GWM = 2*(4.167)+5+10 = 23.333

Damage of a standard Crit
4*(4.166)+5+10 = 31.667

Applying superiority dice as +damage
2d6+mod+1d12 = 2(3.5)+5+6.5 = 18.5
With GWF+GWM = 2*(4.167)+5+(7.333)+10=30.667

Crit when applying superiority dice as +damage
4*(4.167)+5+2*(7.333)+10 = 46.333

Hit rate vs AC 15
AC-(STR+Prof-GWM) = 15-(5+6-5) = Hit on a 9+
(21-9)/20 = 60% hit rate

Applying superiority dice as +hit
AC-(STR+Prof+SD-GWM) = 15-(5+6+6.5-5) = Hit on a 2.5+
(21-2.5)/20 = 92.5% hit rate

Expected outcome of a single attack
([Damage of a Crit * d20 outcomes that Crit] + [Damage of a standard hit * d20 outcomes that standard hit] + [Damage of a miss * d20 outcomes that miss])/(all possible d20 results)

Base Fighter
([31.667 * 1]+[23.333 * 11]+[0 * 8])/20 = 14.417

Champion
([31.667 * 3]+[23.333 * 9]+[0 * 8])/20 = 15.250

Battle Master (SD on +damage)
([46.333 * 1]+[30.667 * 11]+[0 * 8])/20 = 19.183

Battle Master (SD on +hit)
([31.667 * 1]+[23.333 * 17.5]+[0 * 1.5])/20 = 22.000

Now as there are only 6 superiority dice that can be used in a single combat, Battle Master will only be dealing more damage for those 6 attacks, after which Champion will be playing catchup while the Battle Master is forced to rely on Base Fighter attack damage.

This will take 29 additional attacks (35 total including the Manuever attacks) for the Champion to pull ahead if the Battle Master is using their Superiority Dice as +damage,
and 49 additional attacks (55 total including the Manuever attacks) to pull ahead of the Battle Master using their Superiority Dice as +hit.

And this is assuming a single combat with no new rolling of initiatives to trigger Relentless or short rests to replenish Superiority Dice.

Every Superiority Dice spent on turning a miss into a hit will take on average 8.1 additional attacks to make up the difference, while every superiority dice spent on adding to damage will take 4.72 additional attacks.

In practice this isn't easy to gauge how many rounds that will take. The Champion will more frequently get the benefit of the GWM granting a Bonus Action Attack, so will more frequently have an additional attack per round.

Critical hit rates
Battle Master: 20 of a d20 = 5% chance
Chance of getting at least one crit per Attack Action
= 1-Pr(not a crit)^(number of attacks)
=1-(1-0.05)^4 = 18.549%

Champion: 18-20 of a d20 = 15% chance
Chance of getting at least one crit per Attack Action
=1-(1-0.15)^4 = 47.799%

So the Expected DPR = [Attacks + Pr(at least one crit)] * Expected attack Damage

Battle Master
+hit: 4.18549 * 22.000 = 92.081 DPR
+damage: 4.18549 *19.183 = 80.290 DPR
no dice left: 4.18549 * 14.417 = 60.342 DPR

Champion
4.47799 * 15.250 = 68.289 DPR

Now I need to say the Champion is still delivering decent damage, but that lead that the Battle Master gets from just 6 Superiority Dice is brutal.
If you can reliably get advantage, that gap will close considerably, but will still leave the Champion behind a small margin if the Battle Master has Superiority Dice to spend.

[Frogreaver]

Ok, so trying out this damage comparison .
(math done on spreadsheet, rounding to three decimal places)

Both Champion and Battle Master will be compared using the same setup.

Weapon: Two Handed 2d6 (Greatsword or Maul seems the standard for fighter DPR discussions)
Feat: Great Weapon Master (Both subclasses interact favourably and we're already using a 2H)
Fighting Style: Great Weapon Fighting (non-damaging Fighting Styles might be more appealing, but when comparing DPR we should use something that is reliably interacting with the DPR)
Race: None (not concerned with niche flavour builds and optimized picks)
Magic items: None (not reliably in player's control)

Lv1 Base: Starting STR score 15 from standard array, and GWF
Lv4 ASI: GWM
Lv6 ASI: STR +2, STR 15 -> 17
Lv8 ASI: STR +2, STR 17 -> 19
Lv12 ASI: STR +1 (& +1 to another non concerning stat or half-feat), STR 19 -> 20
Lv14/16/19: ASI's not used for this

Calculating as lv20; Prof = +6, Superiority dice as d12's, Superior Critical range of 18-20

Enemy AC: 15 (high enough to not be outclassed by a high +hit modifier, but low enough to be reasonably expected AC to encounter regularly)

Damage of a standard hit
2d6+mod = 2(3.5)+5 = 12
With GWF+GWM = 2*(4.167)+5+10 = 23.333

Damage of a standard Crit
4*(4.166)+5+10 = 31.667

Applying superiority dice as +damage
2d6+mod+1d12 = 2(3.5)+5+6.5 = 18.5
With GWF+GWM = 2*(4.167)+5+(7.333)+10=30.667

Crit when applying superiority dice as +damage
4*(4.167)+5+2*(7.333)+10 = 46.333

Hit rate vs AC 15
AC-(STR+Prof-GWM) = 15-(5+6-5) = Hit on a 9+
(21-9)/20 = 60% hit rate



All this sounds good so far. I handle normal attacks and crits slightly differently but it should be the same end result. In this case I would use .6*(Damage on an attack) + .05*(Extra Damage on a crit - would only be 8.33)


Applying superiority dice as +hit
AC-(STR+Prof+SD-GWM) = 15-(5+6+6.5-5) = Hit on a 2.5+
(21-2.5)/20 = 92.5% hit rate

Expected outcome of a single attack
([Damage of a Crit * d20 outcomes that Crit] + [Damage of a standard hit * d20 outcomes that standard hit] + [Damage of a miss * d20 outcomes that miss])/(all possible d20 results)

I don't agree with this part. There's alot wrong here so let's unpack a little.
You would want to calculate your chance of converting a miss into a hit when a superiority dice is used on a given range. I'm going to assume a naive range - when you miss and a superiority dice would help.

Vs 15 AC with +6 hit
Chance of exactly a 12 - 1/12 * chance a 12 helps (35%) = 1/12*0.35
Chance of exactly a 11 - 1/12 - chance a 11 helps (35%) = 1/12*0.35
Chance of exactly a 10 - 1/12 - chance a 10 helps (35%) = 1/12*0.35
Chance of exactly a 9 - 1/12 - chance a 9 helps (35%) = 1/12*0.35
Chance of exactly a 8 - 1/12 - chance a 8 helps (35%) = 1/12*0.35
Chance of exactly a 7 - 1/12 - chance a 7 helps (35%) = 1/12*0.35
Chance of exactly a 6 - 1/12 - chance a 6 helps (35%) = 1/12*0.30
Chance of exactly a 5 - 1/12 - chance a 5 helps (35%) = 1/12*0.25
Chance of exactly a 4 - 1/12 - chance a 4 helps (35%) = 1/12*0.20
Chance of exactly a 3 - 1/12 - chance a 3 helps (35%) = 1/12*0.15
Chance of exactly a 2 - 1/12 - chance a 2 helps (35%) = 1/12*0.10
Chance of exactly a 1 - 1/12 - chance a 1 helps (35%) = 1/12*0.05

Summing this up = 0.2625 -> +5.25 to hit on the attacks you are able to use a superiority dice on.
**But this is only half the problem.

However that's only half the problem because we don't have infinite superiority dice. We have 6 and sometimes we will have enough misses that fall in that miss range for all our superiority dice to be used and sometimes we will have way more misses in that range than we have superiority dice. So we need some idea of our chances for 1 miss in that range, for 2 misses in that range, for 3 misses, etc. Binomial Distribution works great for this so long as we are assuming a number of rounds per short rest (which compared to reality might be a little over optimistic as we never know our number of rounds in a short rest ahead of time with 100% certainty. Once we have that info we can determine the number of misses we convert into hits by taking the results of the binomial distribution which will show the chances for only being able to use 1...N superiority dice and we have an accurate model. *Note that advantage complicates this model

I walk you through that to say this - ultimately you are overestimating the effects of of superiority dice. You are both assuming the turn misses to hits more often when used and that you will always use 100% of your allotment when attempting this kind of strategy. Both assumptions are incorrect. The trick with precision attack is to maximize the result such that you get a high bonus to hit the times you use it while retaining a high probability of using many dice. It turns out to be a maximization problem to determine the most optimal strategy to using precision attack.





Champion
4.47799 * 15.250 = 68.289 DPR



My calc yielded 71.462 DPR for a champion with Crusher and GWM and GWF (vs 15 AC)

[Zhorn]

I just went with the average of 6.5 +hit for a d12 since we're in spherical cow territory. In practice the values are going to be all over the place and we're not going to have exact usage of superiority dice used in a specific way for those first six attacks, averages are just for convenience. Could have plenty of cases of rolling high and not needing to supplement the +hit roll, or we could have a string of near misses with the supplemented Superiority Dice also fails to turn it into a hit. Model just gets too complicated to display all the workings out in a way that can be followed.

Couple of things in your model I've questions on though.


Vs 15 AC with +6 hit
Chance of exactly a 12 - 1/12 * chance a 12 helps (35%) = 1/12*0.35
Chance of exactly a 11 - 1/12 - chance a 11 helps (35%) = 1/12*0.35
Chance of exactly a 10 - 1/12 - chance a 10 helps (35%) = 1/12*0.35
Chance of exactly a 9 - 1/12 - chance a 9 helps (35%) = 1/12*0.35
Chance of exactly a 8 - 1/12 - chance a 8 helps (35%) = 1/12*0.35
Chance of exactly a 7 - 1/12 - chance a 7 helps (35%) = 1/12*0.35
Chance of exactly a 6 - 1/12 - chance a 6 helps (35%) = 1/12*0.30
Chance of exactly a 5 - 1/12 - chance a 5 helps (35%) = 1/12*0.25
Chance of exactly a 4 - 1/12 - chance a 4 helps (35%) = 1/12*0.20
Chance of exactly a 3 - 1/12 - chance a 3 helps (35%) = 1/12*0.15
Chance of exactly a 2 - 1/12 - chance a 2 helps (35%) = 1/12*0.10
Chance of exactly a 1 - 1/12 - chance a 1 helps (35%) = 1/12*0.05

Summing this up = 0.2625 -> +5.25 to hit on the attacks you are able to use a superiority dice on.
Where's this 35% from?
We have a +6 to hit giving our hits on a 9+; 60% hit rate
The 5% chance at crits are inside that 60% hit rate (55% normal damage, 5% critical damage)
Shouldn't you be calculating the applied Superiority Dice on 40% and not 35%?

Then there's how you've divided up the d12 results. I can see what you're attempting, but I'm not quite following why you've split them up to such narrow ranges.
If your d20 roll misses the target number by 1, then 100% of the d12 results will turn it into a hit (1 to 12)
If your d20 roll misses the target number by 2, then 91.666% of the d12 results will turn it into a hit (2 to 12)
...
If your d20 roll misses the target number by 6, then 58.333% of the d12 results will turn it into a hit (6 to 12)
If your d20 roll misses the target number by 7, then 50% of the d12 results will turn it into a hit (7 to 12)
all in 8.333% increments
(we only really care about up to 7 for a target AC of 15 using a +6 modifier, since a 2 on the d20 is our lowest roll that can become a hit since a 1 is a guaranteed miss)

Again, I sorta get what you're going for, I just don't grasp your number selection or why you are adding up your range in that way. Something about it just doesn't feel intuitive to do.


My calc yielded 71.462 DPR for a champion with Crusher and GWM and GWF (vs 15 AC)
Mind sharing the formula and breakdown of your number of this? Just generally curious about where the difference are, and reverse engineering someone else's work without the source numbers is a pain in the patookie.
Was there a weighting for the likelihood of crits on the 1st/2nd/3rd/4th attacks, the combination of any such arrangement, and on none?
I didn't incorporate crusher into the comparison mostly because of how quickly the the model expands to accurately model the chance of transitioning from normal attacks to advantage.

[Frogreaver]

I just went with the average of 6.5 +hit for a d12 since we're in spherical cow territory. In practice the values are going to be all over the place and we're not going to have exact usage of superiority dice used in a specific way for those first six attacks, averages are just for convenience. Could have plenty of cases of rolling high and not needing to supplement the +hit roll, or we could have a string of near misses with the supplemented Superiority Dice also fails to turn it into a hit. Model just gets too complicated to display all the workings out in a way that can be followed.

I understand the attempt - but it will be fairly inaccurate and when small changes in accuracy can make significant changes in DPR then it's going to potentially cause the resulting DPR to be much further off.

Couple of things in your model I've questions on though.


Where's this 35% from?
We have a +6 to hit giving our hits on a 9+; 60% hit rate
The 5% chance at crits are inside that 60% hit rate (55% normal damage, 5% critical damage)
Shouldn't you be calculating the applied Superiority Dice on 40% and not 35%?

Excluding 1's as you cannot change the result of a 1 with precision.


Then there's how you've divided up the d12 results. I can see what you're attempting, but I'm not quite following why you've split them up to such narrow ranges.
If your d20 roll misses the target number by 1, then 100% of the d12 results will turn it into a hit (1 to 12)
If your d20 roll misses the target number by 2, then 91.666% of the d12 results will turn it into a hit (2 to 12)
...
If your d20 roll misses the target number by 6, then 58.333% of the d12 results will turn it into a hit (6 to 12)
If your d20 roll misses the target number by 7, then 50% of the d12 results will turn it into a hit (7 to 12)
all in 8.333% increments
(we only really care about up to 7 for a target AC of 15 using a +6 modifier, since a 2 on the d20 is our lowest roll that can become a hit since a 1 is a guaranteed miss)

Again, I sorta get what you're going for, I just don't grasp your number selection or why you are adding up your range in that way. Something about it just doesn't feel intuitive to do.

Probably because what I said I was doing and what I did were 2 different things. What I actually computed was the impact on chance to hit if you could add the superiority dice to every attack. What you have listed here is correct for what I wanted to compute - "the chance you turn a hit into a miss given given you use the precision dice only when it could help - in this case when you miss and the result isn't a 1". Keep in mind this also can be restricted if you have a different range than 'any miss other than a 1' that you are wanting to explore. So please use your calculation for this part as it's what needs calculated.


Mind sharing the formula and breakdown of your number of this? Just generally curious about where the difference are, and reverse engineering someone else's work without the source numbers is a pain in the patookie.
Was there a weighting for the likelihood of crits on the 1st/2nd/3rd/4th attacks, the combination of any such arrangement, and on none?
I didn't incorporate crusher into the comparison mostly because of how quickly the the model expands to accurately model the chance of transitioning from normal attacks to advantage.

I break it down by attacks in the sequence
1st attack is obviously without advantage so normal DPR calc.
2nd attack has a 15% chance of advantage so I do an Expected Value Calc ([1-.15]*DPR without advantage + .15*DPR with advantage)
3rd attack has a [1 - (1-.15)^2] = 27.75% chance of having advantage and so it's DPR contribution is ([1-.2775]*DPR without advantage + .2775 *DPR with advantage)
...
Bonus Action Attack is chance anything crit and it will have advantage -> [1- (1-.15)^4]*DPR with advantage

It's actually not that bad when you set up a spreadsheet to calc these values.
*Note if you want to factor in action surge contribution to dpr over a day then you would need to compute action surge rounds DPR this same way but with 8 attacks and a potential bonus action attack.

