D&D 5E Comparing Monk DPR

[FrogReaver]

The standard deviation/variance shouldn't be mistaken for a + damage tolerance or the range.

No one has done that.

If you miss your attacks, you are giving up 8d6+10 damage, even with 100+ hp, 38 average damage can be very important to ending the fight early.

you aren't giving up anything by missing

Taking unnecessary risks are bad decisions.

If you had the choice about this ever turn then sure, but we are talking about making this choice once at char gen and being stuck with it the rest of the campaign. It's not a bad decision and has next to nothing to do with any potential TPK's

Variance is never reduced no matter how many rolls you make. You're thinking about the average of rolls versus the expected average roll. 2-4 rolls are definitely not enough to evoke the Law of Large Numbers as a relevant point, though.

I never said it was reduced to 0. I claimed

Don't forget that its about likely scenarios as well. Actually, in the rogue's case, the most likely damage output the rogue produces in a round is 0, almost 4x as likely as their second most likely damage of 31. Their chart is heavily skewed such that alot of their average damage is due to their very high damage upwards of 106 damage theoretically possible but highly improbable. I'm talking a 1.48x10^-7% chance of occuring and less than a 1% chance to do higher than 70 damage. So they have a large chunk of probability on the left-hand side of the curve and a very thin tail skewing all the way to the right.

A fighter making 3 attacks has a mode of 0 for the turn as well. 10% or so of all outcomes will result in 0 damage. That isn't a significant factor to consider though as he is still most likely to hit with at least 1 attack and very likely to hit with 2 of his 3 attacks.

 

[Asisreo]

you aren't giving up anything by missing

You are giving up the worth of your action. You gave up the option to dodge, dash, hide, ready, cast a spell, etc.

If you had the choice about this ever turn then sure, but we are talking about making this choice once at char gen and being stuck with it the rest of the campaign. It's not a bad decision and has next to nothing to do with any potential TPK's

You can make tactical decisions based on this, though. For example, a high-priority target that shouldn't be allowed more time than expected can be targeted by the SnB fighter or Monk for reliable damage while the rogue can pick off low-priority targets. For example, targeting elementals with the rogue while the genie is targeted by the monk.

I never said it was reduced to 0

No, I'm stating that variance is never reduced, period. It is a constant based in the nature of the roll. No amount of rolls will reduce or increase the variance.

A fighter making 3 attacks has a mode of 0 for the turn as well. 10% or so of all outcomes will result in 0 damage. That isn't a significant factor to consider though as he is still most likely to hit with at least 1 attack and very likely to hit with 2 of his 3 attacks.

Compared to a rogue, though, it isn't much comparison. Its a 6.4% chance all attacks miss and do 0 damage per turn. The rogue missing is 2.5x more likely. That's a 16% chance to miss based on the 19AC. Doesn't sound like alot but 16% is very high for level 15 compared to other classes at this level.

And this is also assuming TWF-rogue not using their bonus action for something like disengaging or hiding. If they do that, they have a 40% chance to miss completely which is quite terrible. (By consequence, their DPR drops by about 10 and their variance increases significantly as well. They become worse than a SnB fighter).

 

[Dausuul]

You can make tactical decisions based on this, though. For example, a high-priority target that shouldn't be allowed more time than expected can be targeted by the SnB fighter or Monk for reliable damage while the rogue can pick off low-priority targets. For example, targeting elementals with the rogue while the genie is targeted by the monk.

This doesn't make sense. If the rogue misses, it doesn't matter what they were attacking. If the rogue hits, it is almost always better to put that damage toward killing the same thing the rest of the party is trying to kill--the exception being if you know that creature is very low on hit points. And you very seldom know that.

 

[auburn2]

Variance is never reduced no matter how many rolls you make. You're thinking about the average of rolls versus the expected average roll. 2-4 rolls are definitely not enough to evoke the Law of Large Numbers as a relevant point, though.

