This is my new character generation system that I just employed. I have 7 characters rolled so far. 5 have +12 ability modiers, 1 has a +11 and one has a +13. Essentially, they average out really, really nicely.
The trick is the combo of rolling, applying racial mods, and then using point buy to finish the characters off. You can add more points in step 6 to make more powerful characters. You can delete the rerolls of 1 in step 2 to get slightly lower scores.
Character Generation
1) Characters start with a 3 x 3 grid of possible stats. Across the top of the grid, you list Str, Dex, and Con, and down the side, you list Int, Wis, and Chr.
2) Roll 3d6 to fill the boxes, starting with the top left, moving left to right, top row, then middle row, and last row. When rolling, you may reroll any one 1, once. So if you rolled 5,1,1 you could reroll one of the 1's one time. If the reroll is a 1, then that 1 stands. Ability scores must be rolled in front of the DM.
3) Select six of the scores. Str must come from the Str column, Wis from the Wis row, etc. You may only choose a box score once. You will have three discarded "boxes" when you are finished.
4) If do not like these scores, you may scrap them for a 2nd attempt. If you dislike the 2nd attempt, you can scrap them for a 3rd attempt, but you must keep the final attempt. Once a set of ability scores is scrapped, you cannot go back to it if you don't like your new rolls. I've not had a player yet roll the third set.
5) Once you determine your initial stats, then apply racial modifiers. We are using Pathfinder races, so that usually means you get a +2 to a body score, a +2 to a mind score, and -2 to some racial weakness. Note, this is the only time you can raise a score to over 18. You can never lower a score below 3.
6) Once racial modifiers are in place, you can pick add ability points using the point-buy system. You get 6 points. Raising a 3 to 13 score by 1 costs 1 point. Raising a 14 or 15 by 1 costs 2 points. Raising a 16 or 17 score by 1 costs 3 points. You cannot raise a 18 or higher score using the point buy. You must spend all of your points.
Hope you try it. Let me know what you think...
Aluvial