The XCOM 2 outcome model — hit / crit / graze / miss

The 4-way split

Each shot rolls against four buckets:

• Crit — full damage doubled. Conditional on a hit: P(crit) = P(hit) · crit_chance. Cannot fire on a graze (RAW).
• Hit (non-crit) — full damage in the weapon's range. P(hit non-crit) = P(hit) - P(crit).
• Graze — half damage (floor). Eats into the miss probability — graze is a partial outcome that competes with miss, not with hit.
• Miss — zero damage. P(miss) = 1 - P(hit) - P(graze).

Engine syntax: 1d3+4 @ hit 65 crit 10 graze 15 writes a 5-7 damage assault rifle shot at 65% hit, 10% crit-on-hit, 15% graze. The engine computes the exact-rational mean and full PMF.

Where graze actually shows up in the math

A 65% hit / 15% graze build looks like "you hit 65% of the time" in the tooltip but actually splits as:

• P(crit) = 0.65 · 0.10 = 9.75% (= 39/400)
• P(non-crit hit) = 0.65 - 0.0975 = 55.25% (= 221/400)
• P(graze) = 15% (= 60/400)
• P(true miss) = 1 - 0.65 - 0.15 = 20% (= 80/400)

So the chance you deal some damage is 80%, not 65%. That's the graze contribution — soaking the bottom of the miss bucket into a half-damage outcome.

Side-by-side, same Assault Rifle shot without and with the graze model:

The mean shifts up modestly (graze contributes 0.15 · E[floor(dmg/2)]), but the bigger story is the 0-bar shrinking from 35% to 20%. For chained shots and per-mission momentum, "do I deal any damage at all" matters more than mean DPR.

The crit picture differs from D&D

In D&D 5e, crit is a face-range on the same d20 — nat 20 (or 19-20 with Champion) auto-hits and doubles dice. The same roll decides hit, miss, and crit.

In XCOM 2, crit is a separate post-hit roll. So:

• You can't crit a graze (different bucket entirely).
• You can't crit a miss (the hit roll has to succeed first).
• P(crit) is genuinely conditional — increasing hit chance also increases the crit rate, not just the hit rate.

Comparing a clean Squadsight Sniper Sharpshooter shot vs. a low-percentage flank attempt:

The 95%-hit Squadsight shot has a much tighter distribution with a real damage floor; the 35%-hit flank is a long-tail Hail Mary with most of its mass at zero. Mean comparisons miss this entirely — the per-mission variance picture is what decides whether the shot is worth taking.

What the engine doesn't model (yet)

Two important XCOM 2 mechanics that this Tier-3a substrate doesn't capture:

• Miss-streak protection — XCOM 2 fudges its RNG to reduce frustrating multi-miss runs. The displayed hit-chance is the long-run frequency, but per-encounter the actual P(hit_n) depends on misses 1..n-1. State-carrying Markov-chain extension is scoped (see docs/engine-extensions-queue-and-reactions.md in the repo) but not yet implemented.
• Damage-roll variance per bullet — XCOM 2's damage range comes from a uniform integer roll (5-7 = pick one of {5, 6, 7} uniformly), modeled here as 1d3+4. That's exact for the displayed range. Some weapon perks add bonus dice — those compose with the engine's standard + NdM grammar.

Phase 1 ships the percentage-attack family with hit / crit / graze. Phase 4 (open-ended) extends to stateful Markov chains for the streak-protection / Hard West Luck-pool family.

Build your own shot

The grammar for percentage attacks:

NdM[+K] @ hit <p>[%] [crit <p>[%]] [graze <p>[%]] [rider <expr>]

Trailing % sign is optional. Hit + graze must be ≤ 100. Examples:

• 1d3+4 @ hit 65 crit 10 — vanilla XCOM 2 assault rifle, no graze model.
• 1d4+5 @ hit 50 crit 10 graze 30 — shotgun through half cover.
• 1d3+7 @ hit 95 crit 25 — Squadsight Sniper with full overwatch chain.

See the XCOM 2 weapons page for pre-baked panels covering common loadouts. Full grammar reference at /syntax.