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

The 4-way split

Edition / mod note: the four-bucket model most cleanly applies under Long War 2, which ships an explicit graze band that eats from the miss side. Vanilla XCOM 2 rolls hit / crit / miss; graze only appears as a dodge-mediated demotion — when a hit lands on a target with a non-zero Dodge stat (Vipers etc.), the hit can be demoted to a graze. The engine's graze N% postfix supports both readings; pick the value that matches your scenario.

Each shot rolls against four buckets:

• Crit — full damage plus the weapon's flat crit-damage bonus. 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). Under LW2, eats into the miss probability; under vanilla, it's a post-hit dodge demotion against targets with Dodge.
• 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.

Crit damage convention: the engine defaults to 5e dice-doubling on crit (the d20 tabletop convention). XCOM 2's actual rule is a flat per-weapon crit-damage bonus (typically +2-3 depending on weapon, plus modifiers like Talon Rounds and the Biggest Booms perk) — not a multiplier. For approximate cross-build comparisons, cscale 150 forces the crit branch to ~1.5× base damage, which lines up with typical-weapon crit-damage shape but isn't the in-game formula. Use this page's panels to compare relative DPR shapes; absolute numbers will differ from in-game.

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, and the same reliable-vs-nuke tradeoff that picks 5e weapons applies here at the per-shot level.

Composes with

The four-way outcome model is the per-shot substrate. Layer these on top:

• Miss-streak protection. XCOM 2 modulates per-shot hit chance by recent misses; the streak / Luck-pool pillar covers the state-carrying Markov walk that the engine ships for this exact mechanic. The attacks N streak postfix composes with the per-shot hit / crit / graze grammar.
• 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 — exact across the displayed range. Bonus-dice weapon perks compose via the standard + NdM grammar.

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.

Where this matters in practice

The four-way outcome model and the variance picture it produces are the right substrate for a lot of tactical games beyond XCOM 2.

Phoenix Point / Xenonauts / Jagged Alliance. Same substrate — percentage to-hit, possibly with crit and graze buckets. The grammar transfers directly; only the number ranges shift. Per-shot damage distributions are exact rationals in the same form.

Sharpshooter aim-arc decisions. The 35% flank vs 95% Squadsight question is the per-shot version of the reliable-vs-nuke pillar. High-aim wins below the kill threshold; high-variance wins above. Mean comparisons miss the picture entirely.

BG3 magic missile vs scorching ray, transposed. The auto-hit-vs-roll-to-hit decision in 5e casters is the same shape as XCOM's "guaranteed-graze vs higher-variance shot" — the variance picture transfers, just with different numbers.