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D&D 5E Comparing Monk DPR

FrogReaver

As long as i get to be the frog
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.
 
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Asisreo

Archdevil's Advocate
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

Legend
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

Adventurer
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)
 
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Asisreo

Archdevil's Advocate
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

As long as i get to be the frog
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

Archdevil's Advocate
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

As long as i get to be the frog
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.
 
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FrogReaver

As long as i get to be the frog
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

Archdevil's Advocate
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.
 

Dausuul

Legend
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.
Two priests and a gladiator? Against a 15th-level party? What happened to the genie and elementals? Oh--right, elementals have too many hit points for the rogue to one-shot, which knocks this whole line of argument into a cocked hat.

Your analysis falls apart whenever the enemy does not have anything that can be one-shotted.
 
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FrogReaver

As long as i get to be the frog
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.

IMO, you are still better of focusing down the priests first. They can greatly extend the gladiators survivability with some timely sanctuarys and healing. The only change in plans is if the rogue knew a priest was greatly injured.

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.
Talking about the variance for your attacks in a single round of a 3 round encounter seems rather pointless, no?

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.

It's also alot more correct

Not doing so leads your focus on variance to incorrect conclusions.

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.
Which isn't really the correct methodology as those rounds aren't independent events when it comes to damage. Damage is cumulative. The amount of damage you have done to an enemy on the previous turn informs how much cumulative damage you are going to do next turn. Cumulative damage is what we actually care about, as it's cumulative damage that kills the enemy and denies them any future actions
 

Xeviat

Hero
Supporter
To get the discussion back on track, I did a little analysis of my own, since I have some spread sheets from my own efforts at class analysis.

I too believe the monk is largely fine at levels 1-10. It's level 11+ where they start to get weird. I think looking at the subclasses will reveal what's going on here:

Open Hand, Tranquility: This is a free, very extended casting of a 1st level spell. But, since it ends early when you attack, it will only be beneficial in the first round of combat, and not offensively. This is hardly worth a Warlock Invocation, and needs a damage booster.

Shadow, Cloak of Shadows: This can grant advantage at the start of a fight, but that doesn’t even remotely equate to an extra attack’s worth of damage. Needs a damage booster.

Four Elements, Disciple of the Elements: Since these take an action, and cost ki, they only really get in the way of your other features. Tasha’s “ki-fueled attack” feature helps, but this needs a damage booster.

Long Death, Mastery of Death: This doesn’t increase damage round to round. It will help keep you up, though. This needs a damage booster.

Sun Soul, Searing Sunburst: For 1 ki and your action+bonus, you can make 4 attacks at 1d8+5ish. That’s about 38 damage. For 1 ki, you can throw a 4d6 sunburst, or 14 damage. You’d have to catch 3 enemies in the burst to exceed this damage. Very situational. For 2 ki, I almost think you’re better off using Searing Arc Strike if you’re fighting one major target with multiple allies. This doesn’t feel like an overall damage improvement, just a different option, so the subclass still needs a damage buff.

Drunken Master, Drunkard's Luck: This will increase damage a bit, but not equivalent to a whole attack. This can still use a damage booster.

Kensei, Sharpen the Blade: This is a cheap magic weapon spell, which would normally cost 3, 6, or 9 spell points and have concentration, but it only lasts a minute instead of an hour. It’s just a new “spell” to spend ki on, so not a real damage boost, though it will boost short term damage. The subclass could still use a real damage boost.

Mercy, Flurry of Healing and Harm: Finally a true damage boost! This adds damage nearly equivalent to 1 attack (Martial Arts Die + Wis mod, instead of + Dex and potential unarmed enhancement bonuses) that’s potentially added as a rider once to up to 2 attacks (if you use both attacks with a flurry, your chance of landing this “extra attack” goes up).

Astral Self, Body of the Astral Self: Another damage boost. This extra damage is very similar to Mercy’s, but instead of having Wisdom mod it benefits from unarmed enhancement bonuses and it benefits you even if you aren’t using flurry (and you have up to 4 chances to ‘land’ it).

Now, both Mercy and Astral Self have portions of their 11th level features that aren't just damage. As such, I think we could 'afford' to simply go through and add a damage feature to each of the other Monk Traditions. This damage should be on the order of a single attack, but not quite as universally applicable (the fighter is the only one who gets such universality).

Here's some quick thoughts:

Open Hand, Improved Flurry of Blows: Add 1 extra unarmed attack to martial arts, and flurry is now 3 unarmed attacks. Pure and simple. The miss chances, instead of 1/round bonus damage if one attack hits, lessens it over Mercy.

Shadow, Shadow Strike: Give them some sneak attack. Once per turn, you can deal extra damage equal to your martial arts die to one creature you hit with an attack if you have advantage on the attack roll. You don't need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn't incapacitated, and you don't have disadvantage on the attack roll.

Four Elements, Fist of the Elements: I use a fully rewritten way of four elements monk, but here's a quick fix. When you use flurry of blows, you deal extra cold, electricity, fire, or thunder damage (your choice) on your unarmed attacks equal to your Wisdom modifier.

Long Death, Death's Touch: When you use flurry of blows, you deal extra necrotic damage on your unarmed attacks equal to your Wisdom modifier.

Sun Soul, Searing Fist: When you use flurry of blows, you deal extra fire or radiant damage (your choice) on your unarmed attacks equal to your Wisdom modifier.

