This is odd to me, because when I offer players point buy vs 3d6, they pick point buy almost every time. So I have this theory that players pick 4d6, over point buy, because it lends itself to higher stats, and the randomness of rolling is just a red herring.
Well, let's unpack this a little. 3d6 vs point buy and 4d6 vs point buy are pretty different comparisons. Both point buy and 4d6 are methods that will tend to insulate a PC from very low stats. And with 4d6 being the
long-preferred convention (since 1e days), offering up 3d6 is going to seem relatively punitive to most D&D players. So it's no surprise that people want to avoid the 3d6 if offered an alternative, even if they tend to prefer a random method.
The desire for random results, while leavened by methods to make the lower results less likely, may not simply indicate a just a desire for higher stats since it may also indicate a desire for those stats to be independently derived. That's something random stats can do that point buy cannot because with point buy, any points going into one stat value will suppress the values of the other stats. You can't buff without nerfing, and that's an optimization process a lot of people don't necessarily like. Including me. I don't like it
AS A DM because I'm not too keen on my players inhabiting that mindset with such a small (but important) set of values.
Point buy has its place in character generation - in games where points buy virtually everything the character can do like Champions/Hero, GURPS, and Mutants and Masterminds. But just between the 6 stats of D&D? I think it does more harm to the play experience than good.
So now I offer point buy, 3d6 or free pick. That way it's clear what each person is actually after. And, not surprisingly, 3d6 is almost never the pick. This aligns with my theory, but the sample size of a few dozen players isn't exactly ironclad.
Of course people will take free pick over 3d6. That's pretty much a no-brainer because 1) you get exactly what you want, 2) you only get low results if you
want them, and 3) all of the stats values are independently derived from each other.