# D&D GeneralLies, Darn Lies, and Statistics: Why DPR Isn't the Stat to Rule them All

#### Snarf Zagyg

##### Notorious Liquefactionist
Supporter
Far too often, we see a clickbait-y youtube video. You know. Shocked looking woman. Big red arrow.

WHY (insert a class here) SUCKS.

Or maybe it's a post here. Or an essay elsewhere. And the person says that they have proven how much a class, or a spell, or an option SUCKS because they have run the numbers. That's right, DPR (damage per round) proves as an absolute fact that something sucks. AND YOU CANNOT ARGUE WITH THE POWERS OF MATHS AND LOGIC!

Before you start angrily pounding on the keyboard to tell me how wrong I am, please note the following: math is fun. Math is good. There is nothing wrong with optimizing your characters, if that's your thing. No kink-shaming here. Instead, I am going to discussing a more fundamental issue- specifically, the very real limits of DPR to "prove" the worth of a character. More importantly, I think it's important to examine the over-reliance on a single, limited-use statistic .... When all you have is a hammer, every problem looks like it can be solved by DPR analysis.

One of the interesting things that you often see pop up in conversations about D&D and 5e is discussions about optimization, or, put another way, so-called "whiteroom theorycrafting." Since these conversations pop up so often, and have in various more, or less, sophisticated forms since the 1970s, I thought I'd put together a handy primer as to why DPR is an overused tool that does not have the explanatory people claim it does and does not accurately of fully measure class viability, build viability, or the proverbial "fun."

The main reason for I am doing this is because I have seen multiple people say in these threads that this is just math, and it's just a question of X > Y. Now, given that most of the debates about relative worth and the proper use of statistics have already been extensively hashed out in another arena, I am going to be making many analogies to that fertile ground.

CAUTION: Extremely large amount of sports-like substance ahead! You have been warned!

A. One stat to rule them all, one stat to find them, one stat to bring them all, and in the darkness bind them.

Imagine you were a baseball fan. I know, that's probably nigh impossible on this website. But just .... imagine, like John Lennon. Now someone approaches you and says, "I have a statistic that accurately measures how good a baseball player is! The better a baseball player is at this single statistic, the better a baseball player is, period. Because the main goal in baseball is to hit the ball, I give unto you .... BATTING AVERAGE! It's math, so you can't argue with that."

Unfortunately for this person I just conjured up to make this point, there are some well-known issues with batting average. The threshold problem is that there are other aspects of the game ... let's call them "pillars," that batting average can't measure. If you wanted to say that baseball had "three pillars" of batting, pitching, and defense, then batting average only measure one of those three pillars. Which is a problem! How can you use one statistic, even a good one, when it doesn't capture everything that the player does in the game?

"Okay," says Señor Strawman. "Maybe it doesn't capture all three pillars, but at least it tells us who is muy macho in the batting pillar!" Unfortunately, it doesn't. Batting average doesn't measure batting very well. It's better than just not knowing any numbers at all. However, batting average doesn't take into account important factors about offense (batting) like .... getting on base without hitting the ball ("walks"), or whether the batter is really good at "going nova" (hitting doubles, triples, and home runs). All batting average does is measure the most basic statistic possible. It provides more information than no information, but its limitations (if they are not recognized as such) could end up with someone making the following serious errors:

1. In 2019, Jacob deGrom (.200 BA) < Harold Ramirez (.276 BA) (Pillar error; deGram was a Cy Young winner as a pitcher, and Ramirez was a light-hitting outfielder on the worst team in the league)
2. Hank Aaron (career .305) < Bill Lamar (career .310) (factor error; Aaron is a hall-of-famer and second all time in home runs, Lamar was a journeyman who played for nine seasons with 19 home runs for his career).

This should show the issue with over-reliance on a single statistic! Now, as anyone who follows baseball knows (all three of you reading this), you can get better statistics. If you want to measure offensive production, you can include walks (OBP) and power (Slugging) and even combine them and normalize them into a really good statistic (OPS+). And you can try and capture defensive value, and pitching, and try to include that into a single, comparative statistic (there are variations of this, an how to calculate it, but a common one is "WARP" or Wins Above Replacement Player).