This is absolutely not true. The sample variance changes with every measurement (roll). Even if the sample distribution exactly matches the expected distribution for a population, the sample variance will still be larger than the population variance because the denominator in the sample variance is based on the number of measurements (rolls) minus 1 while the population variance is based on the size of entire population (no minus 1)

As the number of rolls in a sample approaches the total number of rolls in the entire population, the variance of the sample will approach the variance of the population. It will generally approach the population variance from above (i.e. getting smaller with more rolls). It is possible for the sample variance to be smaller than the population variance, but that is abnormal for a large sample and represents a bias in the sample. It would also call into question whether the sample is in fact part of the population (i.e. is the RNG or dice loaded)

 

[Asisreo]

This is absolutely not true. The sample variance changes with every measurement (roll). Even if the sample distribution exactly matches the expected distribution for a population, the sample variance will still be larger than the population variance because the denominator in the sample variance is based on the number of measurements (rolls) minus 1 while the population variance is based on the size of entire population (no minus 1)

I was assuming they meant the population variance, though this is what happens when we don't talk in more rigorous terms (and also me not having alot of rest).

Yes, just like expected value, the variance of a sample approaches the variance of the population over every trial. And this variance is much more likely to be larger and decrease towards the population variance.

This doesn't mean that the population variance changes, though. It would be like equating an infinitesimal difference between the population mean and the sample mean approaches 0 as the number of trials approaches infinity for sufficiently large number of trials to a fluctuating DPR. We use the expected value as the DPR value and expected value is the population mean, which doesn't change.

 

[FrogReaver]

No, I'm stating that variance is never reduced, period. It is a constant based in the nature of the roll. No amount of rolls will reduce or increase the variance.
Compared to a rogue, though, it isn't much comparison. Its a 6.4% chance all attacks miss and do 0 damage per turn. The rogue missing is 2.5x more likely. That's a 16% chance to miss based on the 19AC. Doesn't sound like alot but 16% is very high for level 15 compared to other classes at this level.

The Damage Distribution for 2 attacks is notably different than the damage distribution of a single attack. That the Distributions are different will cause the variance for those distributions to change.

It's almost like you want to keep each attack as it's own independent event but that's not the way probability works when adding together for damage.

 

[Asisreo]

This doesn't make sense. If the rogue misses, it doesn't matter what they were attacking. If the rogue hits, it is almost always better to put that damage toward killing the same thing the rest of the party is trying to kill--the exception being if you know that creature is very low on hit points. And you very seldom know that.

Minions will tend to have less HP than their bosses. There are exceptions but the important part is reducing the action economy of the opposing side as quickly as possible. Let's say there are 2 priests and a Gladiator. If the rogue targets the priests, he will easily hit and kill them within a single attack (ignoring actual AC). If the rogue targets the Gladiator, he will contribute to the kill but the action economy won't change unless he's in kill-range already.

Tactically, its best to remove as many opposing characters from the playing field as possible.

As someone with higher kill potential, you're more valuable at action denial than just straight attrition. Just like how a wizard is better off casting Hypnotic Pattern than Fireball in most situations except ones with higher Wis saves or where you can actually kill with the spell.

The Damage Distribution for 2 attacks is notably different than the damage distribution of a single attack. That the Distributions are different will cause the variance for those distributions to change.

It's almost like you want to keep each attack as it's own independent event but that's not the way probability works when adding together for damage.

Not every attack, every round.

This discussion was originally about Damage per Round, yes? Well, the damage per round isolates the average of the attacks per round. And while there's the average, looking at the dispersion of the data also gives a more whole picture of the damage.

The reason why is because we can predict or at least control the number of attacks in a round without any complexity from the target's side. The damage dice is also independent of the target and the accuracy is based solely on AC which we've set as an arbitrary constant.

We can't predict the average amount of rounds something will last without an idea of the rest of the party, which can be exhausting to set-up and calculate. If the discussion was "How much total damage can we expect from a monk with a party of so-and-so?" or "How many rounds will this creature last if these characters did this while the monk attacked?"

Aside:
The reason why a single attack with 2d6 isn't the same as two attacks with 1d6 (ignoring crits and accuracy) is because in the first instance, you convoluted the 2 d6 graphs first, then applied the accuracy assignments. In the second instance, you first apply the accuracy assignments then you convolute the adjusted d6 graphs.

The difference is that one looks like a triangular shape while the other has a flat shape that then slopes downward linearly. They have the same expected value but they interact much differently.

 

[FrogReaver]

Not every attack, every round.

