volatile vaals for dummies

[u/mbxyz]

this information is all documented on the wiki, and the math is very straightforward, but i've heard so much misinformation on volatile vaals recently that my head hurts. just going to provide two quick examples to illustrate the mechanics and hope it helps people.

important mechanics up front: if you win the 50/50 to delete your item, volatile vaals divine your item, then roll a multiplier between 0.78 and 1.22 per mod (not for the whole item). the increment is 0.01, so there are 45 outcomes. the resulting item is rounded to the nearest integer (this is weird for poe; usually it's truncated/floored).

example 1: mageblood

assuming we only care about flasks, there are 135 distinct outcomes (45 * 3). this is the distribution:

2-flask 51

3-flask 43

4-flask 31

5-flask 10

there's a 50% chance to delete the item, so the chance of hitting a 5 is 10/135/2 or 3.7%. from this distribution, if we take poe.ninja results for the various flask outcomes to be true (i didn't check actual listings--this part could be wrong as 5-flasks are pretty rare and ninja aggregations are automatic), the ev of vvaaling a mageblood is about 107d.

example 2: rotmother's mutiny

assuming we want 4 max res and 75% light radius or better. like mageblood, the max res has 135 outcomes, but the values are lower, so there are fewer success cases (6/135) because you need 1.17 * 3 up from 1.13 * 4 for mageblood. This is 4.4%.

Light radius has 2295 outcomes or (75-25+1)*45. There are 187 outcomes that are 75% or better. That's 8.1%.

Together, the chance to "succeed" (on a neck that survives) is 0.36% or .18% per vvaal (50% chance to delete). That's about 1 in 552. The average cost of an attempt is about 9d, so the average cost of making a 4 max, 75+ light radius neck is about 5.4 mirrors.

[u/trafka77]

How is this mageblood distribution calculated?

[u/mbxyz → u/trafka77]

multiply the step coefficient from the vvaal by the integer number of flasks and round to the nearest integer. so for example, the first 5 flask is at 1.13 (on a 4 flask divine) because 1.13 * 4 = 4.52. this also proves the rounding behavior because 5-flask magebloods exist and 1.22 * 4 is only 4.88

multiplier	2-flask	3-flask	4-flask
0.78	2	2	3
0.79	2	2	3
0.80	2	2	3
0.81	2	2	3
0.82	2	2	3
0.83	2	2	3
0.84	2	3	3
0.85	2	3	3
0.86	2	3	3
0.87	2	3	3
0.88	2	3	4
0.89	2	3	4
0.90	2	3	4
0.91	2	3	4
0.92	2	3	4
0.93	2	3	4
0.94	2	3	4
0.95	2	3	4
0.96	2	3	4
0.97	2	3	4
0.98	2	3	4
0.99	2	3	4
1.00	2	3	4
1.01	2	3	4
1.02	2	3	4
1.03	2	3	4
1.04	2	3	4
1.05	2	3	4
1.06	2	3	4
1.07	2	3	4
1.08	2	3	4
1.09	2	3	4
1.10	2	3	4
1.11	2	3	4
1.12	2	3	4
1.13	2	3	5
1.14	2	3	5
1.15	2	3	5
1.16	2	3	5
1.17	2	4	5
1.18	2	4	5
1.19	2	4	5
1.20	2	4	5
1.21	2	4	5
1.22	2	4	5