This is a letter to the optimizing community at large. My key point: Stop looking just at DPR.
The concept of "damage per round" (DPR) has dominated in optimization circles for quite some time - the label itself appeared around the rise of 4th edition, but aspects of it showed up during 3.5 as well. The basic idea is to calculate an expected value of damage output (considering accuracy) under a specific circumstance (i.e. "sustained DPR", "spike DPR", etc.), and if your numbers go up, you win. And this works fine, under some circumstances.
The problem? Actual gameplay isn't one of those circumstances. DPR itself is utterly blind to how the game is actually played, even by hardcore optimizers.
This post is about why DPR doesn't actually matter during gameplay, and why it should be shelved at the table. ...Well, truth be told, DPR does matter... when summarizing long-term averages. Long-term averages are the domain of design, such as the game designer or the optimizer during character building. They are most certainly not the domain of round-by-round rolling, such as what happens during a single game session (or even one combat round). It's the difference between expecting to roll a 7, and actually rolling a 7 - different results governed by different (but related) math, sensitive to different parts of the game.
Let's look at some problems with looking at DPR as a round-by-round / in-game metric. Once it's clear what the problem is, I'll propose a better solution.
The short and sweet version: Combat is played as a series of actions. Enemy actions can be stopped by damage, but only if that damage depletes your target's last hit point - enemies fight equally well with 100 HP or with 1. DPR seeks to maximize expected damage, ignoring the target's current HP and the actual discrete result of your dice, as well as the potential consequences of your opponent getting an action. Focusing on DPR causes you to look only at the damage, instead of the result of that damage - whether or not your attack will actually defeat the monster. It is, in essence, a can't-see-the-forest-for-the-trees situation, where you lose sight of the true objective of combat.
To begin, let's talk dice. Fundamentally, any game that involves dice is governed by the laws of probability and statistics. I could go on at length about this, but for our purposes, the only things that matter here are averages, variance, and frequencies.
- The average gives you what result you "expect" for a roll. It doesn't actually have to be a number you can actually roll. For a single die, it's the mean result - add up all the sides and divide by the number of sides. For multiple dice, or conditions with rerolls, you weight these values by their frequencies: the "average" of 2d6 is 7, while the "average" of 2d6 (rerolling 1s and 2s) is 8.33. (Note to math geeks: What we're describing here is "expected value", not a true 'average'. But common parlance here uses them as synonyms on this board, so I'll call it an average.)
- The variance of a roll is a measure of how spread-out, or "swingy", it is. A roll with low variance is more likely to produce a result close to the average (expected value), while a result with high variance may produce more extreme values (high or low).
- The frequency of a roll refers to how often it shows up, and in this case I'm always talking about a number you can actually roll. In some cases, the "most frequent" (modal) result works out to the same as the average - 2d6's average of 7 is also its most frequent result - but the two are NOT the same, and shouldn't be confused. For instance, on 1d6, all six numbers show up with equal frequency (and the average result, 3.5, will never show up, since it's an impossible roll), while 2d6 (rerolling 1s and 2s) will produce a 9 most frequently (even though it has an average of 8.33).
When people focus on DPR, they put all the emphasis on averages. After all, in the long run, the average of your actual rolls will tend towards the theoretical average for that roll - that's the central limit theorem at work.
The problem is, the average on a roll is not the same as what you actually roll. On any individual roll, variance dominates, so much so that knowing your average or most frequent result is not the same as knowing what you will actually roll. (Incidentally, this is also the central limit theorem at work - the game, round-by-round, relies on single rolls rather than the average of a string of rolls, and a single roll is definitely not a sufficiently large sample.)
All of this falls from the central limit theorem itself. As the number of rolls increases, the results of those rolls will tend towards a normal distribution, with a mean of the expected value of the roll. This is why DPR - which is functionally a measure of that expected value - is so effective a measure in the long run: It tells you where that bell curve is centered. Contrariwise, as the number of rolls decreases, this becomes less and less true. On a single roll, the expected value - including DPR - is pretty much totally invalid, especially in the cases where it happens to be a result that can't appear on the dice (i.e. you never roll 3.5 on 1d6). On small numbers of rolls, signal (the average) fades in importance, and noise (the variance) dominates. Therefore, on the short term (say, round-to-round), using a metric that ignores variance (i.e. DPR) is a poor choice, even though it's a perfectly valid measure as the number of rolls increases. You need to account for the variance - specifically, the frequency of each particular outcome, and how those outcomes translate into your success or failure - and for that, we need a new metric.