[Zhorn]

Probably because what I said I was doing and what I did were 2 different things.That explains a lot. I kept looking over those numbers in your previous post thinking "this makes no sense at all"


What I actually computed was the impact on chance to hit if you could add the superiority dice to every attack. What you have listed here is correct for what I wanted to compute - "the chance you turn a hit into a miss given given you use the precision dice only when it could help - in this case when you miss and the result isn't a 1". Keep in mind this also can be restricted if you have a different range than 'any miss other than a 1' that you are wanting to explore. So please use your calculation for this part as it's what needs calculated.
ok, so posting what I understand your calculation to actually be

Miss by 1, 12 results on a d12 will yield a successful hit (100.000%), times the 5% range it exists on = 5.000%
Miss by 2, 11 results on a d12 will yield a successful hit (91.667%), times the 5% range it exists on = 4.583%
Miss by 3, 10 results on a d12 will yield a successful hit (83.333%), times the 5% range it exists on = 4.167%
Miss by 4, 9 results on a d12 will yield a successful hit (75.000%), times the 5% range it exists on = 3.750%
Miss by 5, 8 results on a d12 will yield a successful hit (66.667%), times the 5% range it exists on = 3.333%
Miss by 6, 7 results on a d12 will yield a successful hit (58.333%), times the 5% range it exists on = 2.917%
Miss by 7, 6 results on a d12 will yield a successful hit (50.000%), times the 5% range it exists on = 2.500%

Sum of the above calculations = 26.250%
Divide by 5% to convert into a d20 equivalent modifier = +5.25

That makes more sense to explain where those values came from.

[Frogreaver]

That explains a lot. I kept looking over those numbers in your previous post thinking "this makes no sense at all"


ok, so posting what I understand your calculation to actually be

Miss by 1, 12 results on a d12 will yield a successful hit (100.000%), times the 5% range it exists on = 5.000%
Miss by 2, 11 results on a d12 will yield a successful hit (91.667%), times the 5% range it exists on = 4.583%
Miss by 3, 10 results on a d12 will yield a successful hit (83.333%), times the 5% range it exists on = 4.167%
Miss by 4, 9 results on a d12 will yield a successful hit (75.000%), times the 5% range it exists on = 3.750%
Miss by 5, 8 results on a d12 will yield a successful hit (66.667%), times the 5% range it exists on = 3.333%
Miss by 6, 7 results on a d12 will yield a successful hit (58.333%), times the 5% range it exists on = 2.917%
Miss by 7, 6 results on a d12 will yield a successful hit (50.000%), times the 5% range it exists on = 2.500%

Sum of the above calculations = 26.250%
Divide by 5% to convert into a d20 equivalent modifier = +5.25

That makes more sense to explain where those values came from.

Yea, sorry for the confusion.

[Man_Over_Game]

It is worth noting that, if there are not enough attacks in a combat that deserve Precise Attack, the Battlemaster still has access to Riposte, which is basically an extra attack in that round. Not sure if it's worthwhile to compare it to Precise Attack (that'd be another mess of calculations), but I'd wager that the prospect of making an extra attack per round would probably tilt the favor towards the BM by ruling out most circumstance.

[DwarfFighter]

Ok, so trying out this damage comparison.
(snip)


Interesting stuff going on here, and it pretty much seals the deal that the BM is the better class. However, nobody ever rolled 3.5 on a d6, so the fine-grained averages are not telling the story you'll see during a game.

I expect the players will see the Battle Master doing a few points better than the Champion while he's spending his Superiority dice (4 attacks per round at level 20? They'll be gone quick if he doesn't pace himself!) and the Champion will spike with more frequent criticals. True or not, the Champion is going to look like the bigger damage-dealer when he gets crit-lucky, and the BM's overall advantage won't be all that obvious.

Add in the fact that the Battle Master can do special moves that are going to weigh in on how he uses his Superiority dice, which is going to be great for controlling the encounter but does distract from the pure damage output.

Finally, it isn't all about dealing out all the damage all the time - at level 20, when was the last time you reduced an enemy to exactly 0 hp? The excess damage counts for nothing, and if you paid a resource for it, e.g. a Superiority dice, that was wasted. The Champion has very few resource expenditures to worry about, but the Battle Master must make the consideration and the gamble of whether or not to spend his dice, and that gamble can sometimes fail to pay off.

Seems to me that the Champion is still in the game :)

-DF

[Man_Over_Game]

Interesting stuff going on here, and it pretty much seals the deal that the BM is the better class. However, nobody ever rolled 3.5 on a d6, so the fine-grained averages are not telling the story you'll see during a game.

I expect the players will see the Battle Master doing a few points better than the Champion while he's spending his Superiority dice (4 attacks per round at level 20? They'll be gone quick if he doesn't pace himself!) and the Champion will spike with more frequent criticals. True or not, the Champion is going to look like the bigger damage-dealer when he gets crit-lucky, and the BM's overall advantage won't be all that obvious.

Add in the fact that the Battle Master can do special moves that are going to weigh in on how he uses his Superiority dice, which is going to be great for controlling the encounter but does distract from the pure damage output.

Finally, it isn't all about dealing out all the damage all the time - at level 20, when was the last time you reduced an enemy to exactly 0 hp? The excess damage counts for nothing, and if you paid a resource for it, e.g. a Superiority dice, that was wasted. The Champion has very few resource expenditures to worry about, but the Battle Master must make the consideration and the gamble of whether or not to spend his dice, and that gamble can sometimes fail to pay off.

Seems to me that the Champion is still in the game :)

-DF

Mmm...kinda. You can choose when to use Superiority Dice, but you can't choose when you Crit. It might make sense for you to use a Superiority Dice on a dragon with 50% HP, but it would not make sense for me to Crit on a CR 1 with 50% HP.

Simply the fact that the human element can reduce waste in only the Battle Master means your suggestion might have actually hurt the Champion's odds even further. We're talking about averages here, hitting a training dummy with infinite health for a damage comparison, but circumstance will almost always sway towards the one with more choices, especially if they were already equals.

[Willie the Duck]

Seems to me that the Champion is still in the game

Oh yes, the situation is much more complex once it hits real play. If the Battlemaster hits a short rest with superiority dice still in the hopper (or spends them where they are unneeded, perhaps for fear of the former situation), the Champion starts to look better. If an enemy gets in a telling blow because the Champion has no burst-damage/takedown option*, then the Battlemaster starts to look better. And of course, if you get to a knock-down, drag-out fight at level 18+, and your Champion is busy not-dying because of Survivor (while the Battlemaster merely gets another superiority die), or we're not talking combat and remarkable athlete goes head to head with the battlemaster skill-bonus maneuvers, well then the situation gets downright muddy.
*other than action surge, which we will assume each has used judiciously (although the BM may be able to use these better, what with a 'trip, then massively-multiple capitalize upon said advantage' routine)


Simply the fact that the human element can reduce waste in only the Battle Master means your suggestion might have actually hurt the Champion's odds even further. We're talking about averages here, hitting a training dummy with infinite health for a damage comparison, but circumstance will almost always sway towards the one with more choices, especially if they were already equals.

Not inherently. Choices mean you have to make them, and make them right. I think the lesson here is that the battlemaster is definitively better as player prescience approaches perfection.

[Man_Over_Game]

Not inherently. Choices mean you have to make them, and make them right. I think the lesson here is that the battlemaster is definitively better as player prescience approaches perfection.

But then the opposite means that the system will work in your favor. I think it's pretty common sense to believe that having the option to make a decision is better for success than it being decided randomly. It's the reason why Shield is considered more valuable than Shield of Faith.

We're talking about choosing where your DPR goes and where it doesn't. Even if mistakes are made, shouldn't choice still perform better than random?

[bid]

Sum of the above calculations = 26.250%
Divide by 5% to convert into a d20 equivalent modifier = +5.25
I have 2 issues with this.

- first: this calculation goes off-by-6, which means you think that creature is AC10 when it's actually AC16. That's fairly unbelievable, players have a better instinct than that.
As written, all SD will be gone in the first 20 rolls for little effect. This both over-evaluate and under-evaluate the damage into a random value.

- second: this DPR approach assumes infinitely many rounds while actual usage might go from 5-minute day to until-out-of-hp short rest. This is acceptable when there are no resource to spend and is just as valid as ignoring misses (e.g. GWM makes 12*.65 vs 22*.40 different from 12 vs 22). But it's not the case here.
I feel "true DPR" should be calculated backward from the damage and number of turn done until out-of-hp.

For instance, using easy numbers:
- level 11 fighter receives average 5 damage per round and lasts 25 rounds before going out of HP.
- that's 75 attack rolls that will do 480 damage
- the DPR is 480/25 ~ 19 DPR
- champion has 4 extra crit for 480+28/25 ~ 20 DPR
- BM converts 4 SD into hits for 480+48/25 ~ 21 DPR
This approach doesn't hide anything. If you disagree and think it should last 30 rounds, you are arguing on facts that many players have experienced.

And if you are unlucky and always kill creatures that have 2 hp left, you can say I killed 10 creatures and lost 100 damage to overkill... and subtract it from your DPR.
*That's the joke: you lose as much from overkill than you gain from your archetype

[Frogreaver]

But then the opposite means that the system will work in your favor. I think it's pretty common sense to believe that having the option to make a decision is better for success than it being decided randomly. It's the reason why Shield is considered more valuable than Shield of Faith.

We're talking about choosing where your DPR goes and where it doesn't. Even if mistakes are made, shouldn't choice still perform better than random?

If the Battlemaster could maintain DPR while picking when to do the damage t that may be true, but precision attack tends to add more DPR than simply getting a +1d12 + non damage rider.

Meaning that in order to do damage now you actually end up giving up DPR and while tactically this may be the better choice sometimes it’s rarely clear when it’s actually going to be so.

Though there is a method to account for such at least to some degree. Look at Nova damage for the champion and for Battlemaster


Oh yes, the situation is much more complex once it hits real play. If the Battlemaster hits a short rest with superiority dice still in the hopper (or spends them where they are unneeded, perhaps for fear of the former situation), the Champion starts to look better. If an enemy gets in a telling blow because the Champion has no burst-damage/takedown option*, then the Battlemaster starts to look better. And of course, if you get to a knock-down, drag-out fight at level 18+, and your Champion is busy not-dying because of Survivor (while the Battlemaster merely gets another superiority die), or we're not talking combat and remarkable athlete goes head to head with the battlemaster skill-bonus maneuvers, well then the situation gets downright muddy.
*other than action surge, which we will assume each has used judiciously (although the BM may be able to use these better, what with a 'trip, then massively-multiple capitalize upon said advantage' routine)

Yes, but given a certain number of combat rounds per short rest and a specific heuristic to using precision attack we can actually calculate how often he will use each number of superiority dice on precision attack before the next short rest. This isn't incalculable and while complex it's not in the realm of absurdly complex yet.


I have 2 issues with this.

- first: this calculation goes off-by-6, which means you think that creature is AC10 when it's actually AC16. That's fairly unbelievable, players have a better instinct than that.

This isn't actually what's happening at all. The goal is to pick a range where if we miss by at most X we use precision attack and compute based on that heuristic. We haven't even addressed the variable of imperfect player knowledge regarding that yet. Nor exactly what value X really should be - in this example we used miss by 1 to 7 but it was an example showing how things worked and not a claim that using precision on a miss by 1-7 was optimal.


- second: this DPR approach assumes infinitely many rounds while actual usage might go from 5-minute day to until-out-of-hp short rest. This is acceptable when there are no resource to spend and is just as valid as ignoring misses (e.g. GWM makes 12*.65 vs 22*.40 different from 12 vs 22). But it's not the case here.
I feel "true DPR" should be calculated backward from the damage and number of turn done until out-of-hp.

That's a terrible methodology that adds variables and convolutes what's actually going on for no good reason.


And if you are unlucky and always kill creatures that have 2 hp left, you can say I killed 10 creatures and lost 100 damage to overkill... and subtract it from your DPR.
*That's the joke: you lose as much from overkill than you gain from your archetype

I agree that we should compensate by overkill but not via what actually happens as your example suggests but instead by a weighted average of what all can happen. It has a larger effect than most realize.

[bid]

That's a terrible methodology that adds variables and convolutes what's actually going on for no good reason.
It depends if you prefer white room to real word or not...
I prefer an approach that doesn't hide anything.

You cannot synthesize those real-word variables into a single number. That'd just denature the result.

[Willie the Duck]

But then the opposite means that the system will work in your favor. I think it's pretty common sense to believe that having the option to make a decision is better for success than it being decided randomly. It's the reason why Shield is considered more valuable than Shield of Faith.
We're talking about choosing where your DPR goes and where it doesn't. Even if mistakes are made, shouldn't choice still perform better than random?
Again, not inherently. If you consistently choose incorrectly (say, for instance always put the extra DPR on attacks that would have finished the opponent anyways, or always save your bonus for a crunch time that never happens*), then a consistent blanket bonus would serve you better.
*I don't play many video games, but I've seen a persistent internet meme about some super-duper recharge potion that you are supposed to use on boss fights, and how people consistently save them until the end of the game 'in case they'll need them later')

That's why I think that, while I agree that the Champion is a little under-tuned, the conceptual idea they were chasing is a valid one--it is the subclass for people who might have option paralysis, or not want to manage the strategy of when-to-use, or similar. These are the players for whom a Champion or slightly-better-Champion-like archetype is appropriate.


Yes, but given a certain number of combat rounds per short rest and a specific heuristic to using precision attack we can actually calculate how often he will use each number of superiority dice on precision attack before the next short rest. This isn't incalculable and while complex it's not in the realm of absurdly complex yet.
Oh absolutely not. It would, however, require a set of sample situations -- say, a set of combats against an array of opponents, where order matters (since battlemaster maneuver usage decisions is such an important part of the analysis). And I think getting any two of us to agree on what a set of scenarios representative of actual play looks like could prove an absurdly complex ask. :smallbiggrin:

[Frogreaver]

Again, not inherently. If you consistently choose incorrectly (say, for instance always put the extra DPR on attacks that would have finished the opponent anyways, or always save your bonus for a crunch time that never happens*), then a consistent blanket bonus would serve you better.
*I don't play many video games, but I've seen a persistent internet meme about some super-duper recharge potion that you are supposed to use on boss fights, and how people consistently save them until the end of the game 'in case they'll need them later')

That's why I think that, while I agree that the Champion is a little under-tuned, the conceptual idea they were chasing is a valid one--it is the subclass for people who might have option paralysis, or not want to manage the strategy of when-to-use, or similar. These are the players for whom a Champion or slightly-better-Champion-like archetype is appropriate.


Oh absolutely not. It would, however, require a set of sample situations -- say, a set of combats against an array of opponents, where order matters (since battlemaster maneuver usage decisions is such an important part of the analysis). And I think getting any two of us to agree on what a set of scenarios representative of actual play looks like could prove an absurdly complex ask. :smallbiggrin:

You are still making it way to complicated. You need to assume enemy AC, number of combat rounds between short rests and superiority dice and action surge usage heuristics. That’s all you need to compute a traditional DPR number for a Battlemaster.


It depends if you prefer white room to real word or not...
I prefer an approach that doesn't hide anything.

