Divine Smite — when does burning a spell slot on a swing pay off?

The smite contribution per swing

Divine Smite (5e RAW): after a successful melee weapon attack, spend a spell slot to deal 2d8 radiant damage on a 1st-level slot, +1d8 for each slot level above 1st (max 5d8 at 4th). The smite is a rider on the attack — the engine's increment-(6) construct exactly. On a crit the smite dice double too, just like the base damage.

For a single longsword swing at +9 to-hit against AC 15:

• P(non-crit hit) = 14/20
• P(crit) = 1/20
• P(miss) = 5/20

The smite contribution per swing (1st-level slot, 2d8) is then:

(14/20)·E[2d8] + (1/20)·E[4d8] = (14/20)·9 + (1/20)·18 = 126/20 + 18/20 = 144/20 = 7.2

Added to the base 1d8+5 per-attempt mean of 147/20 = 7.35, the full per-swing mean with smite is 291/20 = 14.55 — roughly double. That's the headline "smite is huge" effect every Paladin guide opens with.

The base swing vs. swing-with-smite, side by side

The full per-attempt distributions show the shape change clearly: smite doesn't move the miss bar (no smite on a miss), it just stretches the hit / crit tails further to the right.

The crit-doubled tail is where smite earns its slot. On a base swing the crit deals 2d8+5 (mean 14); with smite at 1st-level the crit deals 2d8+5+4d8 (mean 32). The slot doesn't just add 9 damage on average — it adds 18 on the lucky 5% of swings.

Per-slot expected damage by slot level

Same single attack profile (1d8+5 @ AC15 +9), varying the slot level burned on the smite. Per-attempt mean grows linearly with the slot level, exactly as you'd expect from a linear damage rider.

Linearity falls out: each slot level adds 1d8 = 4.5 mean on a hit, scaled by P(hit-or-crit) = 15/20, plus the extra crit doubling on the 1/20 crit branch — (15/20)·4.5 + (1/20)·4.5 = 72/20 = 3.6 per slot level, exactly the column-to-column gap above. Upcasting is fungible at the table: one 4th-level smite ≡ four 1st-level smites in expected damage.

The slot-policy question — first-hit vs. only-on-crit

The per-swing math is settled — the player's actual decision is which hits to spend slots on. Two natural policies, both common at real tables:

1. Smite-first-hit: at the start of the round, commit to smiting whichever attack hits first.
2. Smite-only-on-crit: only spend a slot when the attack rolls a natural 20 (or 19 for Champion).

The two policies have wildly different per-slot efficiency because crit-doubling makes the same slot deliver twice the damage. Per slot spent, against the same target:

The constant 1.875× is exact: on a hit the smite is undoubled; on a crit it's doubled. The conditional probability of crit given that a slot is spent is P(crit) / (P(hit) + P(crit)) = 1/15 for smite-first-hit (so per-slot damage is (14/15)·X + (1/15)·2X = (16/15)·X), but 1 for smite-only-on-crit (per-slot damage = 2X). The ratio 2 / (16/15) = 30/16 = 15/8 = 1.875 is independent of slot level and base damage — a rare invariant in D&D math.

The catch — slot-spend rate

Smite-only-on-crit's 1.875× efficiency comes with a brutal caveat: you only spend a slot on the rare crit. With one swing per round, P(spend) is 1/20 = 5%; over a 10-round combat day you'd expect 0.5 slots spent. Most Paladins go to long rest with half their slots untouched under this policy — those untouched slots are 0-damage no matter how efficient they would have been.

Extra Attack at level 5 helps: P(at least one crit per round) = 1 − (19/20)² = 39/400 ≈ 9.75%. The crit rate doubles to ~19% against advantage, and to ~14% with Elven Accuracy's third die. Improved Critical (Champion 3, crit on 19-20) doubles the base crit rate. Stacking advantage + Champion 3 + Extra Attack gets a level-5 multiclass Paladin/Champion to about 36% spend-per-round on crit-only smite — comfortably enough to clear a typical slot inventory across a 6-encounter day.

For builds without the crit-fishing infrastructure, the realistic policy is hybrid:

• Smite on every crit (always 1.875× more efficient).
• Smite on the killing blow even without a crit (you need the HP burst to drop the target this round).
• Smite the last hit of a long combat to clear excess slots before short/long rest renders them moot.

The Extra Attack picture

Per-round (two swings, level 5+ Paladin) — same base profile, no smite vs. smite-on-each-hit (1st-level slot, 2d8):

The right panel is "spend a slot on each hit" — a worst-case profligate use. Per-round mean is 29.1, but it costs you a slot per swing that connects (~94% of rounds spend at least one slot, ~75% spend two). Compare against one slot at 4th-level on a single swing (1d8+5 @ AC15 +9 rider 5d8): same slot cost, same expected damage on the hit, but only one chance to crit-double. The "burst at higher slot vs. drip at lower slot" tradeoff is exactly the same shape as the Magic Missile vs. Scorching Ray question.

Sharpshooter and Smite — the multiclass stack

Smite is melee-only RAW, but Paladin/Hexblade and Paladin/Ranger multiclasses can carry equivalent on-hit damage riders into ranged builds. Hex (1d6 every hit, no slot cost) and Hunter's Mark (1d6 every hit, concentration) stack with smite as separate riders. Engine compose:

That's a Hex / Hunter's Mark profile — every hit picks up the flat 1d6 even without spending a slot. Free per-hit damage that lasts the whole combat (concentration permitting), at no slot cost beyond the initial 1st-level Hex/HM cast. The build-defining choice between "concentration on a buff" vs "concentration on a damage rider" turns largely on this number: flat 1d6 · P(hit-or-crit + small-crit-bonus) per swing per round, accumulated over the combat.

Try it yourself

↦ /strike/1d8+5 @ AC15 +9 — base longsword swing, no smite ↦ /strike/1d8+5 @ AC15 +9 rider 2d8 — 1st-level smite ↦ /strike/1d8+5 @ AC15 +9 rider 3d8 — 2nd-level smite ↦ /strike/1d8+5 @ AC15 +9 rider 4d8 — 3rd-level smite ↦ /strike/1d8+5 @ AC15 +9 rider 2d8 *2 — Extra Attack with smite each hit ↦ /strike/1d8+5 @ AC15 +9 rider 2d8 c19 — Champion crit-fish smite ↦ /vs/base/+smite — overlay the two distributions

Drop an HP value into any URL via ?hp=N to convert the per-attempt distribution into kill-probability against a target of that HP. Drop ?r=radiant:99 to model a target with high radiant resistance and watch the smite contribution shrink — most fiends and undead are vulnerable to radiant, not resistant, but the corner case is worth knowing.