Concepts → Split-typed damage and resistance
Splitting damage across types is a hedge against resistance
A flaming sword does 1d8 slash + 1d4 fire instead of
1d12 slash. Same dice budget, similar mean — but the
flaming sword keeps doing damage when the target is slash-resistant.
Split damage trades a tiny bit of expected output (in the no-resistance
case) for a huge insurance payout against type-specific resistance.
The setup
Two attack profiles, same dice budget (2d6) and same mean (12):
-
Mono:
2d6+5slashing. Range 7–17, mean 12. -
Split:
1d6+5slashing +1d6fire. Range 8–17, mean 12. Same dice rolled, just one of them is fire instead of slashing.
Vs an unresisted target the two profiles produce essentially identical kill probabilities — same mean, similar shape. The interesting case is when the target resists one of the types.
Worked example: how the mean shifts under resistance
5e "Resistant" halves damage of the resisted type (rounded down per
outcome). For percentage resistance (Diablo / PoE / Last Epoch
style) the engine uses floor(damage × (1 − pct/100))
per outcome. Numbers below are exact-rational means, hand-derived
from the engine's per-component math:
| Slash resist | Fire resist | Mono mean | Split mean | Winner |
|---|---|---|---|---|
| 0% | 0% | 12 | 12 | Tie (same mean, same shape almost) |
| 50% | 0% | 23/4 = 5.75 | 15/2 = 7.50 | Split by 1.75 |
| 50% | 50% | 5.75 | 5.5 | Mono squeaks ahead by 0.25 |
| 100% (immune) | 0% | 0 | 3.5 | Split — only split lands at all |
| 0% | 100% (immune) | 12 | 17/2 = 8.5 | Mono — fire portion wasted |
The pattern: split wins when one type is heavily resisted and the other isn't. Split ties or slightly loses when neither type is resisted, or both are resisted equally. It's an information hedge — when you don't know which type the enemy will resist, the split distribution of damage is the lower-variance bet.
The math: per-component resistance is multiplicative
For mono damage D against r% resistance:
E[damage_taken] = E[D] × (1 − r/100)
For split damage D₁ + D₂ against per-type resistances
r₁ and r₂:
E[damage_taken] = E[D₁] × (1 − r₁/100) + E[D₂] × (1 − r₂/100)
When the means are equal (E[D₁] = E[D₂] = E[D]/2) and
both resistances are equal (r₁ = r₂ = r) the two formulas
collapse — split has no advantage. As soon as r₁ ≠ r₂,
split's lower variance pays off: it takes the average resistance, while
mono is fully exposed to whichever resistance the target happens to have
against your one type.
(The actual engine math floors per outcome rather than per expectation, so the numbers diverge slightly from the closed-form means above — especially at small dice. The qualitative story is identical.)
Try it yourself
Where this matters in practice
-
Baldur's Gate 3 and 5e flame-tongue / frost-brand weapons
— the
+1d4elemental rider isn't just bonus damage; it's a hedge. Against a slash-resistant golem the elemental portion carries the swing. Worth more on enemies with high physical resistance, less against enemies with broad elemental resists. - Diablo 4 / Path of Exile elemental builds — pure fire builds wreck cold-vulnerable trash but fold against fire- immune rares. Mixed-element builds (lightning + cold + fire) trade peak DPS for resistance-agnostic consistency. Same math, different scale.
- Multi-attack mixed-weapon strategies — a Smite-loaded warhammer (radiant rider) into the same target as a flame-bound dagger (fire rider) covers more resistance bands than two of the same weapon would.
-
Spellcaster element selection — choosing
Chromatic Orbover a fixed-element spell is exactly the hedge: you pay a small caster-level cost to pick the type at cast time, which is the most extreme version of split damage (perfect resistance information at the cost of one die).