XCOM 2 weapon damage math — exact rationals for every shot

The recurring XCOM shot questions, in one click each

The per-shot math players keep re-asking. Each card links to either the live engine or the worked-out concept pillar.

• How does the four-way outcome model actually work?

  Hit / crit / graze / miss as exact rationals. Why graze matters more than its 15% suggests, and why the displayed hit-chance is a long-run average that hides per-encounter shape.

• 65% Assault Rifle — what's the real distribution?

  A standard mag-tier rifle shot at 65% to-hit, 15% crit, no graze. The full PMF, the conditional crit branch, and the per-mission variance picture.

• 35% flank vs 95% Squadsight — which shot wins?

  Same Sniper, two extreme aim profiles. The 95% Squadsight shot has a real damage floor; the 35% flank is a long-tail Hail Mary. Mean comparisons miss the variance picture entirely.

• Half-cover graze — does the 15% really change things?

  Graze isn't just "softer miss" — it eats into miss probability, turning a 65% hit / 20% miss into 65% hit / 15% graze / 5% miss. The full damage profile shifts more than the hit-chance suggests.

• Crit-fishing on Sharpshooter — when does +crit pay?

  High-aim Sharpshooter chains rack up +crit bonuses. Once P(crit | hit) crosses ~25%, the conditional crit branch becomes a meaningful chunk of expected damage.

• High-aim reliable vs low-aim nuke — which build kills more?

  Same expected damage, very different per-mission distribution. The reliable-vs-nuke pillar applied to the per-shot level — high-aim wins below the kill threshold, high-variance wins above.

• XCOM 2 streak protection — how much does it actually shrink miss-streak risk?

  The hidden mechanic that boosts hit chance after consecutive misses. Modeled as a state-carrying Markov walk over a 5-shot chain, with the variance-reduction picture worked out alongside Hard West's Luck pool (different state primitive, same family of variance softeners).

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.

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):

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.

Streak protection — the hidden RNG-fudging

XCOM 2 silently boosts a shot's effective hit chance after consecutive misses, capping the realistic miss streak well below what a fair coin-flip model would produce. The engine models this as a state-carrying Markov walk: each chain strike's hit chance is modulated by the current miss-streak counter, with the counter advancing on miss / resetting on hit.

Postfix grammar: attacks N streak. Per the Steam Community / Long War community datamining, the real rule is linear +15% (Commander) or +10% (lower difficulties) per consecutive miss, no cap, and the boost only activates when the base hit chance is ≥50%. The engine ships both rules: the streak preset uses the Commander +15-per-miss ladder, and the ≥50% gate is enforced at evaluation time so low-aim chains see no boost (matching the in-game behaviour). Worked-out math and the variance-reduction picture vs unprotected chains live in the Luck and streak protection pillar. Companion to /games/hard-west/ for the Hard West deterministic dodge-pool variant (different state primitive, same family of variance softeners).

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.