Your approach hides everything. Consider 2 PC's with everything else the same but different hp values. Your methodolgy leads you to conclude that the PC with the higher hp does more damage. Except that's only true if the enemies deal more damage than the lower hp PC has hp. That's not a very likely event in itself and is further complicated by the fact that enemy damage is dependent on the damage the party has dealt - meaning even if we agree that a PC with the same setup but more hp than another does more damage - we still can't take this information and compare a PC with more hp and less damage to a PC with less hp and more damage.

As I said it complicates and convulutes everything that is actually going on.


You cannot synthesize those real-word variables into a single number. That'd just denature the result.

I'm sure you have heard of Expected Value?

[Man_Over_Game]

You are still making it way to complicated. You need to assume enemy AC, number of combat rounds between short rests and superiority dice and action surge usage heuristics. That’s all you need to compute a traditional DPR number for a Battlemaster.

Agreed. I didn't explain correctly, but the intent of my comment wasn't to say that "Battlemaster is better", but that, for the sake of circumstance, it probably isn't in the Champion's favor. That is, a rebuttal to the idea that "circumstance matters". It does matter, just not in a way that's helpful for this discussion.

If a Champion is better because a wasted crit isn't a wasted resource, an equal counter can be made to say that the Battlemaster chooses when he gets value. There's no point in bringing it up, when all it adds is doubt.

[Frogreaver]

Agreed. I didn't explain correctly, but the intent of my comment wasn't to say that "Battlemaster is better", but that, for the sake of circumstance, it probably isn't in the Champion's favor. That is, a rebuttal to the idea that "circumstance matters". It does matter, just not in a way that's helpful for this discussion.

If a Champion is better because a wasted crit isn't a wasted resource, an equal counter can be made to say that the Battlemaster chooses when he gets value. There's no point in bringing it up, when all it adds is doubt.

Yea I agree there. I think I would have just summarized it as - circumstances matter but without being able to see the future we cannot say for sure whether doing 1d12 extra damage now is better than waiting for a later moment in a later encounter to do +1d12 extra damage. That is, if we cannot actually say when a battlemaster is better off doing his extra damage then making the argument that you can use it when you want doesn't make it any more effective than it being truly random.

[bid]

If a Champion is better because a wasted crit isn't a wasted resource, an equal counter can be made to say that the Battlemaster chooses when he gets value. There's no point in bringing it up, when all it adds is doubt.
The Church of Champion never lets their beliefs be shaken by facts.


Your approach hides everything. Consider 2 PC's with everything else the same but different hp values.
Consider the opposite:
- how many hp do you need for both champion and BM do the same damage before dropping?
- If our party only has 10 rounds of combat per day, how do they compare?

Those are real-life question to which a synthetized number can give an answer. GIGO.

[Man_Over_Game]

The Church of Champion never lets their beliefs be shaken by facts.


Consider the opposite:
- how many hp do you need for both champion and BM do the same damage before dropping?
- If our party only has 10 rounds of combat per day, how do they compare?

Those are real-life question to which a synthetized number can give an answer. GIGO.

Final question, how many rounds of combat are there between each Short Rest? Is 5 asking too much? Is 3?

[bid]

Final question, how many rounds of combat are there between each Short Rest? Is 5 asking too much? Is 3?
I'd say 5-10, but every player will have a different answer to that and it's ok.
Maybe you'll have some who'll insist on 25 rounds, but those are outliers.

[LudicSavant]

Final question, how many rounds of combat are there between each Short Rest? Is 5 asking too much? Is 3?

One should be wary of assuming a flat number of rounds, because a direct effect of greater burst is to shorten the number of rounds that Team Monster (or some subset thereof) gets to take meaningful actions in. This shortening is the very reason a practical optimizer even cares about doing more damage in the first place.

[Man_Over_Game]

One should be wary of assuming a flat number of rounds, because a direct effect of greater burst is to shorten the number of rounds that Team Monster (or some subset thereof) gets to take meaningful actions in. This shortening is the very reason a practical optimizer even cares about doing more damage in the first place.

Alrighty, number of encounters then.

[LudicSavant]

Alrighty, number of encounters then.

I usually assume around 2 average per short rest (reflecting the "6-8 encounters per 2 short rest day" suggestion of the DMG) as a baseline.

[Man_Over_Game]

I usually assume around 2 average per short rest (reflecting the "6-8 encounters per 2 short rest day" suggestion of the DMG) as a baseline.

Sorry, I'm just trying to figure out how many resets the Battle Master should get. Beyond Action Surge, it's the only notable difference between the two that a Short Rest impacts.

[Zhorn]

This is why I tried to gauge the number of attacks per superiority dice used it would take to make up the difference rather than number of rounds, since that's a number that's easier to estimate reliably.

[LudicSavant]

This is why I tried to gauge the number of attacks per superiority dice used it would take to make up the difference

That sounds like a workable method! Eliminates the need for assumptions.

[Zhorn]

That sounds like a workable method! Eliminates the need for assumptions.
The math I used for this part is pretty minimal

Every Superiority Dice spent on turning a miss into a hit will take on average 8.1 additional attacks to make up the difference, while every superiority dice spent on adding to damage will take 4.72 additional attacks.
Number of attacks needed = [Difference between expected attack damage A and C]/[Difference between expected attack damage C and B]
'expected attack damage' is after accuracy has been accounted for
A is the BM's attacks with superiority dice (19.183 and 22.000)
B is the BM's attacks without superiority dice, ie; base fighter (14.417)
C is the Champion attacks (15.250)
With A>C>B

Mine was of course using the values I calculated in that post, but depending on your own method that'll be different when using a different model.
Still, sub in your own and it should still be in the same ballpark area.

[Frogreaver]

That sounds like a workable method! Eliminates the need for assumptions.

But it doesn't actually work. It takes a relatively large number of rounds to have say a 95% chance of using all your dice on precision attack using anything smarter than a use it anytime you miss kind of heuristic.

Or to say it another way, you can't actually consider precision attacks to be front loaded because you can't actually front load it. It takes a relatively large number of rounds to ensure you are able to use all 6 and an even larger number if you want to only use precision attack when you have a high probability of converting to a hit.

Thus, number of rounds between short rests cannot be removed from precision attack analysis.


The math I used for this part is pretty minimal

Number of attacks needed = [Difference between expected attack damage A and C]/[Difference between expected attack damage C and B]
'expected attack damage' is after accuracy has been accounted for
A is the BM's attacks with superiority dice (19.183 and 22.000)
B is the BM's attacks without superiority dice, ie; base fighter (14.417)
C is the Champion attacks (15.250)
With A>C>B

Mine was of course using the values I calculated in that post, but depending on your own method that'll be different when using a different model.
Still, sub in your own and it should still be in the same ballpark area.

Precision attack would also have a rate of use and if there aren't adequate rounds in the day to use it all the times you want using your preferred heuristic then you can't say the champion needs to 'catch up' to the damage provided by all the uses of it. Which takes us directly back to the question of how many rounds are in the short rest.

[Hael]

But it doesn't actually work. It takes a relatively large number of rounds to have say a 95% chance of using all your dice on precision attack using anything smarter than a use it anytime you miss kind of heuristic.


I’m struggling to see this. The player isn’t coming from this with zero knowledge. Instead he has likely gotten a feel for the optimal heuristic. He has access to the number of rounds the DM tends to play combat, potential meta game knowledge of AC, avg number of fights per short rest etc. In practice a good player will tend to be close to ideal damage maximization if that’s what leads to the optimal outcome (in practise it’s probably CC that matters more but that’s a different issue). Hence he’s going to be close to the best case scenario where if he has x die, then x misses are turned into hits. Alternatively, if there aren’t that many rnds, then a few of those will be converted into straight ripostes or something like that, just to get the dmg out.

[LudicSavant]

But it doesn't actually work. It works insofar as it allows you to make fewer and narrower assumptions than the alternative, even if the number of assumptions is still not zero.

[Frogreaver]

But it doesn't actually work. It takes a relatively large number of rounds to have say a 95% chance of using all your dice on precision attack using anything smarter than a use it anytime you miss kind of heuristic.

Or to say it another way, you can't actually consider precision attacks to be front loaded because you can't actually front load it. It takes a relatively large number of rounds to ensure you are able to use all 6 and an even larger number if you want to only use precision attack when you have a high probability of converting to a hit.

Thus, number of rounds between short rests cannot be removed from precision attack analysis.



Precision attack would also have a rate of use and if there aren't adequate rounds in the day to use it all the times you want using your preferred heuristic then you can't say the champion needs to 'catch up' to the damage provided by all the uses of it. Which takes us directly back to the question of how many rounds are in the short rest.

To put this in perspective
=Binom.Dist(5,'4*8',0.2,'Cumulative') = 36.0191%

That is give the following assumptions:
1. The 0.2 comes from our Precision attack heuristic is to use precision attack when we miss by 1-4.
2. We make 4 attacks per round
3. We go through 8 rounds of combat
4. We want to see the probability that we use 5 or fewer dice on precision attack.

The result here is that we have a 36.02% chance to use fewer than our 6 superiority dice. Solving for the weighted average number of superiority dice used yields 5.3 superiority dice. That is the actual battlemaster damage from precision attack in this scenario is 11.67% lower than you listed.


It works insofar as it allows you to make fewer and narrower assumptions than the alternative, even if the number of assumptions is still not zero.

They aren't fewer or narrower. They are flat out incorrect.


I’m struggling to see this. The player isn’t coming from this with zero knowledge.

Of course not. I would never assume that. This critique holds even when the player is using a fairly intelligent heuristic.


Instead he has likely gotten a feel for the optimal heuristic. He has access to the number of rounds the DM tends to play combat, potential meta game knowledge of AC, avg number of fights per short rest etc. In practice a good player will tend to be close to ideal damage maximization if that’s what leads to the optimal outcome (in practise it’s probably CC that matters more but that’s a different issue).

I agree with all of this. What are you reading me as saying that makes you think I disagree?


Hence he’s going to be close to the best case scenario where if he has x die, then x misses are turned into hits.

Depends on what you mean by best case scenario. If you mean a scenario where he has uses 6 dice on high probability precision attacks because that's the highest DPR manuever he has then I'd say there's a significant chance of that not happening unless the time between short rests is significantly longer than we would normally consider.

If you mean he's not going to naively waste abilities then I agree. He will be close to the maximum he can output, it's just the maximum he can output isn't typically going to be 6 superiority dice going to high probability precision attacks.


Alternatively, if there aren’t that many rnds, then a few of those will be converted into straight ripostes or something like that, just to get the dmg out.

Assuming he can predict the number of rounds with that degree of certainty and do fairly complex math in his head on the fly then yes. For example, if you have 1 round of combat left is it better to go ahead and use it on a +damage dice maneuver or wait incase you get to use precision attack. At what point does one 'cut their loses' and use the guaranteed damage manuever?

I would say you actually significantly overrate a players ability to predict the number of rounds left in the short rest, you significantly overrate his ability to make complex calculations on the fly to determine the 'best' time to use superiority dice for maximum DPR output. Even though I agree that the player will have a decent idea of these things - it will be far from perfect.

[LudicSavant]

They aren't fewer or narrower. They are flat out incorrect.

What assumption have I made that is incorrect?

[Frogreaver]

What assumption have I made that is incorrect?

The assumption that precision attacks damage is independent of the number of rounds. In the post you quoted I just showed that assumption was incorrect by way of counterexample (and not a ridiculous out in left field one either, but a fairly typical case study)

[LudicSavant]

The assumption that precision attacks damage is independent of the number of rounds.

Ah, so an assumption I didn't actually make. :smallannoyed:

[Greywander]

I'm curious how it affects the math if we're a half-orc, seeing as this gives us an extra damage die on crits (which will disproportionally affect Champions). My understanding is that with a greatsword or maul this only adds 1d6 damage, not 2d6, so we'd want to use something like a greataxe to get an extra 1d12 instead. This means using Slasher instead of Crusher, which offers its own utility in combat but will hurt our DPR if we don't have another source of advantage. Alternatively, since there don't seem to be any d12 bludgeoning weapons, we could use a warhammer instead for 1d10 if we really wanted to use Crusher, though a maul might have higher DPR even with the smaller extra crit die.

It just seems like critfisher builds generally want to either be an elf for Elven Accuracy or be a half-orc for Savage Attacks, and seeing as how we're talking about GMW it makes sense to run the tests as a half-orc. I don't expect this to make the Champion jump ahead of the Battle Master, but it might close the gap somewhat.

DPR isn't everything, though. Lategame that regen can be pretty nice, and Tasha's added some juicy fighting styles, making the extra one Champions get a lot more appealing. Battle Masters have their own tricks, as well, so a direct comparison is difficult.

[Frogreaver]

Ah, so an assumption I didn't actually make. :smallannoyed:

Everyone can read the context of the conversation up to this point. It's apparent to everyone what we were talking about based on our back and forth exchange on the topic.

[Zhorn]

Everyone can read the context of the conversation up to this point. It's apparent to everyone what we were talking about based on our back and forth exchange on the topic.
Clearly I'm not included in that 'everyone'. This current string of posts has me more confused than ever over what you're on about.

[LudicSavant]

I'm curious how it affects the math if we're a half-orc, seeing as this gives us an extra damage die on crits (which will disproportionally affect Champions). My understanding is that with a greatsword or maul this only adds 1d6 damage, not 2d6, so we'd want to use something like a greataxe to get an extra 1d12 instead. This means using Slasher instead of Crusher, which offers its own utility in combat but will hurt our DPR if we don't have another source of advantage. Alternatively, since there don't seem to be any d12 bludgeoning weapons, we could use a warhammer instead for 1d10 if we really wanted to use Crusher, though a maul might have higher DPR even with the smaller extra crit die.

It just seems like critfisher builds generally want to either be an elf for Elven Accuracy or be a half-orc for Savage Attacks, and seeing as how we're talking about GMW it makes sense to run the tests as a half-orc. I don't expect this to make the Champion jump ahead of the Battle Master, but it might close the gap somewhat.

DPR isn't everything, though. Lategame that regen can be pretty nice, and Tasha's added some juicy fighting styles, making the extra one Champions get a lot more appealing. Battle Masters have their own tricks, as well, so a direct comparison is difficult.

Adding in Half-Orc is pretty easy to do in either my DPR Calculator or AnyDice.

The complicated part includes
- the element of player choice and gambling against unknown future events in the Battle Master's decision tree. For example, you hypothetically could decide to only use a smite-like maneuver on a crit... but doing so runs the risk of not actually getting to use all your maneuvers before a short rest arrives.
- the element of team benefits (for example, granting Advantage to teammates with Crusher).
- the impact of things that don't do damage directly, like status effects.

[Frogreaver]

Clearly I'm not included in that 'everyone'. This current string of posts has me more confused than ever over what you're on about.

You presented a method. Ludic praised it for eliminating assumptions. I claimed your method wasn't actually correct because it assumed you could use 6 superiority dice on precision attack despite the number of rounds that were in the short rest. Ludic defended it saying "It works insofar as it allows you to make fewer and narrower assumptions than the alternative, even if the number of assumptions is still not zero." I again claimed it didn't work because the assumptions in it were incorrect. At that point Ludic claims she never made that assumption.

Hopefully that helps.



- the element of team benefits (for example, granting Advantage to teammates with Crusher).


Oh wow. I didn't realize that aspect of Crusher till you just mentioned it. I'm even more impressed with the feat. *When I read it my mind inherently added a "your attacks" to it instead of leaving it as "attacks".