Drunken Master, added to Drunkard's Luck: Once per turn, when you miss with an attack, you can make an additional unarmed attack at advantage.

Kensei: really tempted to just give them extra attack (2), but only when using sharpen the blade.
 

doctorbadwolf

Heretic of The Seventh Circle
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?
Because you still want the gladiator to go down as quickly as possible. So you send the guy who excels at ganking single low-hp targets without being stopped by tanks after those targets, and put the sticky tank on their bruiser, and if they have a skirmisher as well you use control to lock them down if possible/available.

A well designed encounter is one in which there isn’t an obvious best strategy with no downsides.
 

Dausuul

Legend
Because you still want the gladiator to go down as quickly as possible. So you send the guy who excels at ganking single low-hp targets without being stopped by tanks after those targets, and put the sticky tank on their bruiser, and if they have a skirmisher as well you use control to lock them down if possible/available.

A well designed encounter is one in which there isn’t an obvious best strategy with no downsides.
This is not a well designed encounter. It's two CR 2 monsters and one CR 5 monster against a 15th-level party! It's barely a speed bump. The obvious best strategy is to ask the DM to handwave it because it's not worth anyone's time to roll dice, much less debate tactics.

But if you replace the speed bump with a real encounter, the monsters have too many hit points for the rogue to gank them in one hit, and the whole question becomes moot. "Send the rogue to kill minions" only works at very low levels or when the opposition is trivial.
 

FrogReaver

As long as i get to be the frog
Because you still want the gladiator to go down as quickly as possible. So you send the guy who excels at ganking single low-hp targets without being stopped by tanks after those targets, and put the sticky tank on their bruiser, and if they have a skirmisher as well you use control to lock them down if possible/available.

A well designed encounter is one in which there isn’t an obvious best strategy with no downsides.
My belief is that killing the priests first will allow the gladiator to go down faster.

But @Dausuul keeps making the better point. It’s a level 15 party against way to weak of opposition. The only reason the given for the rogue to not focus fire is that he can 1 shot 2 of the enemies. It’s an arbitrarily contrived example that likely would never happen in actual play.
 

doctorbadwolf

Heretic of The Seventh Circle
My belief is that killing the priests first will allow the gladiator to go down faster.

But @Dausuul keeps making the better point. It’s a level 15 party against way to weak of opposition. The only reason the given for the rogue to not focus fire is that he can 1 shot 2 of the enemies. It’s an arbitrarily contrived example that likely would never happen in actual play.
I must have missed the set up of PC levels and CR, but I’ve had rogues one-shot very dangerous enemies pretty often at my table. 🤷‍♂️
 

FrogReaver

As long as i get to be the frog
I must have missed the set up of PC levels and CR, but I’ve had rogues one-shot very dangerous enemies pretty often at my table. 🤷‍♂️
The only way a rogue can reliably kill a 27 hp creature on a hit is if he reliably is doing at least 27 points of damage. That’s a pretty high level rogue against a pretty low level opponent.

Lower level rogues can accomplish one shotting much more often and much easier as hp bloat hasn’t really factored in yet. Level 3-7 being a decent sweet spot.
 

doctorbadwolf

Heretic of The Seventh Circle
The only way a rogue can reliably kill a 27 hp creature on a hit is if he reliably is doing at least 27 points of damage. That’s a pretty high level rogue against a pretty low level opponent.

Lower level rogues can accomplish one shotting much more often and much easier as hp bloat hasn’t really factored in yet. Level 3-7 being a decent sweet spot.
Since I didn’t make it clear last post apparently, I don’t care about whatever specific example was being used. Most of the game is at a level where a rogue can one-shot glass cannons without a crit.

Even when the rogue can’t kill a target in one hit, they can easily make a glass cannon useless for the two rounds they take to kill it, which is often much better than just contributing damage to the brute. Especially if they’re built to get frequent reaction attacks, which also tends to make them harder for glass cannons to get away from.

Hell, if I’m designing a set piece battle, it will often be strategically necessary to split focus in order to avoid a TPK, and even in normal fights, enemies understand tactics, too, and will disrupt your attempts to focus fire while trying to focus fire themselves when advantageous.

Rogues and Monks both, using very different means, are very good at making control artillery useless to its team before dying in 1-2 rounds, while others in the team deal with the beefier monster.
 

FrogReaver

As long as i get to be the frog
Since I didn’t make it clear last post apparently, I don’t care about whatever specific example was being used. Most of the game is at a level where a rogue can one-shot glass cannons without a crit.
A level 5 rogue averages 18 damage on a hit. He's only reliably killing CR 1/2 and below enemies in a single hit...


Even when the rogue can’t kill a target in one hit, they can easily make a glass cannon useless for the two rounds they take to kill it, which is often much better than just contributing damage to the brute. Especially if they’re built to get frequent reaction attacks, which also tends to make them harder for glass cannons to get away from.
Attacking and not killing something doesn't make that something useless in any sense of the word.


Hell, if I’m designing a set piece battle, it will often be strategically necessary to split focus in order to avoid a TPK, and even in normal fights, enemies understand tactics, too, and will disrupt your attempts to focus fire while trying to focus fire themselves when advantageous.
I think you overrate your ability to make it necessary for the players to adopt a normally inferior tactic.
 

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