More actions
Probability for an attack to hit = (21 - AC + Mod)/20
Given average damage on hit is D,
Expected damage overall = (21 - AC + Mod)D/20
If using GWM/Sharpshooter, we take a -5 to the Mod and +10 to the damage.
Probability for GWM attack to hit = (16 - AC + Mod)/20
Average damage on hit is D+10
Expected damage overall = (16 - AC + Mod)(D + 10)/20
GWM thus does more expected damage at:
(21 - AC + Mod)D/20 ≤ (16 - AC + Mod)(D + 10)/20
Simplifying:
2 AC + D - 2 Mod ≤ 32
Given probability to hit without GWM P1 and probability to hit with GWM p2.
Average damage on hit is, respectively, D and D+10
GWM thus does more expected damage at: P1 D ≤ P2 (D + 10)
or,
(P1 - P2) D ≤ 10 P2
Whether the probabilities are fractions or percentages does not matter.
In a nutshell:
Given the chance to hit without <feat> P1, the chance to hit with <feat> P2, and expected weapon damage D, using <feat> would be expected to do more damage if (P1 - P2) D ≤ 10 P2 is true.