D&D 5e damage math — the recurring questions, answered exactly

The recurring questions, in one click each

The math everyone's already arguing about. Each card is a direct link to either the live comparison tool or the worked-out concept pillar.

• Greataxe (1d12+3) vs greatsword (2d6+3)?

  Same mean within half a point, very different shapes. Drag the HP slider — greatsword wins below the mean, greataxe wins above.

• Should I take Great Weapon Master?

  Closed-form rule: break-even AC ≈ attack-bonus + 8 for Greataxe-class. With +9 to-hit and a magic weapon, GWM is on against everything except plate-and-shield.

• Sharpshooter break-even AC?

  One AC point lower than GWM: attack-bonus + 7 for Longbow. And at long range, Sharpshooter is correct almost regardless of AC.

• Magic Missile or Scorching Ray at level 5?

  Crossover at AC ≈ 16 with +5 spell-attack mod. Above that, MM's auto-hit reliability beats Scorching Ray's higher mean — and force damage beats fire against a chunk of the Monster Manual.

• GWF reroll — placebo or real?

  Real and not small: ~+0.83 mean on Greataxe, ~+1.33 on Greatsword for the canonical reroll-on-1-or-2 (≈+11% on Greatsword DPR). Plus a quiet variance reduction that helps above the mean and hurts below it.

• Divine Smite — when do I burn the slot?

  Smite-only-on-crit delivers exactly 1.875× more damage per slot spent than smite-first-hit, across every slot level. The constant falls out of crit-doubling — and Champion 3 + advantage is the build that actually clears its slot bag.

• Elven Accuracy worth the +2 ASI?

  Yes if you're at advantage on more than ~30% of attacks. Mean of 3d20kh1 is exact: 1239/80 = 15.4875, and crit rate jumps to ~14% on advantage rounds.

• Champion Fighter crit-fish — does it pay?

  Sometimes. Two builds with identical expected DPR can have very different per-target kill rates — the variance pillar applied to one weapon's crit profile.

• Advantage — really +5 to hit?

  Only at the middle of the AC range. Advantage is worth ~+3 to +5 in the AC 12–16 band, much less at the extremes. The full curve, worked out per AC.

• 3d4+4 vs 1d12+5 — same mean, who kills first?

  Both 11.5 mean. Reliable 3d4+4 wins below the mean; nuke 1d12+5 wins above. Crossover sits exactly at HP 12. The textbook variance paradox.

• 2d6+5 vs 3d4+4 at HP 11 — the upset

  The lower-mean roll wins kills 72.22% to 68.75%. Higher variance helps when the mean sits below the threshold. The single most counterintuitive result in dice math.

• Strahd at level 10 — how many rounds?

  Plan for 3–4 with a typical party at 50–70 aggregate DPR. The renewal-theorem floor is 144/60 = 2.4 rounds; variance pads the realistic count.

• Expected strikes to drop a boss?

  Once HP is past your single-strike maximum, mean wins linearly: E[N] ≈ HP/μ + bounded constant. Variance washes out into a half-strike correction.

5e quick-reference — what AC are we even talking about?

Diceplots' kill-probability questions all bottom out at "what AC and what attack bonus?" Use this as a calibration sheet when you're plugging numbers into the break-even pillars.

Pair these with the GWM break-even table (break-even AC ≈ attack-bonus + 8) and you can read off "is GWM on against this monster?" without doing the arithmetic. At mid-tier with +7 to-hit, GWM's break-even is AC 15, exactly the median of the band.

5e 2024 Weapon Mastery — what the engine models

The 2024 PHB introduced eight Weapon Mastery properties (Cleave, Graze, Nick, Push, Sap, Slow, Topple, Vex). Their interaction with damage math splits into three groups:

• Modeled directly: graze<N> (Graze — common assignments include Greatsword, Glaive) — flat damage equal to your ability modifier on a missed attack. Adds p_miss × N to the per-attempt mean. At moderate AC the DPR uplift is 10–15% over the same weapon without the property; at high AC it's larger because misses dominate.
• Modeled directly: chase N (Vex — common assignments include Shortsword, Rapier, Dart, Shortbow, Hand Crossbow) — N-attack chain where each attack k+1 gets advantage if attack k hit. 2-state Markov walk; engine handles the joint distribution. The full weapon-to-mastery table is in the 2024 PHB Equipment chapter.
• Modeled via aoe primitive: Cleave (Cleave weapons include Greataxe and Halberd — extra attack vs a second adjacent creature on hit) and Nick (Nick weapons include Dagger — extra attack as part of the attack action when wielded as a light off-hand, against a different target) — these are independent attacks against separate targets, modelled as aoe N each H (Binomial kill count). NOT attacks N, which pools HP and over-counts the kill probability by ~3x for grouped enemies.
• Positional / state — out of damage scope: Push (10ft), Sap (target's next attack rolls disadvantage), Slow (-10ft speed), Topple (CON save vs prone). These affect tactical positioning and downstream attack rolls but don't directly add damage. If you want to model their downstream effect, adjust the next attack's hit% / disadv flags accordingly.

2024 Rogue Cunning Strike (trade Sneak Attack dice for effects: Disarm, Knock Prone, Trip, Withdraw, etc.) — the engine's sneak Nd6 postfix takes the die count directly. To model "I spent 1 sneak die for Knock Prone, dealt damage with the rest," reduce N accordingly: sneak (N-1)d6. The effect side (prone, disarm, etc.) is positional and doesn't add to the damage math.

Empowered Evocation × Magic Missile (2024 Wizard 10): adds Int mod damage to one missile per cast. By sum-linearity (each missile rolls independently and they sum), adding Int mod to one missile is identical to adding Int mod to the total — write 1d4+1 attacks N + IntMod for a slot-N missile cast with EE. (For 2014 tables playing the older Crawford shared-roll ruling, the per-missile model and the engine pillar's note both apply.)

Common 5e weapons, with the means computed

All means assume a +3 ability modifier (mid-game STR or DEX 16). Add 1 or 2 for higher modifiers. Click any expression to open the full distribution — including the per-outcome kill probability for any HP target.

Ranged:

Bring your own question

The grid above is what gets re-asked. The comparison tool handles anything you can write — 2d6r1+5 for Great Weapon Fighting, 2d20kh1 for advantage, 3d20kh1 for Elven Accuracy, 1d8:slashing+1d6:fire+3 for typed-damage hedges with per-type resistance via the ?r= query parameter. Full grammar at /syntax.

No accounts, no ads, no on-device tracking. The math runs client-side via a Rust engine compiled to WASM; the same engine ships in the iOS and Android apps with bit-identical results.

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