So, I’m really liking the idea of giving players the option to start with the standard array, an array of 14, 13, 13, 12, 10, 8 and a Feat, or to spend 4 points from their point buy for a Feat... But what if players want to roll stats? Any ideas how a DM might allow players to modify their rolls and get a Feat for it? 3d6 instead of 4d6k3 maybe? Any math magicians know how that would compare statistically to the lowered array and the 23 point buy?
As I replied,
elsewhere, you can use
AnyDice to tune the dice thrown, but first you have to frame the problem. AnyDice showed that the average array with 4d6k3 is 16, 14, 13, 12, 10, 9, (average 12.3, +6). The highest average 23 point array is 12, 12, 12, 12, 12, 11 (11.83, +5) and the most extreme is 15, 15, 13, 8, 8, 8 (11.17, +2). Compare that with 27 points, 13, 13, 13, 12, 12, 12 (12.5, +6) or 15, 15, 15, 8, 8, 8 (11.5, +3). It seems like you want to reduce the rolled array by about 0.5, +1.
So I think your question might be framed - what reasonable dice can I throw that averages about 11.8 and does not change the range? You suggested 3d6, but that is too penalising because it changes the average to 10.50.
1d6+3d6k2 gives about that, i.e. one die in the normal pool of four is rolled separately and must be kept.