Step Deviation Table

Remember. This excludes explosions. This will be filled in as the values matter. This is just to show how I got my numbers.
I will add to this as the numbers show up relevant so I don’t need to re-calculate the values.

Step	Dice Combination	Average	Standard Deviation	Average + 1 SD	Average - 1 SD
8	2d6	7	2.42	9	5
9	1d8+1d6	8	2.87	11	5
10	1d10+1d6	9	3.34	12	6
11	1d10+1d8	10	3.67	14	6
12	2d10	11	4.06	15	7
13	1d12+1d10	12	4.49	16	8
14	1d20+1d4	13	5.87	19	7
15	1d20+1d6	14	6.01	20	8
16	1d20+1d8	15	6.20	21	9
17	1d20+1d10	16	6.44	22	10
18	1d20+1d12	17	6.72	24	10
19	1d20+2d6	17.5	6.25	24	11
20	1d20+1d8+1d6	18.5	6.44	25	12
21	1d20+1d10+1d6	19.5	6.66	26	13
22	1d20+1d10+1d8	20.5	6.84	27	13
23	1d20+2d10	21.5	7.05	29	14
24	1d20+1d12+1d10	22.5	7.31	30	15
25	1d20+1d10+1d8+1d4	23	6.93	29	17
28	1d20+2d10+1d8	26	7.42	33	19
29	1d20+1d12+1d10+1d8	27	7.66	35	19
31	1d20+1d10+2d8+1d6	28.5	7.41	36	21
33	1d20+2d10+2d8	30.5	7.76	38	23
34	1d20+3d10+1d8	31.5	7.95	39	24
36	2d20+1d10+1d8+1d4	33.5	9.01	42	24.5
39	2d20+2d10+1d8	36.5	9.39	46	27

Put the following into Anydice:

output 2d6 \step 8\
output 1d8+1d6 \step 9\
output 1d10+1d6 \step 10\
output 1d10+1d8 \step 11\
output 2d10 \step 12\
output 1d12+1d10 \step 13\
output 1d20+1d4 \step 14\
output 1d20+1d6 \step 15\
output 1d20+1d8 \step 16\
output 1d20+1d10 \step 17\
output 1d20+1d12 \step 18\
output 1d20+2d6 \step 19\
output 1d20+1d8+1d6 \step 20\
output 1d20+1d10+1d8 \step 22\
output 1d20+2d10 \step 23\
output 1d20+1d12+1d10 \step 24\
output 1d20+1d10+1d8+1d4 \step 25\
output 1d20+2d10+1d8 \step 28\
output 1d20+1d12+1d10+1d8 \step 29\
output 1d20+1d10+2d8+1d6 \step 31\
output 1d20+2d10+2d8 \step 33\
output 1d20+3d10+1d8 \step 34\
output 2d20+1d10+1d8+1d4 \step 36\
output 2d20+2d10+1d8 \step 39\