Rethinking Ability Score Generation

Hillary Eylül 22, 2022

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

13.194

100.000

27.546

86.806

28.009

59.259

20.139

31.250

9.491

11.111

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.