User:Sky/GWMath

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.