With that foundation out of the way...
Unless you know monster hp the whole fight there is no better metric than dpr.
If you don't know the monsters current hp you cannot calculate anything based off its current hp. This, you should maximize dpr when you don't know the monsters exact hp value.
I think in general what a good optimizer does, is to minimize the amount of damage - in a broad sense, not just HP - that the enemies can do to him/her and their allies.
That's what you seem to be saying in a round about way.
In my experience the best optimized characters, as far as combat survivabilities goes, are not the ones that do the most damage, but the ones that take the least damage, as long as they still have a way to also deal damage. I see them as a sort of pill box. A bunker from where you can shoot at your enemies but they have a very hard time hitting you. Stacking enough defensive abilities will break D&D much faster than maximizing damage. The best way to defeat enemies are usually control spells like Sleep any way.
I've had players in my group with well optimized characters, where I could not think of a way to hurt the character, except with antimagic or HD dependent spells.
FrogReaver wrote:
I think 5e makes a lot of that advice problematic, because given how the numbers in 5e work - Bonus Action Attacks+Advantage+-5/+10 to hit feats+Precision Attack are going to be really accurate whenever you need them to be. Bonus Action attacks tend to be easily available via a couple of feats and they really smooth out the benefits of -5/+10 damage feats - in essence being Advantage in the form of two attacks that might hit twice.
The question is not whether or not you're optimizing towards DPR or kills, the question is whether or not you're exploiting all the various to-hit options of 5e and utilizing your actions as efficiently as possible. Do you have a bonus action attack? Do you have a consistent reaction? Do you have a way of getting a big bonus to hit(Battlemaster)? Do you have a way of getting Advantage, particularly in the crucial 1st round of a combat?(Assassin Rogue 3/Barbarian 2). Do you have a Nova(Action Surge)...
I feel like this topic came up a few times at least in the 3.5 char op days, and also in 4e. DPR always ended up winning out in the end as the most reliable method if I remember right, even if it's not all that accurate most of the time. Part of the problem with the chance to kill metric has already been explored by both you and FrogReaver- that in play you often don't have perfect knowledge. There are some other points to consider as well. For example, in the first example with the greataxe you only look at the chance to kill the enemy in one round. What's missing from that is that the greataxe is also considerably more likely to leave the orc alive for longer than two rounds than the greatsword is. Quickly using the program you linked to (which is nice, thank you for linking it), given two hits and ignoring crits (I'm lazy, so yes the numbers here aren't perfect) the sword has a ~5% chance to NOT kill the target, while the axe is at ~20% chance of failing to kill. Outside of the orc example, anything with 10 or less hp is more likely to die on the first round to the sword. Essentially, the original example only shows the benefits of high variance while ignoring the drawbacks.
Yep chance to kill changes drastically given minor changes in hp. Go up or down just a little in the monsters estimated hp and you get crazy swings in what is better.
I disagree with your conclusion (DPR doesn't matter), and have several issues with your presentation.
I *do* agree that there is more to consider than just "moar damage all da time!". Heck, sometimes you are better off doing *no* damage and knocking prone, or whatever. So yes, of course if the target is down to 5HP, using SS/GWM is foolish. But that makes your presentation more of an edge case consideration rather than a priority.
Lets look at your example.....
This is reflected at the link: the likelihood of dealing 15 damage on a normal hit with the sword is 2.78%, while the likelihood of the same with the greataxe is 8.33%.
But is it not true in your example that the axe is more likely than the sword take three+ rounds to kill the orc, compared to one or two rounds? Isn't that worth accounting for? But then it gets complicated.
It also has a 1/12 chance of doing 1 compared to the swords 1 in 36.
The Sword is the superior choice not because it does .5 more average damage, but because it's damage is weighted towards the average.
Yunru wrote:
Yunru wrote:
Yunru wrote:
Variance is good in a fight you're likely to lose, and bad in a fight you're likely to win. Most of the time you're likely to win, but the times when you aren't are often higher stakes.
So best bet is carry both 
I thought the OP was going to argue that if you maximize your DPR and start killing everything too easily your DM would just throw harder encounters at you, thus negating the value of all that DPR.
