Ability Score Distribution (more mathematical insanity)

[Misirlou]

Here is probability distribution for a 4d6 roll:

3: 0.08%
4: 0.31
5: 0.77
6: 1.62
7: 2.93
8: 4.78
9: 7.02
10: 9.41
11: 11.42
12: 12.89
13: 13.27
14: 12.35
15: 10.11
16: 7.25
17: 4.17
18: 1.62

Mean Ability Score value: 12.24

On average, a 4d6 array will have a point buy value of 28.72

 

[Misirlou]

Oh, also, I evaluated <8 scores by assigning -1 point for every two points below 8.

 

[stephenh]

You should also take into account that stats can be rerolled if they are considered non vaiable. I can't remember exactly how the PHB (or is it DMG?) defines non viable but it is something like at least one stat of 13 or better and ability mofifiers which add up to +1 or better. There was quite a bit of discussion on a thread about this a few weeks (maybe a couple of months) ago. I think the general agreement on this was that once you took this into account, the average point buy was around about 30-31.

 

[Thanee]

The chance to roll that low is rather slim, however, so it shouldn't have much influence, really.

In the end it boils down to be slightly better than PB 28, which makes it about equal to PB 28, since the latter gives more flexibility and thus should be a bit lower.

Bye
Thanee

 

[frisbeet]

Here's 5d6 drop two lowest. Neglected all that junk about failed character rerolls.

outcome	5d6
18	3.55%
17	7.84%
16	12.02%
15	14.29%
14	14.85%
13	13.57%
12	11.33%
11	8.55%
10	6.04%
9	3.81%
8	2.19%
7	1.16%
6	0.53%
5	0.19%
4	0.06%
3	0.01%