When I first started playing D&D, 3E was my first system. Initially, we played with random dice rolls for generating ability scores; it was what I was familiar with, after playing the Baldur's Gate and Icewind Dale video games (Baldur's Gate 2 came coupled with a 3E character generator, which sparked my interest in the PnP game). It was a year or so into our first game (still the longest game I've ever gotten to run) that we became dissatisfied with rolling ability scores; I believe one of the characters had rolled especially worse than the others, and one character had rolled especially better. We began using point buy.

Quickly after using the standard point buy array in 3E (was it 25 points?), we started to want bigger stats (4d6 drop the lowest always felt like it produced better stats than 25 point buy, since the rules said to throw out especially low rolls). To counter the higher stats for the players, I started giving monsters and NPCs better stats; the players had more fun with their higher stats, and I felt like the game was still balanced.

When 4E came out, point buy and static arrays were the baseline. It made characters balanced, but eventually I began to long to see more organic characters. We quickly discovered that 16, 14, 14, 13, 10, 8 was one of the better arrays: if your 16 and a 14 were put in your race's bonus stats, you'd have a +4, +3, +2, +1, +0, -1 modifier spread. Occasionally, you'd see someone push for a starting 18 (18, 14, 11, 10, 10, 8), or you'd get someone who spread out their ability bonuses (ending with 16, 16, 16, 13, 10, 8), but by and large everyone's stats were the same. Gone were the days of having a high strength wizard or a high charisma fighter.

I don't fully want to go back to rolling, but as a compromise I did think of this idea: Why not roll and use point buy at the same time? The idea is simple; begin rolling your stats, and keep a running tally of what your point buy total is. If you roll 5 scores and still have points left over, use those points to purchase your final score. If one of your rolls puts you over your total, decrease that roll appropriately and round out the rest.

Using 4E's point buy system, here's some stat arrays it could generate, using the 3.5 pointbuy system (modified to include low stats; rather than 25 base, this is 55 base):

Ability	Points	Ability	Points	Ability	Points
4	1	9	6	14	11
5	2	10	7	15	13
6	3	11	8	16	15
7	4	12	9	17	18
8	5	13	10	18	21

14, 14, 10, 6, 9; this leaves 17 points left over, so 15 points buys a 16, and the remaining 2 points over flow into the 9, increasing it to 11: 14, 14, 10, 6, 11, 16

15, 10, 14, 17; this set now has 6 points remaining, which could buy a 9 and a 3, or two 6's.

Any thoughts? Just a random idea really.

2d6+6? I mean, your system is cool and everything too, so whatever works

Because, at least in my opinion, most people won't chose to give their Wizard 17 Str unless they really like role-playing and have no interest in power-gaming. The randomization makes for some interesting characters that normally wouldn't be made. I just think it's a nice variation that adds a bit of chaos to the law of D&D (See what I did there? Hey-o zing!)

People won't give a Wizard 17 Str or whatever because it's not optimal to do that with the current point-buy system. However, if the goal of the game is to try to play some kind of unconventional character archetype, there's nothing stopping the group from deciding they're going to generate characters differently, to support that, like giving more points in the point-buy or coming up with a stat array for each class that is optimized except for some weirdness like that, or... well, whatever they want, really. Like I said, just make one. Randomly rolling stats just removes any player choice, which is not necessary in the least.

I understand what you're saying but I just feel completely differently about it. I guess randomly throwing some dice can create archetypes you wouldn't have thought of, but look at that list of examples you gave-- you just thought of three cool archetypes right off the top of your head, so it's not like it's that hard to generate interesting character archetypes without resorting to pure randomness. And, you know, throwing dice wouldn't even give you that level of depth, you'd have to come up with the background touches like "can understand chaos theory" yourself, the dice would just say "You get Int 16."

So, to make a comment that fits the original topic of the thread, personally, I dislike any sort of random stat generation at all. 

To make a comment that fits the OP, I consider the rolling of dice to represent the chaos function/randomization effect of a game, whether it be in chargen or in the game itself. 
The random part of the game, and the way players respond to it, is part of the unknowability of the game.  I have often allowed PCs to change one or two things to fit an archetype or ideal....but I have always found, with dozens of gamers and literally hundreds of PCS, that the most fun characters develop, as Xev mentions, organically.    All the time.
Yes.  After a while, sincde the mindset it to 'manufacture' instead of 'respond to', of course most players go similar routes.

This is treading dangerously close to the old "rollplayer vs roleplayer" false dichotomy.

In a role playing game, all characters are "manufactured." Players generally show up to the game with some idea of what the game's genre, milieu, and so on are going to be, and some idea how they are going to want to fit into that world. Naturally, these players would like for the mechanics to support them being able to play that chosen character archetype. If they don't, the player probably won't be too engaged in the game, because nothing takes you out of an RPG faster than being stuck with a character you don't really want to play. Sure, sometimes players just don't know or don't care, and at that point, maybe a bit of randomness is fun. But they usually have some idea, and in those cases, not allowing players to "manufacture" their characters (at least to some extent) is simply a recipe for a disappointing game all around.

I see what you are saying here, but I don't think this really has anything to do with how the stats are generated. All point buy or an array do is attempt to assure some degree of mechanical balance, so the guy with all 3's isn't stuck in the party with the guy with all 18's. It's just a starting point. Beyond this, the character generation process can and should be organic. I'd also say it's not just players taking "what they are given" but rather an exchange of ideas-- the GM building the world around the characters while the players build their characters to fit in the world.

A true partnership. Doesn't that better fit your "sex" analogy anyway? 

Yes, that's what I meant. There seems to be a certain belief going around in some circles that "real roleplayers don't care about stats" or "character optimizers are all munchkins who don't roleplay" or whatever, and of course this is nonsense.

That goes back to my initial point. I just don't buy that interesting/weird/off the beaten track characters necessarily require any sort of randomization in order to be created. All it takes is the spark of an offbeat idea-- a random roll can give that, sure, but all that background that really makes the offbeat character so compelling doesn't come from the roll. And it's certainly possible to make a character like that by design, too, and even do something weird with the stats so they look more "organic," while still preserving some semblance of game balance.