[LudicSavant]

You presented a method. Ludic praised it for eliminating assumptions. I claimed your method wasn't actually correct because it assumed you could use 6 superiority dice on precision attack despite the number of rounds that were in the short rest. Ludic defended it saying "It works insofar as it allows you to make fewer and narrower assumptions than the alternative, even if the number of assumptions is still not zero." I again claimed it didn't work because the assumptions in it were incorrect. At that point Ludic claims she never made that assumption.

Hopefully that helps.

It does not help, because the assumption you falsely claim I made



The assumption that precision attacks damage is independent of the number of rounds.


is not only one that features nowhere in any of my statements, it is also an assumption that is unnecessary in order to measure a number of attacks needed to close a gap.

[Zhorn]

No Frogreaver, I mean I don't follow your reasoning at all. LudicSavant I understand.

Order, front loading or whatever else doesn't matter.
lets make a simple representation
A=5, B=10, C=6
For every attack that B is used, there will need to be four attack where A is used for C to keep pace
AAAAB = 5 + 5 + 5 + 5 + 10 = 30
AAABA = 5 + 5 + 5 + 10 + 5 = 30
AABAA = 5 + 5 + 10 + 5 + 5 = 30
ABAAA = 5 + 10 + 5 + 5 + 5 = 30
BAAAA = 10 + 5 + 5 + 5 + 5 = 30
CCCCC = 6 + 6 + 6 + 6 + 6 = 30

if there were a string of A, then C would initially pull ahead, but a few B's would close that gap. We wouldn't say 'catch up' but it's still the same method.
Every use of B alongside C creates a gap of B-C that will take a number of occurrences of of C alongside A for the differences of C-A to close that gap, whether those B's occur at the start or end or anywhere in-between is irrelevant. The length of a round is irrelevant. The number of rounds is irrelevant. The number of short rests or initiative rolls is irrelevant.

We're working with averages and simplified expected outcomes. There's no need to get overly convoluted with the math.

[Frogreaver]

is not only one that features nowhere in any of my statements, it is also an assumption that is unnecessary in order to measure a number of attacks needed to close a gap.

I would say the 'gap' caused by precision attack can only be computed without an assumed number of rounds if one assumes that the number of rounds doesn't affect the damage precision attack causes. Since you have said you aren't making that assumption - how are you computing the damage 'gap' caused by precision attack?

[LudicSavant]

The number of rounds does have an effect, insofar as you might have better opportunities to use your maneuvers given more die rolls (since you can decide to use a maneuver after seeing the roll). For example, a player might decide that they will only use Menacing Attack if they get a crit (thus adding superiority die *2 damage instead of superiority die *1 with each use), or only use Precision Attack if they miss by 1 (thus making each superiority die convert a miss into a hit with 100% success rate), but if there aren't enough attacks per short rest, they (probably) won't get those opportunities often enough to use up all their superiority dice.

But the method I had in mind would simply choose a given strategy and then evaluate find where its breakpoints are (e.g. "if # of attacks is >X, then strategy A is better" etc). We don't need to actually determine how many attacks there are in a day, only how many attacks there would need to be in order to "catch up."

The real problem comes in when we ask how we can quantify things like Crusher's benefit to allies (giving THEM advantage). Since we'd have to know who those characters are, and how many attacks you are likely to be able to make against the guy you already critted before they die anyways, etc.

[Frogreaver]

The number of rounds does have an effect, insofar as you might have better opportunities to use your maneuvers given more die rolls (since you can decide to use a maneuver after seeing the roll). For example, a player might decide that they will only use Menacing Attack if they get a crit (thus adding superiority die *2 damage instead of superiority die *1 with each use), or only use Precision Attack if they miss by 1 (thus making each superiority die convert a miss into a hit with 100% success rate), but if there aren't enough attacks per short rest, they (probably) won't get those opportunities often enough to use up all their superiority dice.

Agreed!


But the method I had in mind would simply choose a given strategy and then evaluate find where its breakpoints are (e.g. "if # of attacks is >X, then strategy A is better" etc). We don't need to actually determine how many attacks there are in a day, only how many attacks there would need to be in order to "catch up."

As a counterexample consider these 2 strategies.
Strategy 'A' = Use all your dice as fast as possible
Strategy 'B' = Use your dice only when you miss by 1 or crit

Now let's have two cases:
Case '1' = There is a single round in the short rest.
Case '2' = There are 10,000,000 rounds in the short rest.

In Case '1' Strategy 'A' should be clearly better.
In Case '2' Strategy 'B' should be clearly better.

Thus proving that the additional damage caused by using a specific strategy is dependent upon the the number of rounds in the short rest. This implies that any computed 'gap' you need to 'catch up' by is going to change depending on the number of rounds per short rest

[LudicSavant]

As a counterexample consider these 2 strategies.
Strategy 'A' = Use all your dice as fast as possible
Strategy 'B' = Use your dice only when you miss by 1 or crit

Now let's have two cases:
Case '1' = There is a single round in the short rest.
Case '2' = There are 10,000,000 rounds in the short rest.

In Case '1' Strategy 'A' should be clearly better.
In Case '2' Strategy 'B' should be clearly better.

Thus proving that the additional damage caused by using a specific strategy is dependent upon the the number of rounds in the short rest

This isn't a "counterexample" because it already agrees with the concept I just explained.


This implies that any computed 'gap' you need to 'catch up' by is going to change depending on the number of rounds per short rest

And this part appears to be wrong. You do not need to know that there are X rounds in the short rest in order to determine whether or not you would catch up in Y rounds.

For example, let's say Strategy C is better in the long term, and Strategy D better in the short term -- their performances vary based on how many rounds there are. You could then determine exactly how many rounds it would take for strategy C to exceed Strategy D. You do not need to actually know how many rounds you will get in order to calculate how many rounds it would take.

[Frogreaver]

No Frogreaver, I mean I don't follow your reasoning at all. LudicSavant I understand.

Order, front loading or whatever else doesn't matter.
lets make a simple representation
A=5, B=10, C=6
For every attack that B is used, there will need to be four attack where A is used for C to keep pace
AAAAB = 5 + 5 + 5 + 5 + 10 = 30
AAABA = 5 + 5 + 5 + 10 + 5 = 30
AABAA = 5 + 5 + 10 + 5 + 5 = 30
ABAAA = 5 + 10 + 5 + 5 + 5 = 30
BAAAA = 10 + 5 + 5 + 5 + 5 = 30
CCCCC = 6 + 6 + 6 + 6 + 6 = 30


In that sense sure but that's not what I'm talking about. As one of my posts above showed, in 8 rounds of combat with 4 attacks per round and using precision attack on a miss of 1-4 you are only averaging 5.3 uses of precision attack. Your calculation would assume 6 uses of precision attack. Thus the gap you are setting is higher than the actual gap. Meaning you are over estimating the number of rounds the champion actually needs to catch up. But more importantly the average # of uses of precision attack will change as your total number of rounds changes. For example, in 4 rounds using the same strategy you will only use 3.16 uses of precision attack. You would have assumed 6 uses here as well. It's that assumption of 6 uses even when you've not made enough attacks to be at 6 uses that is the front loading i'm talking about.


We're working with averages and simplified expected outcomes. There's no need to get overly convoluted with the math.

Trying to simplify like you are is leading you to not calculating the expected outcomes correctly. One doesn't need to be overly convoluted. One needs to be accurate though even if it's not quite as simple as one would like.


This isn't a "counterexample" because it already agrees with the concept I just explained.

I could have swore we were saying different things there. And your comment below leads me to believe that as well.


And this part appears to be wrong. You do not need to know that there are X rounds in the short rest in order to determine whether or not you would catch up in Y rounds.

You do when Y depends on X.

[LudicSavant]

You do when Y depends on X.

:smallsigh:

It is possible to determine that a task would require an hour to complete without knowing whether or not an hour will be available.

[Frogreaver]

:smallsigh:

It is possible to determine that a task would require an hour to complete without knowing whether or not an hour will be available.

I didn't say every Y depended on X so I'm not sure what that has to do with a claim that this Y depends on this X.

[LudicSavant]

I didn't say every Y depended on X so I'm not sure what that has to do with a claim that this Y depends on this X.

Yet again:


This implies that any computed 'gap' you need to 'catch up' by is going to change depending on the number of rounds per short rest

Per your own suggestion, there is some number of rounds where Strategy B exceeds strategy A. We can determine how many rounds that is, without knowing whether or not we will actually play that many rounds.

Your own "counterexample" supports the very concept that people have been trying to tell you.

[Frogreaver]

Yet again:

Per your own suggestion, there is some number of rounds where Strategy B exceeds strategy A. We can determine how many rounds that is, without knowing whether or not we will actually play that many rounds.

We cannot.

Normally when we compare we get something like:

f(x) = p(x) + q(x)
g(x) = r(x)


s.t. x is an integer representing the number of rounds
s.t. p(x) = ax where a is a real number
s.t. q(x) = c where c is a real number
s.t. r(x) = bx where b is a real number and b>a



Then we can say for what x is g(x) > f(x) and this is relatively simple to solve.

However, in the case of precision attack the function would instead be

f(x) = p(x) + q(x)
g(x) = r(x)


s.t. x is an integer representing the number of rounds
s.t. p(x) = ax where a is a real number
s.t. 0.2 is the probability the attack roll lands on a value where you will use precision attack (note this represents the chosen 'use when miss by 1-4' heuristic and can be changed but will yield different results)
q(x) = h*d * innerproduct(y , z ) where y is the vector <1,2,3,4,5,6,6,6,....> and z is the vector <binomal.dist(1,nx,0.2,0), binomal.dist(2,nx,0.2,0), ....>
s.t. h is the chance precision attack turns a miss to a hit
s.t. d is the damage done when you hit
s.t. n is the attacks per round
s.t. r(x) = bx where b is a real number and b>a



I am not aware of any method that can be used to solve r(x) > p(x) + q(x) given the above equations.

[bid]

To put this in perspective
=Binom.Dist(5,'4*8',0.2,'Cumulative') = 36.0191%

That is give the following assumptions:
1. The 0.2 comes from our Precision attack heuristic is to use precision attack when we miss by 1-4.
2. We make 4 attacks per round
3. We go through 8 rounds of combat
4. We want to see the probability that we use 5 or fewer dice on precision attack.

The result here is that we have a 36.02% chance to use fewer than our 6 superiority dice. Solving for the weighted average number of superiority dice used yields 5.3 superiority dice. That is the actual battlemaster damage from precision attack in this scenario is 11.67% lower than you listed.
Now that is useful. Thank you for showing me how to use this tool.

Seems about right for champion when I try a sanity check:
=Binom.Dist(0,'4*8',0.05,'Cumulative') = 20% of never rolling 19,
=Binom.Dist(1,'4*8',0.05,'Cumulative') = 52% of rolling 19 no more than once.
=Binom.Dist(5,'4*8',0.05,'Cumulative') = 99.5% of rolling 19 no more than 5 times.

I tried and it seem 0.2 is not 1-4 but 1-5 {.208 = (12+11+10+9+8)/12/20}
=(5×12−5×(5-1)÷2)÷12÷20 is the general excel equation for your precision attack heuristic.

Lets see how it looks around that point:
=Binom.Dist(5,'4*8',0.208,'Cumulative') = 32% of not spending all 6 with off-by-5
=Binom.Dist(4,'4*8',0.208,'Cumulative') = 17% of not spending 5 with off-by-5
=Binom.Dist(5,'4*8',0.238,'Cumulative') = 19% of not spending all 6 with off-by-6
=Binom.Dist(4,'4*8',0.238,'Cumulative') = 9% of not spending 5 with off-by-6
=Binom.Dist(5,'4*8',0.262,'Cumulative') = 12% of not spending all 6 with off-by-7
=Binom.Dist(4,'4*8',0.262,'Cumulative') = 5% of not spending 5 with off-by-7
You really have to take bad options to be likely to spend most SD that fast. It might be better to waste some as +1d12 damage if you want to maximize your damage output and know the day will be short.


OTOH, you don't have to spend all your SD to do better...
Trying an extremely low spending limit:
=Binom.Dist(2,'4*8',0.05,'Cumulative') = 77% of rolling 19 no more than twice.
=Binom.Dist(2,'4*8',0.208,'Cumulative') = 2% of not spending 3 with off-by-5
You have 77% of rolling 19 less than 3 times and be limited to (2d6)*2 or 14 damage.
You have 2% of doing less than 3 SD and be limited to (2d6+3)*2 or 20 extra damage.

You really need enough combat round to spend all your SD or champion never has a chance to catch up.
EDIT: silly me used level 3 improved critical instead of the level 15 one. not fixing it further than this caveat.

[SLOTHRPG95]

@Frogreaver I think you and @Ludic are talking past each other further and further with your abstracted statements. If I understand you correctly, your original objection to @Zhorn's methods was that he assumed (implicitly) that all 6 superiority dice would be used for precision, hence maximizing the initial gap between Champion's damage output and the BM's. You pointed out that the number of attacks/rounds before all 6 can be used for precision is not fixed, and hence the damage gap is not fixed for relatively small numbers of attacks.

Specifically, you could model the required number of attacks/rounds with a negative binomial distribution: use of precision is a "failure" and you want to know the number of successes before hitting six failures, with total number of attacks then being successes plus six. Given that the Champion will always do better as number of attacks tends to infinity, the BM needs to pull ahead early, or it'll just always be behind. If the BM uses a superiority die every time an attack is missed by 6 or less, then the distribution for the number of attacks before all superiority dice are used is 6 + NB (6, .3), which has a mean value of 20 attacks.

Although I think your original objection is sound in theory, in practice at 20th level there won't be many inter-SR periods where you don't get off at least 20 attacks. That's just three rounds if you action surge twice. Hence, at least at 20th level, which was under discussion given 6d12 sup. dice and four attacks per round etc., the variable gap size becomes a non-issue. You don't need 10M rounds to optimally use your sup. dice for DPR, you only need (on average) about three. Of course, this will vary at other levels but it's too late at night to do a breakdown for all levels based on size of sup. dice, number of dice, number of attacks per round, etc.

Hope this clarifies some confusion on all sides.

[LudicSavant]

We cannot.

If you could not determine a number of rounds where B exceeds A, then you could not make statements like the following:


In Case '1' Strategy 'A' should be clearly better.
In Case '2' Strategy 'B' should be clearly better.

If you believe that you cannot determine a number of rounds where B would exceed A, how did you determine that B would exceed A in case 2?

[Frogreaver]

If you could not determine a number of rounds where B exceeds A, then you could not make statements like the following:



If you believe that you cannot determine a number of rounds where B would exceed A, how did you determine that B would exceed A in case 2?

Why did you ignore the rest of my explanation?

[LudicSavant]

Why did you ignore the rest of my explanation?

You didn't actually explain why anything I said is wrong. As SLOTH pointed out it looks like you're just talking past me. :smallconfused:

[Frogreaver]

@Frogreaver I think you and @Ludic are talking past each other further and further with your abstracted statements. If I understand you correctly, your original objection to @Zhorn's methods was that he assumed (implicitly) that all 6 superiority dice would be used for precision, hence maximizing the initial gap between Champion's damage output and the BM's. You pointed out that the number of attacks/rounds before all 6 can be used for precision is not fixed, and hence the damage gap is not fixed for relatively small numbers of attacks.

Yes, thank you.


Specifically, you could model the required number of attacks/rounds with a negative binomial distribution: use of precision is a "failure" and you want to know the number of successes before hitting six failures, with total number of attacks then being successes plus six. Given that the Champion will always do better as number of attacks tends to infinity, the BM needs to pull ahead early, or it'll just always be behind. If the BM uses a superiority die every time an attack is missed by 6 or less, then the distribution for the number of attacks before all superiority dice are used is 6 + NB (6, .3), which has a mean value of 20 attacks.

