Concepts → Great Weapon Master break-even

Great Weapon Master — at what AC does `-5/+10` stop being worth it?

The single most-asked min-max question in 5e: when does eating a −5 penalty to your attack roll for +10 to damage still come out ahead? It depends entirely on your attack bonus. The break-even AC follows a closed-form rule worth memorising — and the engine computes the underlying damage distributions exactly.

The setup

Great Weapon Master (the 2024 version, "Heavy Weapon Master" in some printings, but the −5/+10 trade is the same in both editions): when you swing a heavy weapon, you can choose to take −5 on the attack roll. If the attack lands, deal +10 damage.

The question is the same one every Fighter, Barbarian, and Paladin asks at character creation: does the trade pay off, or am I just missing more often for nothing?

The math

Two quantities matter:

Hit chance. Against AC A with attack bonus +B, you hit on a roll of A − B or higher on the d20 — so the base hit chance is (21 − A + B) / 20, clamped to the [5%, 95%] band that natural-1 / natural-20 enforces.
Expected damage on hit. The mean of your weapon damage roll. For a Greataxe with +3 STR mod, that's E[1d12+3] = 9.5. For a Greatsword with +3, E[2d6+3] = 10.

Damage-per-round (DPR) without GWM:

DPR_without = hit_chance(A, B) · E[base_damage]

With GWM, hit chance drops by 5 (because the −5 penalty is equivalent to facing AC A + 5), and damage gains a flat 10:

DPR_with = hit_chance(A + 5, B) · (E[base_damage] + 10)

Break-even is where these are equal — solve for AC and you get a clean rule.

The break-even table

Numbers below assume a Greataxe (1d12+STR) for the base damage. The break-even AC shifts by ~1 if you use a Greatsword (2d6+STR, mean 10) or a Halberd / Pike (1d10+STR, mean 8.5) — the headline pattern is identical.

Attack bonus (`+B`)	STR mod	E[base damage]	Break-even AC	Below this AC, GWM wins
`+5`	`+3`	`9.5` (1d12+3)	`≈ 13`	AC ≤ 12 — most early-game enemies, plus Knights
`+7`	`+4`	`10.5` (1d12+4)	`≈ 15`	AC ≤ 14 — covers low-tier monsters and most humanoids
`+9`	`+5`	`11.5` (1d12+5)	`≈ 17`	AC ≤ 16 — covers everything except plate + shield
`+11`	`+5` + magic weapon +1	`12.5` (1d12+6)	`≈ 19`	AC ≤ 18 — covers nearly every enemy in the Monster Manual

The pattern: break-even AC ≈ attack-bonus + 8 for a Greataxe-class weapon. With a magic weapon at higher tiers, GWM is essentially always on. At low levels with a mediocre attack bonus, it's only worth the trade against lightly-armoured targets.

The damage rolls themselves

The +10 isn't free — it shifts the entire damage distribution right by 10 points. Click into either panel to see the per-outcome rationals; tap a bar to read off P(damage = N) exactly.

1d12+5

min 6 max 17

6 8.33%
7 8.33%
8 8.33%
9 8.33%
10 8.33%
11 8.33%
12 8.33%
13 8.33%
14 8.33%
15 8.33%
16 8.33%
17 8.33%

1d12+15

min 16 max 27

16 8.33%
17 8.33%
18 8.33%
19 8.33%
20 8.33%
21 8.33%
22 8.33%
23 8.33%
24 8.33%
25 8.33%
26 8.33%
27 8.33%

Note the shape doesn't change — variance stays at (12² − 1)/12 = 143/12 for either roll, since the flat +10 is a constant offset. What changes is the mean and where the threshold-crossing probabilities land.

When GWM is wrong

Three regimes where the rule breaks down and the table above misleads:

You have advantage. Advantage on the attack roll changes the hit-chance math non-linearly — see advantage and disadvantage for the curve. Short version: with advantage, the −5 penalty is much less costly because you're rolling twice. GWM becomes correct ~2 AC points higher than the non-advantage table suggests.
You're using Bless or some other +1d4 to-hit floater. Each +1 to attack expected from Bless is roughly equivalent to facing 1 lower AC. Add Bless's mean (+2.5) to your effective attack bonus when reading the table.
The target has a kill threshold you're chasing. Mean DPR isn't the question if you need to finish a specific HP threshold in this round — see variance and kill probability. The +10 from GWM helps less than you'd expect when the target is below your single-swing maximum already; it helps more than you'd expect when the target is just above.

Try it yourself

↦ /vs/1d12+3/1d12+13 — base vs GWM, +3 STR ↦ /vs/1d12+5/1d12+15 — base vs GWM, +5 STR ↦ /strike/1d12+5 — Greataxe damage distribution

Drag the HP slider in any /vs view above. Below the GWM mean, the +10 is dominant; well above, the to-hit penalty starts mattering more — same logic as the kill-probability lesson applied per-attack.