You're conflating simulation with insanely detailed and unpractical simulation. You always need some simplification and abstraction to have a functioning game. "These things are big and strong in the fiction, so they get bonus to the score that measures physical strength in the game" is a simulation.

Except, again, I'm not. There's an extremely easy, simple, low-cost way to represent the necessary degrees of variability: not having rigidly-fixed racial ability scores. Which is what I've said. Repeatedly. And which you've ignored, repeatedly, because apparently I gave too many examples. When I express my argument in straightforwaed terms, you brush it off as unimportant or unrealistic; when I ground it in explicit, actual examples from real-world statistics, it is too confusing to respond to. This whole process is deeply infuriating and, as a result, I won't be engaging with you about it any further. We have reached the "circular arguments and ignoring what is being said" stage and I just don't have the desire to do that.

Nobody has said they can't be strong. All I am saying is that, as a simple statistical fact, actual population dynamics reflect such a degree of variation that, even when you have a robust and well-selected sample, you WILL find that most (and possibly ALL) individuals don't actually have all of the traits that they "should" have to be in that population. Natural populations are not like dog breeds, where they're obsessively pruned to maintain a standard--or, rather, they're very much like actual dogs, who

*frequently* fall short of a breed standard even when absolutely purebred. (As an example, I once owned a Parson Russell Terrier that was about half as much again as large as he "should" have been, despite being purebred. One of his brothers was even larger. They'd have failed the breed standard, despite having clear purebred documentation going back four generations.) Natural populations can exhibit seemingly extreme variation. Player characters are, almost by definition, members of the extremes of their culture and species. We should expect, in any serious simulation, that they would be quite likely to diverge from the norms of their species in many ways, physiology being one of them.

This...just...

You have to realize that this makes your argument entirely circular. You were asked to explain why these things worked for simulation when they don't conform to how statistics work, whereas the new set of approaches (everyone has flexible racial ability scores, but DMs can request, as they always have been able to, that players "play to type" etc.) actually DO conform so. When then challenged about how one gets the simulation required...you then justify it with the numbers you wish to use. The numbers are justified by simulation and the simulation is justified by the numbers. Perfectly circular.

(Also, I utterly despise that this loading of terms is a thing. ASIs come from levels. Racial ability bonuses come from race. Calling racial bonuses "ASIs" would be like calling all class-based number bonuses, like bonus rage damage, "PB." It's confusing and inaccurate, but used solely because it's faster.)

Yes, which is weird. Starting cap however is different for different species, and that is what will matter for most of the game (most campaigns end before level ten, so the theoretical cap is not reached by species without ASIs, assuming point buy.)

Why should it be different though?

ASI alone shifts standard deviation,

It literally doesn't, because it mathematically cannot. Changing the location of the center of a distribution by adding a constant value to all numbers in that distribution has literally, actually zero impact on the spread of that distribution. This is a mathematical fact. You can re-center any distribution wherever you like on the number line by adding constant values to everything without altering its mean to the slightest degree, and likewise there are infinitely many distributions of the same shape and identical center that have different variances. The two are completely mathematically distinct. (This comes from the definition of SD: you subtract the sample mean away from each data point, so if both the mean and all the data points have been shifted by the same constant, that constant is cancelled out, leaving the SD unchanged.)

But was I defending the cap of 20? I was not. I was defending ASIs as a concept.

Only to then use these very racial ability bonuses as part of the defense. I'm done.

You should see Str 7 Orcs and Dex 7 Elves sometimes as well by that exact reasoning. The bell curve of population doesn't just stop dead at a level only four points below average. You should see the entire spectrum

I am done with this conversation after this, it's become circular and insistent on using math terms factually incorrectly, but this deserves specific reply.

You are incorrect, here, because by default rules that come even before that, such (sapient, playable) beings simply don't exist--the lowest ability score players can assign by point-buy or array is 8, and 5e doesn't have negative modifiers. Of course, if your generation method is rolled scores, yes! There should be at least the

*possibility* of a Str 3 orc or dragonborn, a Dex 3 elf, etc. They're fantastically unlikely for a variety of reasons, but they should in theory exist. (Rolling four 1s has a ~0.077% chance, or rather, exactly 1 in 6^4 = 1296 chance of getting it on any given roll. The chance of at least one stat of 3 in a group of 5 players (assuming they roll six sets of 4d6 drop lowest and never reroll or reject scores ever) is about 2.3% per campaign. You could alternatively say you expect at least one such character, on average, in about every 44 campaigns. Given most campaigns take at least a few months to wrap up, call it three months as a conservative estimate, that's roughly one appearance (on average) in 11 years of gaming, which would seem to fit the "extremely unlikely, but theoretically possible" definition as stated.