I'll have to read up on the negative binomial distribution. I had glanced at it before but didn't think it would help on this problem.

Just to compare your results with my weighted average from the binomial distribution, I only get 5.2 dice used for those same parameters. I tested with using a superiority dice whenever an opportunity arose to use one with those parameters and I got your 6. However, that doesn't align with how superiority dice actually work as no matter how many opportunities you have to use them at most you can only use 6 and so I'm even more convinced the negative binomial distribution won't be useful here.


Although I think your original objection is sound in theory, in practice at 20th level there won't be many inter-SR periods where you don't get off at least 20 attacks.

I think you need many more rounds than that to reach 'effectively 6 dice used'.


That's just three rounds if you action surge twice. Hence, at least at 20th level, which was under discussion given 6d12 sup. dice and four attacks per round etc., the variable gap size becomes a non-issue. You don't need 10M rounds to optimally use your sup. dice for DPR, you only need (on average) about three. Of course, this will vary at other levels but it's too late at night to do a breakdown for all levels based on size of sup. dice, number of dice, number of attacks per round, etc.

Hope this clarifies some confusion on all sides.

I think you have, though I'm curious to hear if you reach the same conclusions I just did about the negative binomial distribution.


You didn't actually explain why anything I said is wrong. As SLOTH pointed out it looks like you're just talking past me. :smallconfused:

That's not what Sloth said.

[LudicSavant]

That's not what Sloth said.

Here's what Sloth said.


@Frogreaver I think you and @Ludic are talking past each other further and further with your abstracted statements.

[Frogreaver]

Here's what Sloth said.

"@Frogreaver I think you and @Ludic are talking past each other further and further with your abstracted statements."

Yes, and this statement is not the same as what you claimed he said.

"As SLOTH pointed out it looks like you're just talking past me."

[LudicSavant]

"@Frogreaver I think you and @Ludic are talking past each other further and further with your abstracted statements."

Yes, and this statement is not the same as what you claimed he said.

"As SLOTH pointed out it looks like you're just talking past me."

"Talking past each other" suggests that you are talking past me, and I am talking past you.

I'm not sure what definition of "talking past past each other" you have that somehow involves you not talking past me. But whatever it is... I think that such definitions are kinda the problem with this whole conversation.

[Frogreaver]

"Talking past each other" suggests that you are talking past me, and I am talking past you.

I'm not sure what definition of "talking past past each other" you have that somehow involves you not talking past me. But whatever it is... I think that kind of thing is the problem with this whole conversation.

Let's ask others. When Person C says you two are talking past each other, is it fair for person B to tell person A, hey this guy pointed out you are talking past me?


Now that is useful. Thank you for showing me how to use this tool.

Seems about right for champion when I try a sanity check:
=Binom.Dist(0,'4*8',0.05,'Cumulative') = 20% of never rolling 19,
=Binom.Dist(1,'4*8',0.05,'Cumulative') = 52% of rolling 19 no more than once.
=Binom.Dist(5,'4*8',0.05,'Cumulative') = 99.5% of rolling 19 no more than 5 times.

I tried and it seem 0.2 is not 1-4 but 1-5 {.208 = (12+11+10+9+8)/12/20}
=(5×12−5×(5-1)÷2)÷12÷20 is the general excel equation for your precision attack heuristic.

Lets see how it looks around that point:
=Binom.Dist(5,'4*8',0.208,'Cumulative') = 32% of not spending all 6 with off-by-5
=Binom.Dist(4,'4*8',0.208,'Cumulative') = 17% of not spending 5 with off-by-5
=Binom.Dist(5,'4*8',0.238,'Cumulative') = 19% of not spending all 6 with off-by-6
=Binom.Dist(4,'4*8',0.238,'Cumulative') = 9% of not spending 5 with off-by-6
=Binom.Dist(5,'4*8',0.262,'Cumulative') = 12% of not spending all 6 with off-by-7
=Binom.Dist(4,'4*8',0.262,'Cumulative') = 5% of not spending 5 with off-by-7
You really have to take bad options to be likely to spend most SD that fast. It might be better to waste some as +1d12 damage if you want to maximize your damage output and know the day will be short.


OTOH, you don't have to spend all your SD to do better...
Trying an extremely low spending limit:
=Binom.Dist(2,'4*8',0.05,'Cumulative') = 77% of rolling 19 no more than twice.
=Binom.Dist(2,'4*8',0.208,'Cumulative') = 2% of not spending 3 with off-by-5
You have 77% of rolling 19 less than 3 times and be limited to (2d6)*2 or 14 damage.
You have 2% of doing less than 3 SD and be limited to (2d6+3)*2 or 20 extra damage.

You really need enough combat round to spend all your SD or champion never has a chance to catch up.

Thanks. I find that to be one of the most useful formulas out there. It really makes working with most complicated probability problems 10x easier.

One nitpick: you said 1-4 wasn't 20% but it is when you are looking at the original d20 which is what you would want to do if you are using this to calculate your opportunities to use superiority dice based on a miss by 1...N heuristic.

Also, in case it's not readily apparent, one can use the non-cumulative version of this formula to get a weighted average for exactly how many superiority dice are being used in an n combat round short rest period. Then one can also calculate the chance of using one of those superiority dice to turn a miss into a hit based on the same 1...N heuristic used in the function. Multiply the number of dice, the chance to turn a miss into a hit and the damage on a hit all together and you would have the amount of damage precision added given n number of rounds.

[LudicSavant]

The assumption that precision attacks damage is independent of the number of rounds.

As I stated myself (https://forums.giantitp.com/showsinglepost.php?p=24998933&postcount=105), "The number of rounds does have an effect, insofar as you might have better opportunities to use your maneuvers given more die rolls (since you can decide to use a maneuver after seeing the roll). For example, a player might decide that they will only use Menacing Attack if they get a crit (thus adding superiority die *2 damage instead of superiority die *1 with each use), or only use Precision Attack if they miss by 1 (thus making each superiority die convert a miss into a hit with 100% success rate), but if there aren't enough attacks per short rest, they (probably) won't get those opportunities often enough to use up all their superiority dice."

Which makes it extraordinarily frustrating that you keep arguing as though I said the opposite. :smallannoyed:

You even provided evidence for my statement, here:


As a counterexample

(Snip)

Thus proving that the additional damage caused by using a specific strategy is dependent upon the the number of rounds in the short rest.

... but said it was a "counterexample." Even though it's an example of what I was saying.

Seriously, every single one of your arguments directed at me appears to be trying to disprove an assumption I never actually made (https://forums.giantitp.com/showsinglepost.php?p=24998902&postcount=96) and that I already said would be an incorrect assumption (https://forums.giantitp.com/showsinglepost.php?p=24998933&postcount=105).

Like, if you have any premise you're trying to prove beyond "damage potential of Precision Attack and/or critfishing is connected to number of rounds" then I don't know what it is, and if that's what you're trying to prove, then I don't know why you're arguing with me about it.

Given that you seem to actually be agreeing with me in things that are supposedly "counterexamples" of my statements, I legitimately am not certain at this point where any possible miscommunication ends and any actual disagreement begins. =\


@Frogreaver I think you and @Ludic are talking past each other further and further with your abstracted statements.

I think so as well.

[Frogreaver]

As I stated myself (https://forums.giantitp.com/showsinglepost.php?p=24998933&postcount=105), "The number of rounds does have an effect, insofar as you might have better opportunities to use your maneuvers given more die rolls (since you can decide to use a maneuver after seeing the roll). For example, a player might decide that they will only use Menacing Attack if they get a crit (thus adding superiority die *2 damage instead of superiority die *1 with each use), or only use Precision Attack if they miss by 1 (thus making each superiority die convert a miss into a hit with 100% success rate), but if there aren't enough attacks per short rest, they (probably) won't get those opportunities often enough to use up all their superiority dice."

Which makes it extraordinarily frustrating that you keep arguing as though I said the opposite. :smallannoyed:

I seem to recall agreeing with this part of your post when you said it because it was exactly what I had been saying all the way up to this point. I could go dig out the quote but I expect you recall this agreement as well.


Seriously, every single one of your arguments directed at me appears to be trying to disprove an assumption I never actually made (https://forums.giantitp.com/showsinglepost.php?p=24998902&postcount=96) and that I already said would be an incorrect assumption (https://forums.giantitp.com/showsinglepost.php?p=24998933&postcount=105).

Obviously I disagree and I think we could argue back and forth all day about whether or not you actually made that assumption. IMO, this branch of the discussion isn't worthwhile to continue.

For what it's worth I will add this: You never directly made that claim.


Like, if you have any premise you're trying to prove beyond "damage potential of Precision Attack and/or critfishing is connected to number of rounds" then I don't know what it is, and if that's what you're trying to prove, then I don't know why you're arguing with me about it.

Given that you seem to actually be agreeing with me in things that are supposedly "counterexamples" of my statements, I legitimately am not certain at this point where any possible miscommunication ends and any actual disagreement begins. =\

There's only one other major thing we have been in disagreement over. Whether we can actually determine the number of rounds where the champion catches up to the battlemaster using precision attack.

I gave a rather detailed post iterating exactly what that this math problem looks like and stating at the end that I don't know of a way to solve it for X. I'm open to you offering suggestions on how to do so. It's definitely possible someone can solve a type of equation I cannot.



However, in the case of precision attack the function would instead be

f(x) = p(x) + q(x)
g(x) = r(x)


s.t. x is an integer representing the number of rounds
s.t. p(x) = ax where a is a real number
s.t. 0.2 is the probability the attack roll lands on a value where you will use precision attack [I](note this represents the chosen 'use when miss by 1-4' heuristic and can be changed but will yield different results)
q(x) = h*d * innerproduct(y , z ) where y is the vector <1,2,3,4,5,6,6,6,....> and z is the vector <binomal.dist(1,nx,0.2,0), binomal.dist(2,nx,0.2,0), ....>
s.t. h is the chance precision attack turns a miss to a hit
s.t. d is the damage done when you hit
s.t. n is the attacks per round
s.t. r(x) = bx where b is a real number and b>a



I am not aware of any method that can be used to solve r(x) > p(x) + q(x) given the above equations.






I think so as well.


Looks like we agree on something else :smallsmile:

[LudicSavant]

For what it's worth I will add this: You never directly made that claim.

Not only did I not make that claim directly or otherwise, I directly and unequivocally made the exact opposite claim (https://forums.giantitp.com/showsinglepost.php?p=24998933&postcount=105), and that still didn't stop you from putting your words in my mouth (https://www.merriam-webster.com/dictionary/put%20words%20in%2Finto%20someone%27s%20mouth). Indeed, you seem to be willing to assume what "everyone's" opinion is (https://forums.giantitp.com/showsinglepost.php?p=24998910&postcount=99), even if the only opinions anyone expressed on the matter contradict you (https://forums.giantitp.com/showsinglepost.php?p=24998924&postcount=103).

Seriously, it is not cool to put your words in someone else's mouth and repeatedly insist they are making claims that you simply assumed was "implied," even after they have in no uncertain terms clarified that that is not their opinion. Nor is it cool to keep demanding someone defend an opinion that they already said they disagree with, and have in fact never agreed with at any point this has ever come up since 5e was published way back in 2014.

[Zhorn]

@Zhorn's methods was that he assumed (implicitly) that all 6 superiority dice would be used for precision, hence maximizing the initial gap between Champion's damage output and the BM's.
Sorta initially... but not exactly as I moved past that into a smaller range of focus immediately after (though it can still be extrapolated out to that)
When talking about the gap in damage and catching up I moved on from comparing the difference in ALL dice being used to just the expected damage gap of a single attack from each of the outcomes of the Battle Master compared to the Champion. Just one single dice on either +hit or +damage vs Champion (I gave a number for both, not just Precision), and then the difference in expected damage of one hit without a dice vs Champion.

It's why I've kept saying that the number of rounds, attacks per round, or how many attacks pass by before all the Superiority Dice are expended doesn't matter, because that wasn't what I was comparing, just the expected damage gaps for singular attacks.

A = (Expected Damage of a Battle Master's attack using a Superiority dice) - (Expected damage of a Champion's attack)

B = (Expected damage of a Champion's attack) - (Expected Damage of a Battle Master's attack without using a Superiority dice)

A / B = Number of additional attacks needed of Champion vs no Superiority Dice to close the gap

This is where I got my 8.1 and 4.72 additional attacks to make up the expected difference per dice spent.
29(35) and 49(55) attack numbers from before the above calculation sound impressive but are clearly impractical.

Important note is the expected damage I was using is already multiplied by the hit%, so Frogreaver's talking about waiting for ideal d20 results to use Superiority Dice on is doubling back onto a detail we'd already simplified to move past. In active play yes we would only use Precision on attacks that missed in a narrow margin, or apply a +damage Maneuver on crits to reliably double the potential damage of the Superiority Dice, but all that is using an entirely different model. Frogreaver's model will be reliant on accurately estimating the length of rounds and the likelihood of 'ideal' conditions within specific timeframes, where as the model I'm using will not care about those details at all.

Frogreaver's model I imagine is going to be a more accurate representation over an adventuring day with multiple encounters, rests, initiative rolls, chances of unused dice, I'm just not bothering with that level of depth. Too many unknowns outside of the control of the players.
Much simpler to keep that scope small in a range that the players can reliably interact with.

Was a superiority dice used, Y/N?
Was it +hit/+dmg?
Here's how many attacks of no-dice that difference is worth.

Short and simple with no need for word of the day vocabulary. And while not the perfection Frogreaver is looking for, it is still accurate enough to ballpark the disparity between the subclasses (which if we're using dice averages is as accurate as we need to be).

[LudicSavant]

There's only one other major thing we have been in disagreement over. Whether we can actually determine the number of rounds where the champion catches up to the battlemaster using precision attack.

Of course you can determine that.

Given X rounds we can determine whether any given strategy performs better in that time period -- indeed, you must on some level know this is possible, given that you make such a conclusion in your own post (https://forums.giantitp.com/showsinglepost.php?p=24998947&postcount=106) (determining that B is better when X = 10,000,000 and A is better when X = 1). So... we could just do this for all values of X. Therefore we can determine the range of X for which any given strategy is ahead of any other given strategy.

[Frogreaver]

Sorta initially... but not exactly as I moved past that into a smaller range of focus immediately after (though it can still be extrapolated out to that)
When talking about the gap in damage and catching up I moved on from comparing the difference in ALL dice being used to just the expected damage gap of a single attack from each of the outcomes of the Battle Master compared to the Champion. Just one single dice on either +hit or +damage vs Champion (I gave a number for both, not just Precision), and then the difference in expected damage of one hit without a dice vs Champion.

That clarifies some as I wasn't aware you were attempting to move to a type of model.

Can you elaborate on how you are computing the damage gap for a single attack?



It's why I've kept saying that the number of rounds, attacks per round, or how many attacks pass by before all the Superiority Dice are expended doesn't matter, because that wasn't what I was comparing, just the expected damage gaps for singular attacks.

The reason it's so important to me to get elaboration on how you are doing this is that depending on how that computation is being done there could easily be similar issues cropping up with this model as with the one before and the details are what will let us see that.


