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2021-04-08, 12:55 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
"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.Last edited by LudicSavant; 2021-04-08 at 01:42 AM. Reason: More specific wording than "that kind of thing"
Originally Posted by ProsecutorGodot
Nerull | Wee Jas | Olidammara | Erythnul | Hextor | Corellon Larethian | Lolth | The Deep Ones
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2021-04-08, 01:00 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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?
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.Last edited by Frogreaver; 2021-04-08 at 01:34 AM.
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2021-04-08, 04:49 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
Originally Posted by Frogreaver
Which makes it extraordinarily frustrating that you keep arguing as though I said the opposite.
You even provided evidence for my statement, here:
Originally Posted by Frogreaver
Seriously, every single one of your arguments directed at me appears to be trying to disprove an assumption I never actually made and that I already said would be an incorrect assumption.
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. =\
I think so as well.Last edited by LudicSavant; 2021-04-08 at 11:01 AM. Reason: Trying to be as clear as possible.
Originally Posted by ProsecutorGodot
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2021-04-08, 08:19 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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 and that I already said would be an incorrect assumption.
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]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. =\
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.
Looks like we agree on something elseLast edited by Frogreaver; 2021-04-08 at 08:21 AM.
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2021-04-08, 09:59 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
Not only did I not make that claim directly or otherwise, I directly and unequivocally made the exact opposite claim, and that still didn't stop you from putting your words in my mouth. Indeed, you seem to be willing to assume what "everyone's" opinion is, even if the only opinions anyone expressed on the matter contradict you.
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.Last edited by LudicSavant; 2021-04-08 at 10:47 AM.
Originally Posted by ProsecutorGodot
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2021-04-08, 10:28 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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).Last edited by Zhorn; 2021-04-08 at 11:05 AM.
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2021-04-08, 10:51 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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 (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.Last edited by LudicSavant; 2021-04-08 at 11:09 AM.
Originally Posted by ProsecutorGodot
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2021-04-08, 10:59 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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.
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
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).
- 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.
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.Last edited by Frogreaver; 2021-04-08 at 11:15 AM.
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2021-04-08, 11:22 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
I don't understand why we can't assume that the Champion will do more damage than the "equivalent" Battle Master that
can't usenever 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?Last edited by x3n0n; 2021-04-08 at 11:26 AM. Reason: s/can't use/never uses/
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2021-04-08, 11:24 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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.
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.Last edited by LudicSavant; 2021-04-08 at 11:33 AM.
Originally Posted by ProsecutorGodot
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2021-04-08, 11:34 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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, TILLast edited by bid; 2021-04-08 at 11:36 AM.
Trust but verify. There's usually a reason why I believe you can't do something.
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2021-04-08, 11:39 AM (ISO 8601)
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2021-04-08, 11:42 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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
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.Last edited by Zhorn; 2021-04-08 at 11:45 AM.
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2021-04-08, 11:50 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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 you guys finish the discussion / methodology)Last edited by Nefariis; 2021-04-08 at 11:52 AM.
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2021-04-08, 11:58 AM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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.Last edited by Frogreaver; 2021-04-08 at 12:04 PM.
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2021-04-08, 12:11 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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
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2021-04-08, 12:25 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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2021-04-08, 12:26 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
Originally Posted by ProsecutorGodot
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2021-04-08, 12:36 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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 can go for whatever interpretation works for him. As long as he's enjoying himself it's all good
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2021-04-08, 12:37 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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
- 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.Last edited by Frogreaver; 2021-04-08 at 12:43 PM.
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2021-04-08, 01:01 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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)
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2021-04-08, 04:02 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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.Last edited by x3n0n; 2021-04-08 at 04:09 PM.
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2021-04-08, 04:03 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
5th Edition Homebrewery
Prestige Options, changing primary attributes to open a world of new multiclassing.
Adrenaline Surge, fitting Short Rests into combat to fix bosses/Short Rest Classes.
Pain, using Exhaustion to make tactical martial combatants.
Fate Sorcery, lucky winner of the 5e D&D Subclass Contest VII!
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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.
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, 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?Last edited by heavyfuel; 2021-04-08 at 04:37 PM.
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2021-04-08, 05:29 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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...it?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).
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2021-04-08, 06:53 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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.Last edited by LudicSavant; 2021-04-08 at 07:43 PM.
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2021-04-08, 07:21 PM (ISO 8601)
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Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?
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 answerLast edited by Frogreaver; 2021-04-08 at 07:25 PM.