XCOM 2 weapon damage math — exact rationals for every shot

XCOM 2 splits each shot into four explicit outcomes — hit, crit, graze, miss. The displayed hit-chance hides what the variance actually looks like, especially once graze is in the model. Every weapon below links to the per-shot distribution as exact rationals — no Monte Carlo, no tooltip rounding, shareable URLs for every aim/cover combination.

The outcome model

In vanilla WotC, every shot rolls against four buckets:

Crit — full damage doubled (or +crit-bonus depending on class). Conditional on a hit: P(crit) = P(hit) · crit_chance.
Hit — full damage in the weapon's range.
Graze — half damage (floor). Eats into the miss probability — a 65% hit / 15% graze build has 80% chance of dealing some damage.
Miss — zero damage. P(miss) = 1 - P(hit) - P(graze).

Worked-out math, why graze matters more than its 15% suggests, and why crit-fishing on Sharpshooter has a different shape than crit-fishing on Ranger — see the XCOM 2 outcome model pillar.

Per-shot distributions, by weapon

Each row links to the live per-shot distribution. Damage ranges taken from typical mid-tier (mag) and late-tier (beam) configurations. Click a slug to open the panel with the exact rational mean, full PMF, and kill-probability curve.

Weapon	Damage range	Default shot	With graze	Notes
Assault Rifle (mag)	`5-7`	`1d3+4 @ hit 65 crit 10`	`1d3+4 @ hit 65 crit 10 graze 15`	Trooper class default, balanced range
Heavy Cannon (beam)	`8-10`	`1d3+7 @ hit 65 crit 10 graze 15`	`1d3+7 @ hit 65 crit 10 graze 15`	Grenadier class, single-target high damage
Sniper Rifle (mag)	`8-10`	`1d3+7 @ hit 35 crit 15`	`1d3+7 @ hit 35 crit 15`	Sharpshooter class, often low-percentage long-range shots
Shotgun (mag)	`6-9`	`1d4+5 @ hit 80 crit 30`	`1d4+5 @ hit 50 crit 10 graze 30`	Ranger class close-range, high crit
Pistol (sidearm, mag)	`5-7`	`1d3+4 @ hit 75 crit 50`	`1d3+4 @ hit 75 crit 50`	Sharpshooter secondary, opportunist build favours crit

The big aim-arc question — how much does +10 to-hit buy you?

A common Sharpshooter loadout question: is Squadsight's reduced crit chance worth the long-range positioning? Compare the same Sniper damage range at 35% hit (low-percentage flank shot) vs. 95% hit (full Squadsight overwatch chain):

1d3+7 @ hit 35 crit 15

min 0 max 13

0 65.00%
1 0.00%
2 0.00%
3 0.00%
4 0.00%
5 0.00%
6 0.00%
7 0.00%
8 9.92%
9 10.50%
10 11.08%
11 1.75%
12 1.17%
13 0.58%

1d3+4 @ hit 95 crit 25

min 0 max 10

0 5.00%
1 0.00%
2 0.00%
3 0.00%
4 0.00%
5 23.75%
6 26.39%
7 29.03%
8 7.92%
9 5.28%
10 2.64%

The 95% build has a tighter distribution and a real damage floor; the 35% build is a long-tail Hail Mary with most of its mass at zero. Mean-only comparisons miss the per-mission variance picture entirely.

Run-and-Gun bursts

Two-shot Run-and-Gun rounds convolve two independent shot distributions. The result skews heavier than the per-shot mean suggests because the worst case (zero hits) has probability (1-P(hit))² — small but non-zero, and the kill-curve at low HP is what determines whether you actually drop the target.

1d3+4 @ hit 65 crit 10

min 0 max 10

0 35.00%
1 0.00%
2 0.00%
3 0.00%
4 0.00%
5 19.50%
6 20.22%
7 20.94%
8 2.17%
9 1.44%
10 0.72%

1d3+4 @ hit 65 crit 10 attacks 2

min 0 max 20

0 12.25%
1 0.00%
2 0.00%
3 0.00%
4 0.00%
5 13.65%
6 14.16%
7 14.66%
8 1.52%
9 1.01%
10 4.31%
11 7.89%
12 12.26%
13 9.32%
14 5.83%
15 1.77%
16 0.94%
17 0.37%
18 0.05%
19 0.02%
20 0.01%

Bring your own shot

Any percentage shot the engine accepts: 1d3+4 @ hit 65 crit 10 for an assault rifle, 1d4+5 @ hit 50 crit 10 graze 30 for a half-cover shotgun shot, 1d3+7 @ hit 95 crit 25 for a clean Sniper Squadsight overwatch. Use the comparison tool to put two builds side-by-side. The engine handles brutal/dr postfixes the same way as the d20 attack path — XCOM 2 itself doesn't have those mechanics, but modded rulesets do.

Full grammar at /syntax.