A = (Expected Damage of a Battle Master's attack using a Superiority dice) - (Expected damage of a Champion's attack)

B = (Expected Damage of a Battle Master's attack without using a Superiority dice) - (Expected damage of a Champion's attack)

A / B = Number of additional attacks needed of champion vs no Superiority Dice to close the gap

I follow this, except for how A is being computed.


Short and simple with no need for word of the day vocabulary. And while not the perfection Frogreaver is looking for, it is still accurate enough to ballpark the disparity between the subclasses (which if we're using dice averages is as accurate as we need to be).

What I suspect you are doing is using a heuristic s.t. on a hit you apply +1d12 damage and s.t. on a miss you apply precision. There's 2 issues if this is the case.


The first is fairly minor and I think would be an acceptable margin of error for an estimate. There's a 5% chance you roll a natural 1 and get to save the dice for later. Unless that's being accounted for then the value you obtain will be incorrect but only slightly so and still good enough to be used as an estimate IMO.
The second is much more important. You are assuming a very 'naive' superiority dice use heuristic. Meaning that any damage value you get that the superiority dice is causing will be lower and possibly significantly lower than what a 'smarter' heuristic could produce. Implying that your method (assuming I'm accurately capturing what you are doing) would be underestimating the number of rounds the Champion needs to catch up.


Conclusion - for the given heuristic your model would provide a good estimate. But, there are many other more damaging heuristics your method would not apply and it's this fact that makes me claim that overall it's not a good approach to this problem.


Of course you can determine that.

Given X rounds we can determine whether any given strategy performs better in that time period

If this isn't what you mean then let me know...

I'm assuming you are getting at something like: Let X=1, compute the values for champion and battlemaster and see who does more damage. If it's the battlemaster then Let X=X+1. Repeat until the champion does more damage.

Except you've not given any guarantee that the champion will ever do more damage than the battlemaster and so we can easily get stuck in an infinite loop. This is directly related to the 'famous Halting Problem' in computer science which is a provably unsolvable problem.

So, in order for this method to work we would need to know for certain that at some point the champion will do more damage than the battlemaster - which may be totally true, but we can't just assume that's the case.

[x3n0n]

So, in order for this method to work we would need to know for certain that at some point the champion will do more damage than the battlemaster - which may be totally true, but we can't just assume that's the case.

I don't understand why we can't assume that the Champion will do more damage than the "equivalent" Battle Master that can't use never uses maneuvers.
It seems like we clearly can assume that, if I am tracking to the correct scenario.

The dice-less Battle Master is a vanilla Fighter; no unusual bonuses.
The Champion is identical, except it has a 15% crit rate instead of a 5% crit rate, so as the number of attacks goes to infinity, its additional damage dealt goes to infinity (at the rate of "extra damage per crit" times 10%).

(If Crusher enters the picture, then the Champ looks even better because that greatly accelerates both the hit and crit rates for the rest of the Champ's turn.)

Did I miss something?

[LudicSavant]

If this isn't what you mean then let me know...

I'm assuming you are getting at something like: Let X=1, compute the values for champion and battlemaster and see who does more damage. If it's the battlemaster then Let X=X+1. Repeat until the champion does more damage.

Except you've not given any guarantee that the champion will ever do more damage than the battlemaster and so we can easily get stuck in an infinite loop. This is directly related to the 'famous Halting Problem' in computer science which is a provably unsolvable problem.

Okay, no. Just... no. You're not going to run into the Halting Problem or hit infinite loops. There are a finite number of seconds, and therefore rounds, in a day. And you can stop counting well before then.


I don't understand why we can't assume that the Champion will do more damage than the "equivalent" Battle Master that can't use never uses maneuvers.
It seems like we clearly can assume that, if I am tracking to the correct scenario.

The dice-less Battle Master is a vanilla Fighter; no unusual bonuses.
The Champion is identical, except it has a 15% crit rate instead of a 5% crit rate, so as the number of attacks goes to infinity, its additional damage dealt goes to infinity (at the rate of "extra damage per crit" times 10%).

(If Crusher enters the picture, then the Champ looks even better because that greatly accelerates both the hit and crit rates for the rest of the Champ's turn.)

Did I miss something?

You're correct -- there should be a finite number of rounds before it converges.

In order for that to not be the case, the Champion's attack would have to be no better than the diceless Battle Master's, which isn't the case.

[bid]

One nitpick: you said 1-4 wasn't 20% but it is when you are looking at the original d20 which is what you would want to do if you are using this to calculate your opportunities to use superiority dice based on a miss by 1...N heuristic.
That's why I find it weird...

Miss-by-4 should have 4 values:
- off-by-1 which is 12/12 success
- off-by-2 which is 11/12 success (miss on 1)
- off-by-3 which is 10/12 success (miss on 1-2)
- off-by-4 which is 9/12 success (miss on 1-3)
When I add them, I get (12/12 + 11/12 + 10/12 + 9/12) * 0.05 = 42/12/20 ~ 17.5%

Compare to 1-5 which is (12/12 + 11/12 + 10/12 + 9/12 + 8/12) * 0.05 = 50/12/20 ~ 20.8%


Our results should be the same, what assumption makes it different?

EDIT: the non-cumulative use is another nice tool, TIL:smallsmile:

[Frogreaver]

That's why I find it weird...

Miss-by-4 should have 4 values:
- off-by-1 which is 12/12 success
- off-by-2 which is 11/12 success (miss on 1)
- off-by-3 which is 10/12 success (miss on 1-2)
- off-by-4 which is 9/12 success (miss on 1-3)
When I add them, I get (12/12 + 11/12 + 10/12 + 9/12) * 0.05 = 42/12/20 ~ 17.5%

Compare to 1-5 which is (12/12 + 11/12 + 10/12 + 9/12 + 8/12) * 0.05 = 50/12/20 ~ 20.8%


Our results should be the same, what assumption makes it different?

EDIT: the non-cumulative use is another nice tool, TIL:smallsmile:

You are looking at the chance of changing a miss to a hit. I am looking at the chance of missing within a specified range.

[Zhorn]

Can you elaborate on how you are computing the damage gap for a single attack?Between the formula you've responded to in this post, and my post back on page 3, you've already got all my information, formulas, and results, and have commented on them already.


I follow this, except for how A is being computed.
That's on page 3. You suggested to use +5.25 instead of +6.5 to represent the d12 used on Precision Attack.


The second is much more important. You are assuming a very 'naive' superiority dice use heuristic. Meaning that any damage value you get that the superiority dice is causing will be lower and possibly significantly lower than what a 'smarter' heuristic could produce. Implying that your method (assuming I'm accurately capturing what you are doing) would be underestimating the number of rounds the Champion needs to catch up.
Funny since your last take was saying

ultimately you are overestimating the effects of of superiority dice.
... yup... consistent and constructive feedback :smallwink:
You do you, buddy.
As said before; I'm sure your way of doing this will produce a superior model from simulating a larger adventuring day, but that's not the type of model I've any interest in building. Ballpark figures and spherical cow territory is accurate enough for small scale I'm looking at.

[Nefariis]

This is a riveting thread, thank you guys for the discussion!

I'm a huge math nerd and you have me looking a ton of stuff up (it's been a hot minute since my last statistics class).


The issue that I see in this BM 20 vs Champ 20 argument is that it's inherently geared to favor the BM without considering advantage/Elven Advantage.

I know if I create a 20 Champion Fighter I am going to be optimized towards crit fishing and crit fishing damage, which means I will be going for advantage/Elven Advantage

it would be nice to see -


[...] how many rounds it takes the champion to close the gap [...]

when Elven Accuracy comes into play with GWF and a Greatsword

(When you guys finish the discussion / methodology)

[Frogreaver]

Between the formula you've responded to in this post, and my post back on page 3, you've already got all my information, formulas, and results, and have commented on them already.


That's on page 3. You suggested to use +5.25 instead of +6.5 to represent the d12 used on Precision Attack.


Funny since your last take was saying

... yup... consistent and constructive feedback :smallwink:
You do you, buddy.
As said before; I'm sure your way of doing this will produce a superior model from simulating a larger adventuring day, but that's not the type of model I've any interest in building. Ballpark figures and spherical cow territory is accurate enough for small scale I'm looking at.

My last take was based on a model you just said you werent using. Not sure why you are bringing that up like it’s some kind of contradiction based on my comments for the model you ‘seem’ to be using now. And I say ‘seem’ because you are not actually specifying if my current understanding of your model is correct.

As you noted there was some disconnect in my understanding of what you were doing and what you were doing. I’m not sure referring me back to previous posts where that misunderstanding started feels very helpful.

[Zhorn]

My last take was based on a model you just said you werent using. Not sure why you are bringing that up like it’s some kind of contradiction based on my comments for the model you ‘seem’ to be using now.
That last take was on calculating the expected damage of a Precision attack. Not multiple Precision attacks, just the expected damage of one Precision attack. Whether you thought it was for full rounds or a single attack it's still using the same number. Either I've over estimated or under estimated the value of the Superiority Dice, feel free to pick either of the two that makes you happiest :smallwink:

[x3n0n]

when Elven Accuracy comes into play with GWF and a Greatsword

Elven Accuracy can't be used with Str attacks.

The only non-Str way that I know to wield a heavy two-handed melee weapon is Hexblade + Pact of the Blade, requiring 3 levels of Warlock (and thus limiting Fighter to a maximum of 17 levels).

[LudicSavant]

As said before; I'm sure your way of doing this will produce a superior model from simulating a larger adventuring day, but that's not the type of model I've any interest in building. Ballpark figures and spherical cow territory is accurate enough for small scale I'm looking at.

He's not even reaching ballpark figure and spherical cow territory at this point. See his claim about the halting problem.

[Zhorn]

Elven Accuracy can't be used with Str attacks.

The only non-Str way that I know to wield a heavy two-handed melee weapon is Hexblade + Pact of the Blade, requiring 3 levels of Warlock (and thus limiting Fighter to a maximum of 17 levels).
Battlesmith Artificer for INT also is an option for instead of CHA, but is also a 3 level dip, and I think of the two Hexblade will work out better for Hex damage and +Prof to damage on Hexblade's Curse. Plus short rest spell slots will pair up well with the Fighter's short rest everything else.

He's not even reaching ballpark figure and spherical cow territory at this point. See his claim about the halting problem.
He can go for whatever interpretation works for him. As long as he's enjoying himself it's all good :smallwink:

[Frogreaver]

That last take was on calculating the expected damage of a Precision attack. Not multiple Precision attacks, just the expected damage of one Precision attack.

The expected damage of a single Precision attack is not a constant. It depends on a number of variables including:
The heuristic by which you use Precision attack
That's why I keep asking how you are computing this value.

After we determine the expected value of a single precision attack we need to determine the number of precision attacks you are using.


Whether you thought it was for full rounds or a single attack it's still using the same number. Either I've over estimated or under estimated the value of the Superiority Dice, feel free to pick either of the two that makes you happiest :smallwink:

So far I've spoken about 2 cases (neither of which I now believe match up with what you are doing).

Using 6 superiority dice to try and turn misses in a specific 'miss range' to hits. Doing this overestimates the damage provided by precision attack. For certain subcases this overestimation may be negligible and for others it may not be substantial.
Using 1 precision attack on one attack. Doing this underestimates the damage provided by precision attack as any competent player can use it in such a way that it produces more damage than this will show.


There's no contradiction here no matter how much you insinuate there is.

[Zhorn]

There's no contradiction here no matter how much you insinuate there is.
Sure thing. If that's the interpretation that makes you happiest we'll say that's the case and that you are absolutely correct. Have fun :smallwink:

[Frogreaver]

Sure thing. If that's the interpretation that makes you happiest we'll say that's the case and that you are absolutely correct. Have fun :smallwink:

It could only be a contradiction if I was talking about the same thing and made 2 contradictory statements. As demonstrated above, I was talking about 2 different things and thus no contradiction.

[heavyfuel]

I honestly think this discussion about Precision Attack is going to lead nowhere.

Is Precision Attack better than a more standard use of a SupDice? Maybe. Maybe not.

The fact remains that if a BM uses all of his SupDice as straight damage+riders it requires the champion to make a ridiculous number of attacks to beat the BM's DPR. Plus, BM has much better control on when to burst, which further increases their DPR (because fewer rounds in a fight means higher DPR over the course of the combat)

[x3n0n]

I honestly think this discussion about Precision Attack is going to lead nowhere.

Is Precision Attack better than a more standard use of a SupDice? Maybe. Maybe not.

The fact remains that if a BM uses all of his SupDice as straight damage+riders it requires the champion to make a ridiculous number of attacks to beat the BM's DPR. Plus, BM has much better control on when to burst, which further increases their DPR (because fewer rounds in a fight means higher DPR over the course of the combat)

I do think there's a significant thing that *hasn't* been calculated yet, which is related to the actual title of the thread: Crusher.

If we add the Half-Orc race and Crusher to both Fighters (clearly more relevant to the Champion) and we assume that you're repeatedly hitting the same target, then all of the attacks after the first crit are at advantage, which is a HUGE deal to the Champ: hit rate on risky strikes goes way up, and crit rate goes from 15% to 27.75% on each of those attacks, each of which is an additional 3d6 if Half-Orc.

first attack crits 0.15 of the time; 4 advantaged attacks to follow (3 more plus GWM bonus)
first attack doesn't, but second does 0.85 * 0.15 = 0.1225; 3 adv attacks
first two don't, but third does (0.85-0.1225=0.7275) * 0.15 = 0.109125; 2 adv attacks
first three don't, but the 4th does 0.618375 * 0.15 = 0.09275625; 1 adv attack
(Sum: 52.56ish% to crit at least once.)

Attaching actual numbers to the above is a pain, which is why I haven't done it, but there's a lot of single-target DPR being left on the table without Crusher and Half-Orc. (Also, a round where you have already gotten a crit is a GREAT time to Action Surge for another 4 advantaged attacks.)
Not to mention, that's advantage for the whole party until your next turn (like a Trip Attack that doesn't screw over your ranged attackers, can hit Huge things, and that the target can't end by standing up), and it's always on.

That said, one Battle Master strategy that didn't come up is "Trip Attack on your first attack of the turn", which similarly gets you a bunch of advantaged attacks if they fail the Str save, which buys advantage for you and potentially for some of your melee teammates and increases your crit rate, raising the likelihood of getting a GWM bonus attack (just not to the same level as the Champ).


Rounds with lots of consecutive attacks are good for the Crusher Champion, so I would expect this to get a lot more lopsided toward the Battle Master as you "level downward"; 3 attacks is much worse than 4 when you're relying on your later advantaged attacks to boost your DPR, while it's nowhere near as big a difference for the BM. Improved Critical is also much less good than Superior Critical is for this purpose, since it greatly reduces the likelihood of an early-in-round crit.

[Man_Over_Game]

I honestly think this discussion about Precision Attack is going to lead nowhere.

Is Precision Attack better than a more standard use of a SupDice? Maybe. Maybe not.

The fact remains that if a BM uses all of his SupDice as straight damage+riders it requires the champion to make a ridiculous number of attacks to beat the BM's DPR. Plus, BM has much better control on when to burst, which further increases their DPR (because fewer rounds in a fight means higher DPR over the course of the combat)

Could just pick an HP value to hit. First to 200 HP is the winner, which should take about 5 rounds of basic attacks.

[heavyfuel]

I do think there's a significant thing that *hasn't* been calculated yet, which is related to the actual title of the thread: Crusher.

If we add the Half-Orc race and Crusher to both Fighters (clearly more relevant to the Champion)

Fair point. I'm not super good with math, but I definitely think this is what we should be focused on given the thread.