The non-optimizer version: Try to kill your opponent before they can hurt you. Failing that, try to hurt them really badly so they'll be closer to dead.
Momar wrote:
LordCorwin wrote:
I think this is a step in the right direction for moving from optimizing damage output of a character to optimizing outcomes, but there is still some direction to go.
In the end, "damage per round" or even "attack chance to kill/defeat" are relevant, but the final focus should move beyond either. The real question should be "Will my action improve outcomes?"
Let me break this down to a couple examples.
LordCorwin wrote:
I always thought DPR was a good measure. Overkill is still killing, and even with a maximized DPR build, you're not going to end most big fights in one round.
A DPR build will end those big fights faster than other builds. This increases survivability. You just don't use GWM/SS vs those little baddies.
Of course, a good DM will change an encounter to meet the challenge. The whole argument becomes moot, unless you're trying to dominate AL games where the DM can't change stuff.
Thanks for confirming. So completely arbitrary hitpoint totals net completely arbitrary preferences. That's what I thought. Since we cannot decide how many hitpoints our characters have to go through, there is no always better weapon. Sometimes 2d6 is better. Sometimes 1d12 is better. As many people here like to point out it sounds like white room calculations that don't really apply to the game at the table. Which is what I think the OP was saying in the first place.
Yunru wrote:
FunkySpunk wrote:
LordCorwin wrote:
Kangodo wrote:
FrogReaver wrote:
Well, I step away for an evening and this happens.
I should probably say that my opening post is a bit hyperbolic - I was trying to provoke responses, and that's what it did. I don't believe DPR is a worthless metric. I just believe it is overused, being the only real quantifiable metric that I've seen on the optimization circuit so far. It's a long-term central tendency measure, and as the time scale shortens, it becomes less and less appropriate a measure, to the point where on a round-by-round basis it can be downright misleading.
(I've edited the math preamble in my original post to explain this a bit more. It's important, but ultimately only to those who care.)
One thing I should have been clearer on: My intention was to talk to people who look at DPR as the goal and show them that damage only really matters inasmuch as it impacts enemy actions. The simplest way to do this through damage (remember, addressing the people looking at damage as their big thing) is to kill the monster, which is what kill rates measure - the point at which damage (and damage alone) translates into something tangible on the action economy. Once that bridge is crossed, we can bring the optimization zeitgeist to the action control that some of the more experienced optimizers espouse (i.e. the God Wizard tactics, or the equivalent in non-casters, similar to 3.5's AoO tanks).
Coredump00 wrote:
Tempest_Stormwind wrote:
FrogReaver wrote:
FunkySpunk wrote:
I think the OP is going between 2 different kinds of optimization.
There is round by round optimization which is much different than character builiding optimization.
The most unoptimized character can still use optimization in his round by round combat decisions. Some of what the OP mentions in terms of optimization has to do with round by round optimization.
However, most optimizers are not nearly as worried about the round by round combat decisions as they are with using optimization to make a character that is optimized to be very good at taking on a variety of foes.
Does chance to kill really tell us anything better than a generic DPR when it comes to character building?
Tempest_Stormwind wrote:
Tempest_Stormwind wrote:
So by this measure, using Conjure Woodland Being to summon Sea Hags is amazing right? Cause for humanoids, its roughly a 25% kill chance a round (50% for any creature if you can subject them to fear another way, and up to 75% if you can Bestow Curse, ++ more with Bane).
Tempest_Stormwind wrote:
JohnnyBlaise wrote:
DPR/DPS tactical thinking is pretty useful when resources are limited to isometric battle maps and MMO style abilities (like in 4th edition), although in 5e, there's more open feel to some things, so DPR can be an over rated notion. In D&D, it is entirely possible a flash flood from a busted dam could soak a bunch of full plate wearing soldiers, and then one guy lifts up his lance or greatsword and draws in a lightning bolt that travels across all the water and platemail, killing the whole group. DPR just doesn't have a way of expressing things like that.
You can be fighting along a cliffside, and use thunderwave or some push action to dish out 20d6 falling damage to someone, plus whatever you did hitting them. Again, not really DPR friendly. You can trip up people by hanging wire nooses in the forest for mounted riders, and then strangle people, wiping them out using exhaustion/suffocation rules, which again doesn't reflect DPR.