But we aren't doing this in D&D. DPR is not WARP, and it's not OPS+. DPR is, at best, the batting average of D&D- a measure that doesn't even try to take into account the full gamut of offensive options, let alone synergies or other pillars or options in the game. Of course, unlike batting average, DPR isn't an observed statistic, but it's conjured out of whole cloth from assumptions ... which will be addressed later, because before that we have another major problem.

B. The is no I in TEAM .... and no D P R in TEAM either!

D&D is a team game. Various editions have made required "roles" or "niches" within the party more or less explicit; famously, in ye olden grognardian days of 1e which I like to bore people about, you'd need to have at least one cleric for healing, and some fighters to defend any fragile magic users, and so on. 5e has really lowered the threshold when it comes to having any particular class that is required, but it is still common (IME) for players to talk to each other to ensure that there is a decent diversity of classes within the party.

More importantly, there are multiple players. While there might be an occasion for "solo play" (DM/player), most campaigns consist of a DM and 4-6 (or more) players. The reason why this is important is the why I am about to move away from baseball ... which is probably a big relief to anyone reading this not from the US. Maybe next time it will be cricket?

Baseball has always been an attractive sport to analyze with statistics because almost every interaction is a 1:1 battle- a pitcher and a hitter that results in an outcome. It's heaven for stats geeks. There are advanced issues ("clutch hitting," defense, "framing pitches," "clubhouse chemistry" and so on), but the core stats are fairly simple and easy to analyze.

Teams games .... they are infinitely more complicated. We can refer to this as the "Battier Issue." In basketball, there was a player, Shane Battier, who didn't have very good statistics when measured by "traditional basketball stats" (points scored, rebounds, assists). But whenever he played, the other players on the court played better. In other words, he was doing the things (defense, setting picks, clearing out the opponent for rebounds) that aren't captured in the statistics for basketball. Battier would make everyone else more successful on the team, but none of the traditional statistics would see his impact.

An example of the exact opposite of Battier would be a player like Ricky Davis; Davis was a gunner, and had a good stretch of averaging just around 20 points a game. But Davis didn't make his teams better. He didn't set screens. He didn't play defense. And his points were scored on a high volume of shot attempts. Traditional statistics that viewed him as a player in isolation without looking at his teammates would completely miss out on the negative impact he had on the team. I mean, you could use your eyes and watch the game ... but stats? Naw.

Basketball, soccer, football (American). These are all sports that are harder to quantify because they are team games. Sure, you know the value of a QB in football by the number of TDs he throws (although that is only part of the picture), but how do you accurately quantify the value of the the offensive linemen that give that QB time to throw?

Anyone who follows professional team sports knows that, increasingly, people are paid vast amounts of money to try and put numbers to a lot of these inchoate issues, like the value of defensive players in soccer, and offensive lineman in football. To quantify (more than just the eye test) how good that 19 year old sweeper on some random club is, and how much of a transfer he is worth. But the point is- it's hard to do. Even the best striker can't score if his team can't get him the ball. Even the best goalkeeper can't block shots if his defense is allowing the other team time to set up clean in the box. There are ways to try and measure it, and teams pay vast amounts of money to try, but the stats can only inform, they can't define.

This gets to the heard of the matter for DPR; because D&D involves a team (a party), and because DPR artificially inflates the measure of the single individual contribution in terms of damage, it necessarily discounts the value of benefits that accrue to the party. That's not to say that these benefits can't be teased out mathematically with difficulty- just that DPR doesn't do that.

Just think about the number of times a character in a campaign you've been involved in has used an ability, spell, or even just used the help action ... and what that might have done. Synergies, team play, all of that matters, and none of that is captured by DPR.

C. Philly, man, they even boo Santa Claus.

The last point is a little more abstract, but is worth reiterating, because while the effects are more nuanced in sports, they are dramatic in D&D. In many sports, you will play an entire season of six months just so you have home field advantage in the playoffs- the opportunity to play at home. This can be as subtle as having an extra game at home in a seven game series. But this matters! Everything from sleeping in your own bed (and not a hotel) to knowing the field, to the pressure that the home crowd puts on the referees, to more esoteric things, like the altitude of different places, can make a difference. Anyway, it's a truism that where you play matters. To briefly go back into stats, you will often see home/away or park-adjusted statistics to account for this.