As for half-orc on both BM and Champ... Eh... I'm willing to go for it just because I'm confident the BM will out-DPR the Champ regardless, but if they are both equally optimized, then the BM is better of going for another race.


Could just pick an HP value to hit. First to 200 HP is the winner, which should take about 5 rounds of basic attacks.

Playing devil's advocate, I think pro-Champion people would complain that this unfairly benefits the BM as they can nova better than the champ.

Maybe say the target HP and AC is equal to 8 times the average HP for (CR/3)=Level?

Why CR divided by 3? Because if we assume a 4 people party of level 6, then a CR 6 encounter is considered Easy. But if it's only one level 6 PC, then the CR should be 2 for it to have the about the same challenge level.

Using this table (https://www.reddit.com/r/dndnext/comments/6ggaza/average_hpsavesetc_per_cr/diq8jmm?utm_source=share&utm_medium=web2x&context=3), we can see the average CR 2 monster has 46 HP and 13 AC, so the first level 6 Fighter to reach 368 damage against AC 13 wins?

[bid]

You are looking at the chance of changing a miss to a hit. I am looking at the chance of missing within a specified range.
Gah! so it should go .15 .20 .25 ... another brain fart last night ><

[x3n0n]

As for half-orc on both BM and Champ... Eh... I'm willing to go for it just because I'm confident the BM will out-DPR the Champ regardless, but if they are both equally optimized, then the BM is better of going for another race.

Yes, Half-Orc is definitely a Champ-specific optimization, and I would argue that Crusher probably is too.

I threw this together: https://docs.google.com/spreadsheets/d/1O5I0mI9ehVmQGDQQHYgt2hv3K7gS9Qz1vjhXviX00lU/edit?usp=sharing

Assuming that my math is right, a 20th-level Half-Orc Champion Fighter w 20 Str, GWM, and Crusher, making only risky strikes, will deal 80.377 DPR to a single target with AC 15.
The parameters are target AC, to-hit bonus (6 for GWM), bonus damage per hit (15 for GWM), average damage per die (4.133 for GWF d6).

[LudicSavant]

I honestly think this discussion about Precision Attack is going to lead nowhere. You are correct to think so, because Precision Attack is already a solved problem. We have recursive AnyDice programs for calculating it for whatever strategy you like. Like the one I posted in the Samurai vs BM DPR analysis in the Eclectic thread.

Frogreaver’s idea that comparisons involving Precision Attack are literally unsolvable due the halting problem of all things is just... a whole lotta nothing.

The real obstacle to just spitting out a calc right this second is questions like “who are your party members and how much do they benefit from Crusher granting them Advantage after you crit?”

I mean, that's solvable too, you just have to know those variables, since Advantage has different levels of benefit for different parties.

[Frogreaver]

I do think there's a significant thing that *hasn't* been calculated yet, which is related to the actual title of the thread: Crusher.

Crusher isn't that bad to calculate.

Let a = the damage per attack without advantage
Let b = the damage per attack with advantage
Let c = chance to crit
Let d = chance to not crit

Then we would compute the damage of each attack n in the sequence of the turn as follows:

Case n=1: a
Case n=2: da + cb
Case n=3: d^(2)*a + ( 1 - d^2 )*b
...
Case n=n: d^(n-1)*a + ( 1 - d^(n-1) )*b
Case bonus action attack from GWM: ( 1 - d^(n) )*b

Sum that up and you have the answer

[Greywander]

I do think there's a significant thing that *hasn't* been calculated yet, which is related to the actual title of the thread: Crusher.
[...]
Not to mention, that's advantage for the whole party until your next turn (like a Trip Attack that doesn't screw over your ranged attackers, can hit Huge things, and that the target can't end by standing up), and it's always on.
This is likely the key to closing the gap between the Champion and BM. It's also very difficult to calculate (because it heavily depends on the rest of the party), so it might be necessary to lean on anecdotal evidence from people who have played both Champs with Crusher and BMs, or been in parties with both. Rogues and paladins will certainly be very happy to have you around. Honestly, this probably works best if other people in the party are also optimized for critfishing, so by providing advantage for them you increase the odds of even more crits.

[Frogreaver]

This is likely the key to closing the gap between the Champion and BM. It's also very difficult to calculate (because it heavily depends on the rest of the party), so it might be necessary to lean on anecdotal evidence from people who have played both Champs with Crusher and BMs, or been in parties with both. Rogues and paladins will certainly be very happy to have you around. Honestly, this probably works best if other people in the party are also optimized for critfishing, so by providing advantage for them you increase the odds of even more crits.

That’s the pro crusher side to party play. There’s also the con crusher side where someone else has already given your team advantage. In which case crusher add little benefit.

[heavyfuel]

You are correct to think so, because Precision Attack is already a solved problem. We have recursive AnyDice programs for calculating it for whatever strategy you like. Like the one I posted in the Samurai vs BM DPR analysis in the Eclectic thread.

The real obstacle to just spitting out a calc right this second is questions like “who are your party members and how much do they benefit from Crusher granting them Advantage after you crit?”

I mean, that's solvable too, you just have to know those variables, since Advantage has different levels of benefit for different parties.

I'll be honest and say that I only skimmed the Precision Attack discussion and did not see your solution :smallbiggrin:

So, let's make up these variables to see how it affects the party's DPR.

I think that, outside some really edge cases, you're going to have - at best - 2 other chracters that rely on attack rolls other than the Champ and, thus, benefit from the Advantage.

Let's say, Champion + Melee Swashbuckler Rogue + EB focused Warlock. That seems almost ideal for the Champion.

Champion lv 6 stats: 20 str, Maul
Rogue lv 6 stats: 18 Dex, Rapier and Dagger
Warlock level 6 stats: 18 Cha, Agonizing Blast as an invocation

Compared to a BM using the best DPR possible (same Rogue and same Warlock on the party)

Is this solvable? (honest question here)

[LudicSavant]

The damage output of Crusher is affected by...

- Who your party members are and how much they benefit from Advantage.
- When in the turn you grant Advantage
- How many attacks you can make on the monster you just granted Advantage against before it dies and you need to switch to a new target (e.g. this value will sometimes be less than "all of the attacks the party can make in one round")

Edit:


I'll be honest and say that I only skimmed the Precision Attack discussion and did not see your solution :smallbiggrin:

There's a solid guide for doing Battle Master calcs on AnyDice here: https://www.reddit.com/r/3d6/comments/gf111s/anydice_tutorial_part_3_state_the_great_weapon/

The program allows you to choose whichever strategy you like (e.g. "I use Precision Attack if I miss by 5 or less") and calculate using that.

Separately, you can also calculate how many attacks, on average, it'd take you to exhaust all your superiority dice using any given strategy. For example if you say that you will only use a superiority die on a crit, you can calculate how many attacks would be necessary in order to get 6 crits (on average).

[x3n0n]

Crusher isn't that bad to calculate.

Let a = the damage per attack without advantage
Let b = the damage per attack with advantage
Let c = chance to crit
Let d = chance to not crit

Then we would compute the damage of each attack n in the sequence of the turn as follows:

Case n=1: a
Case n=2: da + cb
Case n=3: d^(2)*a + ( 1 - d^2 )*b
...
Case n=n: d^(n-1)*a + ( 1 - d^(n-1) )*b
Case bonus action attack from GWM: ( 1 - d^(n) )*b

Sum that up and you have the answer

The formula above is slightly complicated because the pre-crit attacks are known not to be crits, so I would need to account for a different set of conditional probabilities.

I split it up by cases in the spreadsheet linked in my most recent response above yours.

0 non-crits, a crit, 4 advantaged attacks
1 non-crit (hit or miss), a crit, 3 advantaged
2 non (mm, mh, hm, hh), a crit, 2 advantaged
3 non, a crit, 1 advantaged
4 non-crits

(And the probabilities added up to 1 at the bottom, giving me confidence that I exhausted the cases correctly.)

[LudicSavant]

So, let's make up these variables to see how it affects the party's DPR.

I think that, outside some really edge cases, you're going to have - at best - 2 other chracters that rely on attack rolls other than the Champ and, thus, benefit from the Advantage.

Let's say, Champion + Melee Swashbuckler Rogue + EB focused Warlock. That seems almost ideal for the Champion.

Champion lv 6 stats: 20 str, Maul
Rogue lv 6 stats: 18 Dex, Rapier and Dagger
Warlock level 6 stats: 18 Cha, Agonizing Blast as an invocation

Compared to a BM using the best DPR possible (same Rogue and same Warlock on the party)

Is this solvable? (honest question here)

I'd expect that you could at the very least get a ballpark estimate.

[x3n0n]

I'll be honest and say that I only skimmed the Precision Attack discussion and did not see your solution :smallbiggrin:

So, let's make up these variables to see how it affects the party's DPR.

I think that, outside some really edge cases, you're going to have - at best - 2 other chracters that rely on attack rolls other than the Champ and, thus, benefit from the Advantage.

Let's say, Champion + Melee Swashbuckler Rogue + EB focused Warlock. That seems almost ideal for the Champion.

Champion lv 6 stats: 20 str, Maul
Rogue lv 6 stats: 18 Dex, Rapier and Dagger
Warlock level 6 stats: 18 Cha, Agonizing Blast as an invocation

Compared to a BM using the best DPR possible (same Rogue and same Warlock on the party)

Is this solvable? (honest question here)

Just to make sure, is that a Half-Orc Champ, starting Str 17, Crusher for 18, Str for 20?
Is the Rogue using alternate TWF rules or something?

First attack crit probability: 10%
First doesn't, second does: 9%
Likelihood of a Crusher crit in a given round: 19%

That doesn't sound like much, compared to the BM who is getting guaranteed damage per S.Die and hopefully choosing wisely what maneuver effects to apply.

[Frogreaver]

The formula above is slightly complicated because the pre-crit attacks are known not to be crits, so I would need to account for a different set of conditional probabilities.

No additional conditional probabilities are needed for my calculation. I calculate the DPR contribution of each attack and then sum together. You break the problem into cases and apply a weighted average to each case. Both are acceptable methods to reach the solution.


I split it up by cases in the spreadsheet linked in my most recent response above yours.

0 non-crits, a crit, 4 advantaged attacks
1 non-crit (hit or miss), a crit, 3 advantaged
2 non (mm, mh, hm, hh), a crit, 2 advantaged
3 non, a crit, 1 advantaged
4 non-crits

(And the probabilities added up to 1 at the bottom, giving me confidence that I exhausted the cases correctly.)

Right, one can most surely calculate it using your methodology as well.



Separately, you can also calculate how many attacks, on average, it'd take you to exhaust all your superiority dice using any given strategy. For example if you say that you will only use a superiority die on a crit, you can calculate how many attacks would be necessary in order to get 6 crits (on average).

True and somewhat paradoxical, because knowing it takes X rounds to average 6 crits doesn't actually indicate that on average in X rounds you will be able to use 6 superiority dice on crits.

[heavyfuel]

Just to make sure, is that a Half-Orc Champ, starting Str 17, Crusher for 18, Str for 20?
Is the Rogue using alternate TWF rules or something?

Yes, and yes (I keep forgetting that light weapon only on the offhand is a house rule and not RAW. Still, I don't think the DPR changes at all if we sub it in for two short swords)

[bid]

True and somewhat paradoxical, because knowing it takes X rounds to average 6 crits doesn't actually indicate that on average in X rounds you will be able to use 6 superiority dice on crits.
Mean, median, mode.

I wonder what's the shape of a simple 1-in-10 success.

Shouldn't it be p^6 + 7qp^6 + 28q^2p^6 + 84q^3p^6 + ... so we know each term?
Terms are diagonal from Pascal triangle instead of straight level, right?
1 7 36 120 330 792 1716 3432 6435 ...


That should converge pretty fast with p=.1... we have the mean
and I guess you'll reach success half the time at around 20 rolls (we have median?)
{6 success + 14 failures is 6/20, same as log(.5)/log(.1) ~ 0.3... but I'm really wild ass-guessing here.}

[Frogreaver]

Mean, median, mode.

I wonder what's the shape of a simple 1-in-10 success.

Shouldn't it be p^6 + 7qp^6 + 28q^2p^6 + 84q^3p^6 + ... so we know each term?
Terms are diagonal from Pascal triangle instead of straight level, right?
1 7 36 120 330 792 1716 3432 6435 ...


That should converge pretty fast with p=.1... we have the mean
and I guess you'll reach success half the time at around 20 rolls (we have median?)
{6 success + 14 failures is 6/20, same as log(.5)/log(.1) ~ 0.3... but I'm really wild ass-guessing here.}

As an example.
If you crit 10% of the time then on average you will do 6 crits every 60 attacks. However, one would only average 5.09 uses of superiority dice in that same timeframe.

To compute the Expected value for crits one would take the probability for x crits and multiply that by x for every x from 1...n (where n is the number of attacks). Then that would be summed up. That is your weighted average and how we can show that you average 6 crits in 60 attacks. When looking at superiority dice we would do something similar but a bit different. We still calculate the probability of x crits. But instead of multiplying by x for 1...n we instead multiply by x for 1...6...6 (representing that the best we can do is use 6 superiority dice)

This is also the reason we can conclusively say the champion will eventually overtake the battlemaster in damage given enough rounds, because despite the fact that precision attack's Expected Value is always increasing as the number of rounds/attacks increase, there is still an upper bound on that Expected Value.

[LudicSavant]

These two posts contradict each other.


This is also the reason we can conclusively say the champion will eventually overtake the battlemaster in damage given enough rounds



Except you've not given any guarantee that the champion will ever do more damage than the battlemaster and so we can easily get stuck in an infinite loop. This is directly related to the 'famous Halting Problem' in computer science which is a provably unsolvable problem.

So, in order for this method to work we would need to know for certain that at some point the champion will do more damage than the battlemaster - which may be totally true, but we can't just assume that's the case.

[Frogreaver]

These two posts contradict each other.

The previous post says we can’t just assume this is the case but that it very may very well be the case. Essentially the case hasn’t been proven yet.

This new post goes on to prove the case.

That’s not a contradiction... so why refer to something as a contradiction when it is clearly not the case?

[LudicSavant]

The previous post says we can’t just assume this is the case but that it very may very well be the case. Essentially the case hasn’t been proven yet.

No. You've been claiming throughout the entire thread that you thought it was outright unsolvable, and that this was your basis for spending multiple pages arguing against the correct answer.


I am not aware of any method that can be used to solve r(x) > p(x) + q(x) given the above equations.

There's only one other major thing we have been in disagreement over. Whether we can actually determine the number of rounds where the champion catches up to the battlemaster using precision attack.

[Frogreaver]

No. You've been claiming throughout the entire thread that you thought it was outright unsolvable, not merely that we "have to show our work."

I'm going to cite the part of my quote you didn't just bold back to you.


So, in order for this method to work we would need to know for certain that at some point the champion will do more damage than the battlemaster - which may be totally true, but we can't just assume that's the case.

[LudicSavant]

I'm going to cite the part of my quote you didn't just bold back to you.

That part of the quote is still wrong. (https://forums.giantitp.com/showsinglepost.php?p=24999532&postcount=129) You can assume that it will catch up because one function is very obviously steeper than the other.

[Frogreaver]

You can assume that it will catch up because one function is very obviously steeper than the other.

Until I proved above that the nonlinear part of that function was bounded above it was untrue that the function was 'obviously' steeper than the other.

[LudicSavant]

it was untrue that the function was 'obviously' steeper than the other.

