3-18 and Modifiers

Rolling 3d6 to generate ability scores (or some permutation thereof) yields a score of 3-18 that has been retained by all versions of DnD since the earliest days.

OD&D had derived statistics based on these scores but they were inconsistent. AD&D was more consistent in that a score of 16+ tended to get you a bonus. 3E systematically set up intervals of 2 for standardized modifiers that applied to multiple things.

If I ever design/heavily modify a game using the 3-18 attribute scale, I think I'll use this scale for derived attributes:
0-1 -3
3-5 -2
6-8 -1
9-12 0
13-15 +1
16-18 +2
19-21 +3

This has the advantage of keeping modifiers small (minimizing the impact of random chance if you use random generation methods). It also has the mathematical flair of making each modifier kick in at the standard deviation. So a +2 modifier is two standard deviations above the norm (Z=2).

I would couple that with a 4 +/- MOD system for as many derived statistics as possible. That puts possible results into a nice 1-7 range, with most results tending to be 4-6 (assuming a 4d6 drop the lowest or similar stat generation system). Ideal for the Rule of Sevens.

For example:
Carrying Capacity = 4 +/- STR mod, measured in stones
# of Hirelings = 4 +/- CHA mod
# of Languages/Skills = 4 +/- INT mod
# of Fate Points = 4 +/- WIS mod
# of Healing Surges = 4 +/- CON mod