It's the same with D&D. There is no such thing as a baseline or whiteroom D&D campaign. Maybe AL comes closest, but that is such a tiny minority of games. Is your campaign battlemap or ToTM? Is it combat-heavy or all about the discovery? Does it include feats and multiclassing? Does it take place mostly in dungeons, in cities, on the water, or even under the water? Are you using any variant rules? The variability of campaigns is so great that is can often swamp out other factors; to use one easy example, think of languages. If your campaign ignores or "Star Treks" the issue of different languages and everyone just kind of understands each other, because reasons, then any spells or abilities involving languages are pretty much useless. On the other hand, if your campaign has detailed rules about languages, with multiple countries with different languages and no common tongue and there is a massive social and exploration component, then those language spells and abilities will be incredibly valuable.

Same abilities, different value, entirely campaign dependent. One person's ribbon ability is another person's awesome ability that they need.

And that's a fundamental issue with DPR. DPR inherently assumes that the campaign is combat-focused so that DPR is important and that the campaign features the type of varied, yet generic, combat that would make DPR the correct measure of combat effectiveness. Neither assumption is necessarily incorrect, but both assumptions will quickly be tested by campaigns that don't match those assumptions. Moreover, as noted above, it does not account for the synergies of party play, necessarily discounting how different characters can be used to increased the overall effectiveness of the party.

D. Conclusion.

None of this is to say that DPR is completely useless. To use an analogy, if someone says, "Hey, a rapier does d8 damage, and a scimitar does d6 damage" then noting that d8 > d6 (in isolation, ignoring weapon properties) is useful information!

And that's what DPR, done well, can be. Useful information. But like so many statistics, over-use, or over-reliance on it without understanding the limits and the issues of it leads to hubris and saying that things "suck" without proper foundation. Now, before it is said that I would level this accusation without providing helpful analysis, what would I do to improve the current analysis?

That's both simple and complicated. The primary problem is that D&D, unlike most sports, doesn't have a large catalog of observed games for statistics. Now that we have twitch, and critical role, and other publicly broadcast games, maybe someone could start compiling that.... but that's neither here nor there. But there is always going to be a difference between "white room" stats and statistics in play. This may change with Beyond and the VTT, but we would need to see it in action.

Other than that, the best way to get useful statistics is to run simulations (Monte Carlo simulations & regression analysis) over and over again with different party compositions and different combats and see the results. There would necessarily be limits to this based upon even more factors (what monsters, how are the PCs making decisions, accounting for spellcasting, accounting for terrain etc.) but it would provide you with more useful information. IMO.

On the other hand, DPR, like batting average, can continue to be a useful component or tool- but primarily so long as its limitations are acknowledged, and its used to compare two things that are already alike. In other words, if you are choosing between two options for your character in order to maximize damage, then DPR is a great tool! It's value diminishes significantly as you start comparing unlike things.

Anyway, thought I'd throw all of this out there. I am quite positive it is uncontroversial.

And one more thing- that youtube video? The one with the shocked woman and the big red arrow. DO. NOT. CLICK. You're welcome.

#### jasper

##### Rotten DM
So what you are saying is Eliminster, Drizzit, and my pc need bubble gum cards.
I think bubble gum cards may have let to the love of stats from baseball people.
Yes even back in 80s people would do DPR and totally forget it is a team game.

#### Xeviat

##### Hero
DPR analysis is good for comparing similar characters, or for spot checking balance. If build A out damages build B and build B doesn't have any substantive benefits over A, then that tells you something.

Rogue's have lower health and often lower HP than Fighters, but Rogues have skill functions that Fighters don't have: that's a trade off. But a Rogue built for damage should be comparable in DPR to a Fighter built for damage. A Wizard should probably be lower, since they have so much more utility.

It's not the end all be all of balance, but it is something to keep in mind.