Speak for yourself. It was quite obvious to me, and apparently to others in the thread too. We've been telling you this thing you think you "just now proved" for four pages.

[Frogreaver]

Speak for yourself. It was quite obvious to me, and apparently to others in the thread too. We've been telling you this thing you think you "just now proved" for four pages.

Saying it's obvious to you or others isn't exactly proving it...

[LudicSavant]

Saying it's obvious to you or others isn't exactly proving it...

We explained why to you, too. Multiple times.

[Frogreaver]

We explained why to you, too. Multiple times.

Faulty reasoning doesn’t actually prove anything.

[strangebloke]

Saying it's obvious to you or others isn't exactly proving it...

We can take you to water, but we can't make you drink.

The BM's damage is (N * X) + Y = D, where

N is the number of rounds between short rests
X is the normal fighter damage per round
Y is the amount added by superiority dice (which is subject to a lot of questions of efficiency, but is ultimately finite)
D is the total damage dealt between short rests


The Champions damage is (N * X) + (N * Z) = D, where

N is the number of rounds between short rests
X is the normal fighter damage per round
Z is the amount added by the improved critical feature and extra fighting style, which scales infinitely with N
D is the total damage dealt between short rests


as N -> Infinity, Z * N will exceed Y, no matter how large Y actually is.

The only question is, how large does N have to be for this to occur. That question is not 'unsolvable' either, just dependent on baseline assumptions like build, magical weapons, and superiority dice strategy.

It's impossible to perfectly model play in a real game because there's a million random factors, but it is possible to get a pretty good idea of what the break even point is, given a set of assumptions.

[LudicSavant]

Faulty reasoning doesn’t actually prove anything.

The correct reasoning has already been provided to you by multiple posters.


We can take you to water, but we can't make you drink.

The BM's damage is (N * X) + Y = D, where

N is the number of rounds
X is the normal fighter damage per round
Y is the amount added by superiority dice (which is subject to a lot of questions of efficiency, but is ultimately finite)
D is the total damage dealt between short rests


The Champions damage is (N * X) + (N * Z) = D, where

N is the number of rounds
X is the normal fighter damage per round
Z is the amount added by the improved critical feature and extra fighting style, which scales infinitely with N
D is the total damage dealt between short rests


as N -> Infinity, Z * N will exceed Y, no matter how large Y actually is.

The only question is, how large does N have to be for this to occur. That question is not 'unsolvable' either, just dependent on baseline assumptions like build, magical weapons, and superiority dice strategy.

It's impossible to perfectly model play in a real game because there's a million random factors, but it is possible to get a pretty good idea of what the break even point is, given a set of assumptions.

Well put, Strangebloke.

[bid]

As an example.
If you crit 10% of the time then on average you will do 6 crits every 60 attacks. However, one would only average 5.09 uses of superiority dice in that same timeframe.
3*7 = 21
5.09*12 = 60
Not an issue.


This is also the reason we can conclusively say the champion will eventually overtake the battlemaster in damage given enough rounds, because despite the fact that precision attack's Expected Value is always increasing as the number of rounds/attacks increase, there is still an upper bound on that Expected Value.
Yeah well... the question is how many times the champion will run out of hp before that point is reached.

If it only needs half its hp, that's nice. If it needs 5 times its hp, that's... meaningless.

[stoutstien]

The new ambush maneuver for Battle Masters is the most recent fly in the ointment. Going before team monster is a pretty big deal and having a way to modify it after you roll is rare or better yet getting a surprise rounds opening an encounter.

[LudicSavant]

What do you think the best possible post-Tasha's Champion build would be, to give it the best chance of standing up in a comparison?

Or at least, if not the best, one of the strongest contenders you could offer?

[heavyfuel]

What do you think the best possible post-Tasha's Champion build would be, to give it the best chance of standing up in a comparison?

Or at least, if not the best, one of the strongest contenders you could offer?

According to a friend: Half-orc; Champion 4, Crusher at 4th; Barbarian 16 for Reckless Attack and Brutal Critical.

Not exactly a Champion (beyond Tier 1, at least) but my friend is insisting that this will be a great character

[LudicSavant]

According to a friend: Half-orc; Champion 4, Crusher at 4th; Barbarian 16 for Reckless Attack and Brutal Critical.

Not exactly a Champion (beyond Tier 1, at least) but my friend is insisting that this will be a great character

I'll take multiclass suggestions too. Though please make the suggestions complete builds (for example, what subclass is the Barbarian? What are the ASIs past 4?)

[Kane0]

According to a friend: Half-orc; Champion 4, Crusher at 4th; Barbarian 16 for Reckless Attack and Brutal Critical.

Not exactly a Champion (beyond Tier 1, at least) but my friend is insisting that this will be a great character

Why Crusher though? If you're using Reckless Attack you won't benefit from its crit effect.

[heavyfuel]

Why Crusher though? If you're using Reckless Attack you won't benefit from its crit effect.

They'd still gain more AC from not having to use RA, and the entire party benefits from Advantage, not just them

[JNAProductions]

They'd still gain more AC from not having to use RA, and the entire party benefits from Advantage, not just them

Right... But that triggers on a crit, which would presumably need Reckless Attack to increase the odds.

It's not a bad build, assuming you go Barb 5 BEFORE anything else, but I wouldn't consider top-notch competitive for this showing.

[J-H]

I don't have DNDB, so please excuse the lack of detail. Here's a shot at a viable champion.
Drow
Dex-based
Feats:
Elven Accuracy
Drow High Magic
Possibly: Invocation feat for Devil's Sight

Bonus Action Feat choices (choose 1 or 2):
-Shield Master for AC, and for shoving to give the party advantage. Sure, your STR isn't going to be super-high, but non-beefy enemies still have a good chance to fail. Gets even better if you can do your bonus action shove after your first attack, but before your extra attacks.
-TWF for an extra attack and +1 AC.
-Poisoner. Stockpile the poison you can make pretty inexpensively, harvest wyvern tails, etc., and be a more drow-y drow. Non-resistant enemies have a decent chance of failing a DC 14 Con save. 2d8 poison is nice, but the really nice part is the Poisoned condition for 1 round. That gives them disadvantage on attack rolls and ability checks. Ability checks include things like "resist being shoved prone" and "resist being grappled by the wizard's Bigby's Hand." Poison your weapon in advance, get a failed save, and then your Shield Master shove has an even better chance of hitting.

Drow gives Faerie Fire 1/day, which grants advantage if it sticks, and a way to detect enemies. Darkness negates sunlight sensitivity... and if drow can't see in their own darkness, pick up the invocation via feat, or take the Blindsight fighting style - or both.
Elven Accuracy gives triple advantage (3d20), increasing crit chances substantially when you have advantage from Darkness, Faerie Fire, or the rest of the party doing something to help.
Drow High Magic gives Detect Magic at will, which is nice. Levitate gives some aerial mobility, and Dispel Magic 1/day is pretty handy.

A Battlemaster or Cavalier can do anything a Champion can do, but Elven Accuracy and multiple methods of gaining advantage substantially helps crit-fishing. Obviously you want a nice flaming rapier or something to take maximum advantage of this, but EVERY fighter wants that.

This actually looks pretty fun to play. I might try it if someone actually starts a game soon (I mostly just DM :-/).

[Kane0]

It's not optimal, but I would have a lot of fun with a build like this:

Half-Elf or Elf Champ Fighter 4-5 / Dao Genielock 2-3 / Scout Rogue 13-14
Trade around stats using Tasha's to start with as much Dex as you can but you also need at least 13 Cha to multiclass.
5 ASIs: Elven Accuracy, Sharpshooter, Crusher, Piercer, one more of your choice (Lucky, Observant, Skulker, etc)

It's a little silly but you're basically a sniper. Get yourself a bow or crossbow or bundle of darts and use your Tasha's Rogue bonus action to get yourself advantage to hit coupled with Elven accuracy. Dao adds +Prof bludgeoning to your attack so you can pair up Piercer and Crusher effects. Sharpshooter extends your range and adds the +10 damage option if you want to take a risk which is mitigated a little by the Archery fighting style. If you miss an important shot you can Action Surge for another attempt or it can be used in conjunction with Cunning Action to GTFO if a situation really goes bad.
Because you're not moving the Scout's reaction is important for when enemies close on you, and when you get a crit off you can instead use cunning action normally to reposition as you have advantage to hit from Crusher, which also does a bit of forced movement to keep people away (but not as much as a traditional repelling blast)
On top of that you have a good spread of skills/tools and a bit of spellcasting plus 2 invocations up your sleeve, so you aren't a one trick pony. Beast Speech, Beguiling Influence, Eldritch Sight, Mask of Many Faces and Misty Visions are all fun options.
That last level is open so you can choose if Fighter's Extra Attack, Warlock's Pact Boon or Rogue's Blindsense is more important to you.

[LudicSavant]

Dao adds +Prof bludgeoning to your attack so you can pair up Piercer and Crusher effects. Interesting idea. Though unfortunately the benefit of the Dao ability will only apply to one of your attacks. So if you wanted to maximize the chance of activating the crit rider, you'd have to hold onto it, and risk a miss with your final attack. Still might work out. Hmm.

Another random thought along these lines -- a Fey-Touched Scribe Wizard could convert Hex to Bludgeoning by also having Catapult or Earth Tremor in their book, thus getting extra per-attack damage and being able to dip multiple damage types for the Tasha half-feats. Notably, those feats do not require the damage to be from a weapon, it can be from spells.

Not sure if any of that would be worth, but it's something to think about, perhaps.

[Kane0]

Though unfortunately the benefit of the Dao ability will only apply to one of your attacks. So if you wanted to maximize the chance of activating the crit rider, you'd have to hold onto it, and risk a miss with your final attack.
Thats okay because as primarily a rogue you’re only attacking once a turn anyways (also why crossbow mastery isnt mentioned).

[SLOTHRPG95]

I don't have DNDB, so please excuse the lack of detail. Here's a shot at a viable champion.
Drow
Dex-based
Feats:
Elven Accuracy
Drow High Magic
Possibly: Invocation feat for Devil's Sight

Bonus Action Feat choices (choose 1 or 2):
-Shield Master for AC, and for shoving to give the party advantage. Sure, your STR isn't going to be super-high, but non-beefy enemies still have a good chance to fail. Gets even better if you can do your bonus action shove after your first attack, but before your extra attacks.
-TWF for an extra attack and +1 AC.
-Poisoner. Stockpile the poison you can make pretty inexpensively, harvest wyvern tails, etc., and be a more drow-y drow. Non-resistant enemies have a decent chance of failing a DC 14 Con save. 2d8 poison is nice, but the really nice part is the Poisoned condition for 1 round. That gives them disadvantage on attack rolls and ability checks. Ability checks include things like "resist being shoved prone" and "resist being grappled by the wizard's Bigby's Hand." Poison your weapon in advance, get a failed save, and then your Shield Master shove has an even better chance of hitting.

Drow gives Faerie Fire 1/day, which grants advantage if it sticks, and a way to detect enemies. Darkness negates sunlight sensitivity... and if drow can't see in their own darkness, pick up the invocation via feat, or take the Blindsight fighting style - or both.
Elven Accuracy gives triple advantage (3d20), increasing crit chances substantially when you have advantage from Darkness, Faerie Fire, or the rest of the party doing something to help.
Drow High Magic gives Detect Magic at will, which is nice. Levitate gives some aerial mobility, and Dispel Magic 1/day is pretty handy.

A Battlemaster or Cavalier can do anything a Champion can do, but Elven Accuracy and multiple methods of gaining advantage substantially helps crit-fishing. Obviously you want a nice flaming rapier or something to take maximum advantage of this, but EVERY fighter wants that.

This actually looks pretty fun to play. I might try it if someone actually starts a game soon (I mostly just DM :-/).

Sounds fun! If relying primarily on rapier for melee and longbow for ranged, Piercer might make a lot of sense for this build. Sure, it's not as flashy as Slasher/Crusher, but as a Dex-based Champion many of your best weapon options will be getting a reliable damage boost, plus bigger crits (which are semi-reliable with EA + Champion).

[heavyfuel]

Okay, so a more serious answer, though it's still only a Champion dip.

Mark of Shadow Elf (+2 Dex, +1 Int) with an initial array of 8 16 14 16 12 8

Arcane Trickster 4 / Champion 4 / AT +12

Feats: Elven Accuracy+Dex at 4, Piercer+Dex at 8, +2 Dex at 12, Sharpshooter at 14, Lucky at 16, +2 Int at 20

Tactics: If you can hide, use Cunning Action to do so, then shoot. If you can't hide, use CA to aim and shoot.

Once you get Haste, cast it on yourself every combat. Sharpshooter and Heavy Crossbow allows you to stay very very far from the fight, so losing Concentration isn't likely. Use your haste action to attack, and use your regular action to ready an attack for as soon as your turn has passed. Though it might be difficult to gain Advantage on the readied attack, this is still a massive bonus to your DPR (assuming you have an ally in melee who can grant you SA)

[Kane0]

Another idea would be something like Champion 11+ / Beast barb 3+ to stack as many Claw attacks as you can using Reckless Attack, then tack on Slasher as a debuff which cancel Reckless Attack penalty and also helps your party. Claws work on the attack action so you also get your free swing when action surging too! Shame it doesn't sync up with dex-based options like Elven accuracy, sneak attack or monk but you can still be a Half Orc for the extra crit damage.

If you really want to be nasty throw in Mobile and simply move away when you're finished savaging someone with crit claws. Then the only thing left to do is find something to do with your Bonus Action when you're not entering rage, like GWM but half of it would go to wasted. A better option might be Orcish Aggression which would sync up with Mobile.

Oh and Hunter Ranger 3 can get you either bonus damage for your crit or an extra attack via reaction or against a second target, because why not, but you'd need some Wis to multiclass and would probably be giving up an ASI to do so.

[Zhorn]

Claws work on the attack action so you also get your free swing when action surging too!
Unfortunately the wording on Claws is the free attack is a "once on each of your turns when you attack with a claw using the Attack action" deal.
I was thinking about a Fighter dip for my current Beast Barbarian to have that and was rather disheartened when noticing that wording.

[Kane0]

Ugh you’re right, can’t catch a break!

[stoutstien]

Ugh you’re right, can’t catch a break!

Still pretty easy to use combo. With adv and 3 attacks, claw has a good enough chance to crit to work with and the speed reduction is very handy for a class who wants to avoid ranged combat as much as possible

[Zhorn]

Still pretty easy to use combo. With adv and 3 attacks, claw has a good enough chance to crit to work with and the speed reduction is very handy for a class who wants to avoid ranged combat as much as possible
And if you don't mind a bit of convoluted weapon dropping/retrieving each round, you can get that up to 4 attacks by level 5 without additional dips or feats, so it is viable for doing with Slasher as your level 4 ASI pick.
(this is just an extract from another thread on the topic a while back, click into it for a listing of all rules references that allow it to work)

Assuming no feats, start each round with a light melee weapon in each hand (also assuming you are already raging at this point with claws)

Step 1: Free actionless drop one weapon
Step 2: Attack Action with claw
Step 3: Free claw as part of the same action
Step 4: Object interaction pick up dropped weapon
Step 5: Extra Attack with that picked up weapon
Step 6: Bonus Action off hand attack with Two-Weapon Fighting
With our end state now matching our starting state.
4 Attacks with a level 5 Path of the Beast Barbarian, all 100% RAW compliant and supported without feats
Just be sure that the one handed light weapons you are using deal slashing damage