That might be why some people feel the 4d6 method generates higher stats than point-buy does. On average the 4d6 method will give you 72 points, which is about same as the standard array--but most people who use point-buy will choose an array with fewer points.
As above, I think the bigger issue is that when we have already controlled for "at least one stat must be 14+, your sum-of-mods must be positive"
and "oh damn, that array sucks even if it
technically counts...ah, just reroll it."
Because 14 10 10 10 10 8 is technically a valid stat array (it has a net modifier sum of +1, and one 14), but most GMs I know would be very likely to say, "Eh....that sucks, and is a lot worse than anyone else's stats. Roll it again." Or something similar.
The moment you let squishy human preference push up the minimum floor, you open the door for rolls to significantly exceed PB. Because now it's not "one set of rolls vs PB". It's "2 or 3 or 4 or...(etc) sets of rolls, vs PB." And of course that's going to make values get bigger.
Personally, I think what this means is that stats should be determined by shuffled cards rather than rolled dice. Because the cards function as genuine randomness...that has the limits of point-buy. And you can even give extra cards of every number 1-6, that way GMs can tailor their stat generation the way they like. Want something 3d6-strict like? Use equal numbers of every card, or start from that and add in some extra 1s and 2s. Want strong stats? Favor big numbers. Etc. If you use only 18 cards, every array is guaranteed to have the same value; if you use more than 18, some "hands" might be more valuable than others, but never by more than a handful of points, enough to perhaps get an extra +1 here or there.
E.g. if the deck were 1+1+2+2+3+3+4+4+4+4+4+5+5+5+5+6+6+6, then you might get lucky and draw one 18...but that means your next-highest-stat can't be higher than 15, and if it
is 15, your third highest stat can't be higher than 12. A much more likely occurrence would be, say, {5,1,2}{4,3,4}{6,4,5}{4,5,1}{2,4,6}{5,6,3} = {8,11,15,10,12,14}--which is more or less the standard array. And while it's possible to get a mere 4 as one of your stats, the odds against that are pretty significant, and essentially guarantee that you'll have otherwise solid stats in other places (since that makes your second-lowest-possible score only 8.)
Still random. Still has the possibility of being assigned-in-order so you end up with a character you did not choose. Doesn't have various ills that dice-rolling would have. And is, to some extent, mildly realistic; few people are absolutely horrible at everything, few people are ridiculously amazing at everything, and
generally folks who have a significant deficiency in one area compensate for it by having developed themselves more in other areas (e.g. a blind person usually has better smell and hearing than a sighted person).
Rerolling stats is a house-rule (in 5E, anyway... it might be different in other editions.) The criteria for rerolling, if any, is up to your group.
If you're capping them at the low end, you should cap them at the upper end also. Otherwise you are shifting the graph... you're favoring higher results, as you said.
Yes, but folks don't see it that way. It's the exact same perception issue as the one that drives the 60%-65% hit rate thing.
A run of bad luck on your stat rolls feels bad to a much worse degree than a statistically-equivalent run of good luck feels good. A
run of bad luck feels more bad than a run of good luck feels good. (An ironic counter-pattern I've seen, though, is that good luck on a single pivotal roll has more good-feel impact than bad luck would have bad-feel impact. My guess is because we correctly "feel" the probability when it's one isolated single roll.) People don't cap the upper end because that feels like taking away """earned""" success, while capping the bottom end feels like preventing unearned suffering.
That's the sort of underlying secondary reason why I don't care for rolling. Most groups take several steps which make rolling
theoretically a lot better........but my luck continues to be bimodal, assiduously avoiding the center of the distribution to favor the two tails instead.