D&D isn't a video game, video games attempt to closely replicate some of the options and drama of D&D, but they fall short. You have way more options in D&D.
In theory, should should have more options in D&D than you do in real life.
Tempest_Stormwind wrote:
JohnnyBlaise wrote:
Treantmonklvl20 wrote:
FrogReaver wrote:
Treantmonklvl20 wrote:
to be fair to the DPR people, some DMs absolutely refuse anything too tactical that can upset whatever it is they plotted. I recall not wanting to get stuck in a number of scenarios while the DM more or less forced the party into situations and suggested they down vote me, and voted half the party right into suicide situations. When you literally aren't permitted to use tactical considerations, the only thing you have left is the hard numbers.
Like, sure, in a tactical situation, a knife that comes with your mess kit and does 1d2 damage is capable of killing a half dozen giants by dropping a landslide of bolders on them as they go through a pass. All you have to do is have a Diviner hook you up with some notion of when they might show up, and then set up a rope. The knife is now doing something like 1000 total damage, divided 6 ways, by cutting the rope that sets off the trap. But some DMs wont allow that. They will say your Diviner powers are crap, and they only have a vague notion of "doom' in a random direction and 'soon'. then they may change the scheduled appearance so the giants show up in 10 minutes instead of 18 hours, so your group has absolutely no chance of setting up a trap. Then suddenly, your 1d2 knife is just a 1d2 knife again, and you have to go back to 2 attacks per round with a greatsword doing 2d6+5.
I'm sure none of you has had this exact experience, but most of you have probably experienced something similar at least once. So it is always good to have some DPR skills in the background, when roleplaying and planning just aren't allowed to influence the success of your story.
FrogReaver wrote:
Treantmonklvl20 wrote:
Wow, Treantmonk, you're really forcing me to re-evaluate my long game here. I originally thought that the way to reach the DPR-heavy crowd was by introducing another calculatable metric that directly impacted actual gameplay. (Kill rates are the most basic way that DPR is translated into a difference in relative actions, which is the fundamental mechanical unit of how a game unfolds. Strategy and tactics ultimately unfold on actions as well (in some cases, preventing initiative from being rolled at all), so by causing DPR fans to think about kill rates, the goal was to get them thinking about actions, on terms that would let strategists enter the zeitgeist.) Your writing has me thinking I should have cut straight to the end, where DPR is seen a one element to an adventurer's success instead of the only thing used to evaluate character options.
(Also, for anyone who thinks I'm being unfair, here's an example from just yesterday. It's comparing Eldritch Blast and Sneak Attack, and zeroes in entirely on DPR. This ignores multiple tactical elements (most obviously Eldritch Blast's range and Sneak Attack's friendliness to critical hits or rerolls, but also that Sneak Attack lacks a V component and is thus silent, and EB can be paired with Repelling Blast (and thus, any environmental advantage, like bonfires, spike pits, or cliffs), and even when looking just at DPR, it makes the assumption that Hex will be up - which carries not only the cost of casting Hex itself, but also the opportunity cost of not having any other concentration spells running). And that's on a straight-up more-or-less white-room comparison, and even there DPR is myopic. This isn't really cherry picking - it's just the most recent time I've seen it.)
Treantmonklvl20 wrote:
Tempest_Stormwind wrote:
Tempest_Stormwind wrote:
Oh and it actually doesn't matter if you understimate or overestimate monster hp. The chances change drastically.
Treantmonklvl20 wrote:
Tempest_Stormwind wrote:
Tempest_Stormwind wrote:
For movement or placement considerations, the best DPS fighter would be one with Crossbow master/Sharpshooter. You can deliver your damage equally at range or in melee.
If you play a Barbarian or Paladin you are forced melee for many of their abilities. That said, these guys do good damage and can provide many different good abilities in melee.
You have to consider do you want more damage or more AC with some of the fighting style picks. If you find yourself being knocked out too much then obviously spending more on defense is a better option than damage. Since your DPS goes to zero if knocked out.
Yes, that said there are so many important factors and good plays in a fight besides damage. Generally speaking though, damage is one of my favorite things to do, especially in 5th were there are less save/suck spells. Doing damage is not always the smartest move on your turn in a fight, example: the dodge action might make more sense even if your normally DPS but your blocking a doorway.