This discussion was originally about Damage per Round, yes? Well, the damage per round isolates the average of the attacks per round. And while there's the average, looking at the dispersion of the data also gives a more whole picture of the damage.

Not even rounds. Damage is cumulative over multiple rounds. For example, the expected value of 2 rounds of attacks is twice as much as the expected value of a single round of attacks. Because the expected value scales linearly with the number of rounds it's easy to talk about the per round damage (DPR) in a meaningful way. That's not the case with variance though. Your variance for a single round of attacks is not the same as your variance for 2 rounds of attacks which is not the same as your variance for 3 rounds of attacks - and there's no easily discernable pattern that we can model how the variance changes with the number of rounds. It's not linear and is a fairly complex mathematical computation to arrive at.

Trying to summarize: DPR is not actually Expected Value (mean) - albeit highly related via giving us a y=Ax formula for the expected value where y is the expected value, A the DPR, and x the number of rounds. Variance is a measure that should be spoken of alongside expected value and not alongside DPR.

 

[FrogReaver]

Minions will tend to have less HP than their bosses. There are exceptions but the important part is reducing the action economy of the opposing side as quickly as possible. Let's say there are 2 priests and a Gladiator. If the rogue targets the priests, he will easily hit and kill them within a single attack (ignoring actual AC). If the rogue targets the Gladiator, he will contribute to the kill but the action economy won't change unless he's in kill-range already.

In that scenario, explain why everyone isn't better off targeting the priests? With the possibly exception of leaving 1 Melee on the Gladiator to threaten an OA to help keep him off your squishies?

Tactically, its best to remove as many opposing characters from the playing field as possible.

Usually yes. But if there's a better target for the Rogue why isn't that also a better target for everyone else?

As someone with higher kill potential, you're more valuable at action denial than just straight attrition. Just like how a wizard is better off casting Hypnotic Pattern than Fireball in most situations except ones with higher Wis saves or where you can actually kill with the spell.

The only way a Rogue is causing action denial is via attrition. It's still unclear why it's better for the rogue to target something different than the rest of the party? Focus fire typically causes enemies to die faster and lose action sooner which has a bit of a snowball effect.

 

[Asisreo]

In that scenario, explain why everyone isn't better off targeting the priests? With the possibly exception of leaving 1 Melee on the Gladiator to threaten an OA to help keep him off your squishies?

There's 3 targets and 2 of them can die within a single attack. Chances are, not everyone will even get the chance to target them. If the Rogue and Paladin fight them, then the fighter should be the one to keep the Gladiator away from the wizard. Not because the fighter wouldn't kill the priests but his consistent damage is more useful for a boss enemy. Even if the turn order is: fighter, priest, rogue...you should still target the Gladiator. If the extra damage from a round of fighter reduces the number of active rounds the Gladiator lives through from 4 to 3, then even though you could have killed a priest, they were more likely to die round 1 anyways and the cost is that you let the Gladiator live for 1 round.

The whole assumption is that the Gladiator's turn is more dangerous than the priest's. The rogue having a higher likelihood to miss altogether reduces the risk of loss since them losing their turn to a miss targeted at a priest costs them a priest's extra action but the price of them missing a gladiator hit costs them a gladiator's extra action which tends to be harder to deal with.

Trying to summarize: DPR is not actually Expected Value (mean) - albeit highly related via giving us a y=Ax formula for the expected value where y is the expected value, A the DPR, and x the number of rounds. Variance is a measure that should be spoken of alongside expected value and not alongside DPR.

We need to make sure we're on the same page. We could be talking about the expected value of single dice roll, a single round, or the entire combat. I've been doing it for a single round.

The problem with evaluating the expected value of the entire combat is that this is alot more unpredictable and context dependent. We see that only 1 attack for a rogue severely hinders them so a constantly hiding/disengaging rogue severely hinders their ability to consistently deal their damage. Same could be said for if a teammate decides to attempt a buff/debuff as their action rather than applying expected damage, which is highly possible. And the swing of the dice in the other direction also makes it harder to evaluate.

When I speak of Variance, I'm speaking of the population variance of each individual round as an independent event since we can control what happens within this round. We cannot control what happens outside our individual turn.