I don't see how you reach that conclusion. The character who hits on 10 rather than 11 has a 10% higher success rate.Let's try to break this down, because this is your first core mistake right here. "Depend heavily upon stat modifiers."
Looking at the mechanics of D&D we can see the following:
To Hit = d20+proficiency+stat mod+weapon mod vs. AC value in most cases. If you have one PC with a 15 in a stat and another who rolled a 16, all else being equal for say a 1st level PC against an AC opponent, you'd have:
d20+2+2 vs AC 15. On a 1-10 he misses, on an 11-20 is a hit
d20+2+3 vs AC 15. On a 1-9 he misses, on a 10-20 is a hit
Seems to me that the odds on hitting the target do not "depend heavily" on the stat difference
And suppose one character's stat in the comparison is 15 (+2) and another's is 18 (+4) then the success rate for the stronger character is 20% higher (succeed 12 in 20 rather than 10 in 20).
It's been shown that the expected result from rolling is higher than that from point buy, hasn't it?And that's even assuming that the person who rolls random stats will always have higher stats than the point buy or array, and that's already been demonstrated to not be true.
In any event, I'm not talking about expected values. I'm talking about actual values. If two players roll their stats, and one gets a 15 as the highest and another an 18, the expected results are irrelevant. One of those players has a greater capacity to impact the fiction, via action resolution, than does the other.
I don't see how this is relevant to my point. Choosing whether to use array or take a gamble on starting conditions - ie the distribution of stat modifiers - doesn't make the outcome of those starting conditions fair. As I said upthread, if the point of the game is to play the same PC for a long time and thereby impact the fiction, the fact that players A, B and C all had the same opportunity to roll a powerful or an underpowerd PC is irrelevant to the fact that the person with the powerful PC has more capacity to impact the fiction, and the one with the underpowered PC has a lesser capacity. And it is those differening capacity which, given the point of the game as I play it, that are unfair.I imagine a typical response you (or someone else) might have to this is, "No, not every stat should be the exact same, but the pool of stat bonuses should be, and the players can choose where to put them." yes, that's true. But the players also choose whether to use array, point buy, or random rolls.
I have neer said that a player who demands that every PC at the table has the same exact score isn't fair. Nor have I said that such a player is fair. I haven't said anything about players demanding anything. That's your word.This sentence above seems to imply that a player who demands that every PC at the table has the exact same score for each of the abilities as every other PC at the table, that is not an immature behavior, and isn't fair*.
I've said that, in a game which (i) is expected to run a long time, and (ii) is expected to be driven by the player's engaging in action resolution, it is not fair if one player has a greater cpacity to impact the fiction via action resolution. And the fact that, at the start of the game, each player had the same chance to roll those better stats is irrelevant to this unfairness.
Why is it unfair? Because it is an inequality in capacity to play the game (by impacting the fiction via action resolution) and that inequality is arbitrary. It is nothing but the result of random rolls made at the start of the game.
I don't really follow this.every PC makes every type of stat roll at some point in the game, whether it be an attack roll, a saving throw, or an ability check. You're talking about how an ability modifier "endures over the course of a game", and how every PC should have the same equality in that measurement. That means, and is dependent on, every PC having the same ability modifier (equal chance) for every one of their stats since every stat is used "over the course of the game."
First, a small thing: it is players who make rolls, not PCs.
Second, different players use their PCs to impact the fiction in different ways. Classes are an important part of this. If player A is playing a rogue, his/her PC's DEX is more important than his/her PC's CON as far as impacting the fiction goes; if player B is playing a fighter, his/her PC's STR is similarly more important than INT; etc.
So it's simply not true that unless all PCs have identical stats their players can't have equal capabilities to impact the fiction.
No it's not.If everyone was given the same choices, complaining about a player who chose to roll and got a higher stat as unfair is literally the same thing as complaining about a player who chose to put his +2 modifier in dexterity when you chose to put a +0 modifier there (both using the same arrays) when you both have to make a dex saving throw.
In the case of the DEX mods, the player who put a 10 into DEX will have put a better score into some other stat, and will - during the course of play - be able to get the benefits of that better score.
Whereas the player whose stats are just superior, due to lucky rolling, has achieved the better prospects with respect to one stat without trading off against other stats. S/he is just better equippped to successfully engage the action resoution mechanics. And hence has an unfair (because arbitrary and unwarranted) advantage in playing the game.
Nonsense. For instance, if every PC has 18 STR and 6 INT, then the players playing fighters would have a better chance to impact the fiction via their PCs than would the players playing wizards.where do you draw the line?
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Basically, in order for your argument to have any sort of weight, you have to get rid of random rolling altogether in the game, and every PC would have to have the exact same stats.
Even within the same class, too, different approaches to build can prioritise different stats.
That doesn't mean that there is no meaningful scope for comparing capacity to impact the fiction.
As far as random rolls are concerned, if every player is getting to roll the dice with every action declaration, then no player is going to be systematically disadvantaged relative to the others (assuming that all are rolling fair dice in an honest fashion).
Of course, if you play a different sort of game, in which action resolution mechanics are not very important, then fairness and unfairness will be different again. But that's not a refutation of my point - it's a reiteration of it!
I find it interesting that you keep talking about "to hit rolls" when I have talked consistently about action resolution. That is more evidence that we approach the game in quite different ways.the success of a to hit roll is a lot more heavily dependent on a random d20 roll than an ability modifier, and the only way to achieve "equity over the course of the game" is to eliminate randomness and make everyone the same.
Putting that to one side, your statement is obviously wrong. To achieve equality of capacity to impact the fiction over the course of the game you don't need to eliminate randomenss. (Of course, you might, but you don't have to.) You just need to make sure that every player has roughly the same range of opportunities to declare actions and roll dice to resolve them, and to make sure that there are enough such opportunities that every player will roll lots of dice, and hence won't be saddled with the results of just a small number of unlikely outcomes.