Concepts → Magic Missile vs Scorching Ray

Magic Missile vs Scorching Ray — when does auto-hit beat higher mean?

Both are 1st-tier blaster spells; both deal roughly comparable damage; one auto-hits, one rolls to-hit per ray. Magic Missile at L1 is 3d4+3 auto-hit; Scorching Ray at L2 is three rays, each 1d6 + spell-attack-modifier vs AC. The exact comparison depends on AC and spell-attack modifier, and the auto-hit on MM tilts the math more than most casters realise.

The setups

Magic Missile (1st level slot)

Three darts at 1d4+1 force damage each, no attack roll, no save. Total per cast: 3d4+3 guaranteed.

3d4+3

min 6 max 15

6 1.56%
7 4.69%
8 9.38%
9 15.63%
10 18.75%
11 18.75%
12 15.63%
13 9.38%
14 4.69%
15 1.56%

Scorching Ray (2nd level slot)

Three rays, each a separate attack roll vs AC, dealing 2d6 fire damage per hit. Mean per ray (assuming hit) is 7. Spell-attack-mod typically +5 at level 5 caster (proficiency +3, ability +2 to +4 depending on progression).

The complication: each ray is independent, so the *number* of rays that land follows a binomial distribution. We can't embed a panel for "3 rays vs AC 15 with +5 attack mod" directly — that's the multi-modal hit chain that's reserved for the typed-damage-plus-conditional-composition layer (see /concepts/ roadmap).

For the math below, we just compute hit chance per ray, then multiply by 3 for total expected rays landed, then by mean per-ray damage.

The math

MM damage: E[3d4+3] = 3·2.5+3 = 10.5 damage. Variance 3·15/12 = 45/12 = 3.75 (small — tight distribution). Force damage; bypasses most resistances.

SR damage against AC A with attack mod +B:

Per-ray hit chance: P(hit) = clamp((21 + B − A) / 20, 0.05, 0.95)
Expected rays landed: 3 · P(hit)
Mean damage per ray on hit: 2d6 = 7
Total expected damage: 3 · P(hit) · 7 = 21 · P(hit)

AC	Attack mod	P(ray hits)	SR expected damage	vs MM at 10.5
`12`	`+5`	70%	`14.7`	SR ahead by 4.2
`14`	`+5`	60%	`12.6`	SR ahead by 2.1
`15`	`+5`	55%	`11.55`	SR ahead by 1.05
`16`	`+5`	50%	`10.5`	tied — SR break-even
`17`	`+5`	45%	`9.45`	MM ahead by 1.05
`20`	`+5`	30%	`6.3`	MM ahead by 4.2

Crossover at AC ≈ 16 with a +5 spell-attack mod. Above that, the auto-hit on MM beats the SR mean despite SR using a higher slot.

The kill-probability angle (the lesson MM keeps winning on)

Mean DPR isn't the question if you need to finish a target at a specific HP. MM's variance is much smaller (3.75 vs SR's variance which depends on the binomial of rays-landed times damage roll — substantially higher). Below the SR mean, the higher-variance SR has the advantage; above the mean, MM's reliability wins.

Concretely: if you need to drop a target from 10 HP to 0, MM's P(deal ≥ 10) is ≈ 50% (roughly, since 10.5 is the mean and the distribution is symmetric around it). SR at AC 14 has expected damage 12.6 but the spread is huge — could land 0 rays (12% chance) and deal 0, or land 3 rays for 6-36 damage. The MM is more likely to deliver the kill on a single cast.

This is the same lesson as variance and kill probability: when your mean sits above the threshold, lower variance wins; when it sits below, higher variance wins. MM's 10.5 mean is right around the threshold for low-tier enemies; SR's higher mean covers more thresholds but with worse reliability per-cast.

The damage-type angle

MM does force damage. Almost nothing in the Monster Manual resists or is immune to force. SR does fire damage. Many planar / undead / fey creatures resist or are immune to fire. Against a fire-resistant target:

SR damage halved: per-hit damage drops from 2d6 to 1d6, expected per-ray to 3.5. Total expected at AC 14: 3 · 0.6 · 3.5 = 6.3.
MM unchanged at 10.5.

So against fire-resistant targets, MM beats SR even at low AC. This is the case for Mephits, lower-tier devils, Fire Elementals (immune), and a non-trivial fraction of mid-tier monsters. MM's damage type is one of its quiet strengths.

See split damage and resistance for the resistance math worked out in detail.

The slot-economy angle

MM is a 1st-level slot; SR is a 2nd. Upcasting MM to a 2nd-level slot adds one dart (4d4+4 = mean 14, vs SR's 14.7 at AC 12). So upcast MM matches SR at low AC and beats it everywhere higher.

The slot-economy argument: at low levels, your 1st-level slots are abundant and your 2nd-level slots are precious. Saving SR for emergencies and using upcast MM as your default single-target damage is the conservative play.

Try it yourself

↦ /strike/3d4+3 — Magic Missile L1 distribution ↦ /kill/3d4+3/10 — MM vs 10 HP target ↦ /strike/2d6 — single Scorching Ray hit