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

[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, "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.

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 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. =\

@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, "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.

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.

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]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 (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

[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, 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.

[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 (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

[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

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
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
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

[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

[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

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

[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

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, 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...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).

[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