#### payn

##### I don't believe in the no-win scenario
I was just thinking recently about how much charoping and The DPR Olympics have died down (not out). I think a lot of that is due to BA and tight math design of 4E and PF2. The gap has been narrowed so its not so important to have these DPR arguments anymore. I mean, folks will still have them, of course, but they no longer take 15 of the top 20 thread topics on EN World. Good times we are living in.

#### Snarf Zagyg

##### Notorious Liquefactionist
Supporter
I was just thinking recently about how much charoping and The DPR Olympics have died down (not out). I think a lot of that is due to BA and tight math design of 4E and PF2. The gap has been narrowed so its not so important to have these DPR arguments anymore. I mean, folks will still have them, of course, but they no longer take 15 of the top 20 thread topics on EN World. Good times we are living in.

True, that. But I am anticipating the official release of 5e: Fast Five and all the Youtube Clickbait videos and optimization guides.

#### payn

##### I don't believe in the no-win scenario
True, that. But I am anticipating the official release of 5e: Fast Five and all the Youtube Clickbait videos and optimization guides.
Oh, I pay no mind to clickbait. Life is better that way.

#### Mistwell

I disagree with the premise. I watch a lot of optimization videos, and almost all of the major ones shifted away from DPR long ago. They usually value things like battlefield control, buffing, defense, tanking, etc.. about as much as anything else. It's been a very long time in fact since I've seen someone who used DPR as the one stat to rule them all. The will mention it, they will use it, but they will put it into a context of other things you can do well so you can balance DPR with those other things.

In other words, the most successful ones got more tools than just a hammer long ago, and I feel like you're behind the times and using an old sterotype which isn't really very accurate these days.

#### Vael

##### Legend
While I didn't know all the players involved, I did understand all the Baseball stats. shudder

This is where the fact that I did the bulk of my DnDing during 4e conflicts with my understanding of how players optimize. I played a few 3.5 campaigns, had a bad time trying to DM, so it was 4e and 5e that I played the most. And 4e introduced roles, and one of my favourite iterations of the Bard. Because the forced movement abilities of a 4e Bard, combined with a feat that grants a free attack as a reaction to getting force moved meant that I could enable a lot of damage ... but is that DPR mine, or the Executioner Assassin with the hard hitting basic attack I kept sliding across the battlefield? Meh, as noted, it doesn't matter, it's a team win.

Still, how much is DPR actually used? In 4e, sure it might work with balancing Strikers, but that's only a quarter (roughly) of the classes. 5e optimization isn't something I obsess over, so I guess I don't read the guides for how much DPR one can squeeze out of a class. I did note that the D4/Treantmonk video did talk a bit about Rogue DPR not being that good, but the control conditions they can measure out can balance that out.

#### OB1

##### Jedi Master
Fantastic write up! Baseball and Football fan here, and even worse than statistics is the new reliance on 'Analytics'. It's the reason that the Dogers have been unstoppable in the regular season the last 6 or so years and yet constantly get knocked out of the playoffs, because their manager so slavishly devotes himself to the analytics that work over 162 games by averaging out, that he fails to recognize the situation in front of him when a single game or inning is what matters. The same is true of the Detroit Lions coach, who blew a huge lead in the Conference Finals last year because he kept doing what the analytics told him instead of reacting to the specifics of the game in front of him.

And how I think this all relates to DPR and white room analysis in general is that there is a limit to what math can tell you about how any particular combat will play out at a specific table in a specific encounter. All the DPR in the world doesn't matter when a player rolls 3 nat 1s in a row and the monster crits on them twice, because if all your party cared about is DPR, and you don't have the healing or control or the ability to flee, you could end up with a TPK.

It's also why the D20, rather than a d6 or d12 is so important to D&D's succss, IMO, because that level of randomness in the game (shored up by 5e's bounded accuracty) means that anything can happen. And if all you do is try to hit home runs, you'll end up striking out a lot more

#### Kurotowa

##### Legend
In other words, the most successful ones got more tools than just a hammer long ago, and I feel like you're behind the times and using an old sterotype which isn't really very accurate these days.
I dunno. I sure see Treantmonk's DPR charts quoted as authoritative analysis in a lots of parts of the Internet. That was the entire basis for the loud outcry that UA Blade Pact Warlocks were overpowered.

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