Rethinking Ability Score Generation

After some consideration of the TROLL charts and the probabilities involved, I realized that I lost the skewed bell curve with my above and below average charts.

Here's some new rules:

• Standard/Average: Roll 3d6. Discard the highest and lowest. Retain the remaining die.
  
• Below Average: Roll 4d6. Discard the highest and lowest. Retain the lowest of the 2d6 that remain.
• Above Average: Roll 4d6. Discard the highest and lowest. Retain the highest of the 2d6 that remain. Boxcars = 7.
  
• Way Above Average: Roll 5d6. Discard the highest and lowest. Retain the highest of the 3d6 that remain. Boxcars = 7, 666 = 8.

The "discard highest & lowest" rule preserves the bell curve effect. For example, here's "below average" (invert for above average):

Value	% =	% ≥	Probability graph
1	13.194	100.000
2	27.546	86.806
3	28.009	59.259
4	20.139	31.250
5	9.491	11.111
6	1.620	1.620

Average =	2.90046296296
Spread =	1.2329578139
Mean deviation =	0.997599451303

Compare that to the modifiers created by 4d6 drop the highest:

Probability distribution:

Value	% =	% ≥	Probability graph
1	5.787	100.000
2	29.707	94.213
3	37.577	64.506
4	21.219	26.929
5	5.324	5.710
6	0.386	0.386

Average =	2.9174382716
Spread =	0.990762073825
Mean deviation =	0.767008649596

The curves aren't identical but they preserve a similar average and a similar shape, specifically, the significant decrease in a likelihood of getting a "6."

We could create a smoother curve that closer approximates the 4d6 drop the lowest curve by doing something like "roll 6d6; drop the two highest and the two lowest; take the highest of the two that remain." However, I think you start to get into diminishing returns as far as time involved and perceived complexity. It will also increase player frustration to throw away their TWO highest rolls.