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  1. - Top - End - #151
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by x3n0n View Post
    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.

  2. - Top - End - #152
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by Greywander View Post
    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.
    Thatís the pro crusher side to party play. Thereís also the con crusher side where someone else has already given your team advantage. In which case crusher add little benefit.

  3. - Top - End - #153
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by LudicSavant View Post
    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 ďwho are your party members and how much do they benefit from Crusher granting them Advantage after you crit?Ē

    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

    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)

  4. - Top - End - #154
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    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:

    Quote Originally Posted by heavyfuel View Post
    I'll be honest and say that I only skimmed the Precision Attack discussion and did not see your solution
    There's a solid guide for doing Battle Master calcs on AnyDice here: https://www.reddit.com/r/3d6/comment..._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).
    Last edited by LudicSavant; 2021-04-08 at 08:20 PM.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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  5. - Top - End - #155
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by Frogreaver View Post
    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.)

  6. - Top - End - #156
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by heavyfuel View Post
    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.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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  7. - Top - End - #157
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by heavyfuel View Post
    I'll be honest and say that I only skimmed the Precision Attack discussion and did not see your solution

    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.

  8. - Top - End - #158
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by x3n0n View Post
    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.

    Quote Originally Posted by LudicSavant View Post
    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.
    Last edited by Frogreaver; 2021-04-08 at 10:31 PM.

  9. - Top - End - #159
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by x3n0n View Post
    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)

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

    Quote Originally Posted by Frogreaver View Post
    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.}
    Last edited by bid; 2021-04-09 at 12:06 AM.
    Trust but verify. There's usually a reason why I believe you can't do something.

  11. - Top - End - #161
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by bid View Post
    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.
    Last edited by Frogreaver; 2021-04-09 at 07:20 PM.

  12. - Top - End - #162
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    These two posts contradict each other.

    Quote Originally Posted by Frogreaver View Post
    This is also the reason we can conclusively say the champion will eventually overtake the battlemaster in damage given enough rounds
    Quote Originally Posted by Frogreaver
    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 LudicSavant; 2021-04-09 at 07:37 PM.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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  13. - Top - End - #163
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by LudicSavant View Post
    These two posts contradict each other.
    The previous post says we canít just assume this is the case but that it very may very well be the case. Essentially the case hasnít been proven yet.

    This new post goes on to prove the case.

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

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

    Quote Originally Posted by Frogreaver View Post
    The previous post says we canít just assume this is the case but that it very may very well be the case. Essentially the case hasnít 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.

    Quote Originally Posted by Frogreaver
    I am not aware of any method that can be used to solve r(x) > p(x) + q(x) given the above equations.
    Quote Originally Posted by Frogreaver
    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.
    Last edited by LudicSavant; 2021-04-09 at 09:29 PM.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by LudicSavant View Post
    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.

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

    Quote Originally Posted by Frogreaver View Post
    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. You can assume that it will catch up because one function is very obviously steeper than the other.
    Last edited by LudicSavant; 2021-04-09 at 10:36 PM. Reason: Brevity.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by LudicSavant View Post
    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.

  18. - Top - End - #168
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by Frogreaver View Post
    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.
    Last edited by LudicSavant; 2021-04-09 at 11:26 PM.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by LudicSavant View Post
    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...
    Last edited by Frogreaver; 2021-04-09 at 11:24 PM.

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

    Quote Originally Posted by Frogreaver View Post
    Saying it's obvious to you or others isn't exactly proving it...
    We explained why to you, too. Multiple times.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by LudicSavant View Post
    We explained why to you, too. Multiple times.
    Faulty reasoning doesnít actually prove anything.

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

    Quote Originally Posted by Frogreaver View Post
    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
    1. N is the number of rounds between short rests
    2. X is the normal fighter damage per round
    3. Y is the amount added by superiority dice (which is subject to a lot of questions of efficiency, but is ultimately finite)
    4. D is the total damage dealt between short rests


    The Champions damage is (N * X) + (N * Z) = D, where
    1. N is the number of rounds between short rests
    2. X is the normal fighter damage per round
    3. Z is the amount added by the improved critical feature and extra fighting style, which scales infinitely with N
    4. 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.
    Last edited by strangebloke; Yesterday at 12:27 AM.

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

    Quote Originally Posted by Frogreaver View Post
    Faulty reasoning doesnít actually prove anything.
    The correct reasoning has already been provided to you by multiple posters.

    Quote Originally Posted by strangebloke View Post
    We can take you to water, but we can't make you drink.

    The BM's damage is (N * X) + Y = D, where
    1. N is the number of rounds
    2. X is the normal fighter damage per round
    3. Y is the amount added by superiority dice (which is subject to a lot of questions of efficiency, but is ultimately finite)
    4. D is the total damage dealt between short rests


    The Champions damage is (N * X) + (N * Z) = D, where
    1. N is the number of rounds
    2. X is the normal fighter damage per round
    3. Z is the amount added by the improved critical feature and extra fighting style, which scales infinitely with N
    4. 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.
    Quote Originally Posted by Alucard_OW
    Generally I recommend reading this thread. LudicSavant is a math freak and if he calculates something, it's accurate.
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    Quote Originally Posted by Frogreaver View Post
    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.

    Quote Originally Posted by Frogreaver View Post
    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.
    Last edited by bid; Yesterday at 11:51 AM.
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    Default Re: Are Champion fighters better now that we have Crusher/Piercer/Slasher?

    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.
    Last edited by stoutstien; Yesterday at 03:26 PM.

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