As I've said many times, there are all kinds of metrics one can use. Criticizing the metric being used doesn't lead to 'math is irrelevant in this discussion'.
But when all you have is a hammer, every problem looks like it can be solved by DPR analysis.
Look, math is hard. Real math, even harder. It's not like we are trying to understand the difference in the lag effects between fiscal and monetary policy by running multivariate analyses using Minitab ...
...but this is a prime example of GIGO. To briefly go through the ways:
1. Some things are amenable to (relatively) simple analysis. For example, baseball tends to be "easy" to quant because most of it is a series of one-on-one interactions (pitcher, hitter). Other things are harder (like defensive stats in baseball). On the other hand, when you take certain sports, like Basketball or Football, you find that while statistics can be incredibly important, they can't tell you everything in isolation because it's a team game (the "Battier" issue ... or the issue with quantifying the effectiveness of a single offensive lineman). Given that D&D necessarily involves
parties of multiple characters interacting, a pure DPR analysis will always fall short. It can be somewhat informative, but never dispositive. Or to use your recent post, it can't answer the X < Y, because it can't account for the synergies that occur due to differing party compositions.
2. A further issue that occurs is the necessary difference between different campaigns and different assumptions. Different campaigns is hard enough (for example, a monk in a social and urban campaign where weapons and armor are not assured will be different than in the recently referenced, "DM SEZ YOU NEVER SHORT RESTS, EVER" campaign). This is further complicated by the nature of the combats. Are they grid or ToTM? Does the DM play the monsters tactically and in waves, or as stupid cannon fodder*. Lots of missiles weapons and low AC? Lots of enemy spellcasters?
3. Then there is the issue of how the player plays the character. DPR doesn't take into account players catering to a class's abilities. "Wait, the monk attacked and destroyed my weapon? What do I do now?" It doesn't measure the "fun" of playing different style. Some people find pure "DPR" and "Tanking" fun, others prefer a tradeoff to allow you to hit and run. It's not right or wrong, it's just different.
4. Which brings up the whole "there's more to the game." DPR doesn't account for all the weird niche abilities that the Monk has. It doesn't take into account the monk not getting hit by missile weapons (let alone flinging them back, if wanted). It doesn't look at the "full picture" of
combat, and combat is just one of the three pillars.
Of course, when these issues are raised, and they are, the usual WhiteRoom response is, "Well, okay, but .... in my opinion, the other monk abilities aren't good, or come too late, or aren't useful for other things, or something something, AND WHAT ABOUT THIS DPR?"
Math is a great tool; but that is all that it is. Here, let me put this in the most basic terms I can:
Imagine you are right. Imagine that you have gone ahead, run the Monte Carlo simulation, done a full analysis with all sorts of party members, and determined that Monks lag by .2 DPR behind "other classes."
Well, someone has to lag, right? There will always be a last class. Whether it's the Monk, or the Beastmaster, or the non Pew Pew Pew Warlock, or exhaustion Berserker, or whatever.
And when people come back and say, "Okay, but I still love the class, and the ribbons, and it's the most fun ..." then what? What does it matter? All you have done is gone back to the main distinction- some people like the class for what it is, and they keep telling you that.
So to reiterate:
A. Your math is not good enough; and
B. Once you do get your math good enough, I'll be happy to look at it and say, "You, Esker, you have done good math. Good Esker!" But it won't change my opinion as to the fun I have playing the class.
*How did we agree to attack them?
All at once.
And how did we attack them?
One at a time.