RPGs where your character miss...A LOT.

[A Black Falcon]

Well, from 3rd edition D&D and on, as you said, they mostly replaced "determine character stats with dice rolls" with "determine character stats with point-buy", which means that you can't get lucky and end up with a super-amazing character stats-wise, but also means that that element of randomness (and potential really bad stats, if you follow the rules for the pen & paper game and just take the first numbers you're given (though for the computer games, just trying again until your stats are higher is fine with me... :))) is gone.

So yeah, there's point buy. It's in most 3rd or 3.5 edition D&D computer games too (starting with Pools of Radiance: Ruins of Myth Drannor or, for Interplay games (and actual good RPGs), Icewind Dale II). I prefer die-roll stat-generation, myself, I think. :)

Technically you're supposed to roll a bunch of numbers, then decide which numbers go with which stats, without doing much rerolling... I think adjusting the numbers by moving points from one category to another might be okay, but yeah, you're not supposed to just keep rolling until you get great stats. But in the computer games, there is so much benefit to doing that, and no penalty, so I usually do that... but I don't think I would in the pen & paper game. Not that you have the choice, if you follow the rules for 3.5... though in the 3.5 campaign I played a few years ago, we did use die-roll stat generation and not point-buy. :) (Or maybe we could use either, and I did die roll? Not sure.)

I do like the eventual option to always have you start out with the max possible HP for your first level, though... it is kind of unfair to mages who start out with something like 1d4HP at the beginning of the game in D&D 1st and 2nd editions... that's such a small amount already.