How does the Evocation wizard's Empowered Evocation feature work with the Magic Missile spell?

Question

The Evocation wizard's Empowered Evocation feature (PHB 177) reads:

Beginning at 10th level, you can add your Intelligence modifier to the damage roll of any wizard evocation spell you cast

I have an evoker with a 16 intelligence (+3 modifier). I cast Magic Missile as 1st level targeting 3 different creatures. Would I:

1. Add int bonus to each roll: 3 x (1d4 + 4)
2. Split int bonus equally between each: 3 x (1d4 + 2)
3. Split int bonus however I want: 1d4 + 1, 1d4 + 2, 1d4 + 3

If I cast Magic Missile as 1st level targeting 1 creature would I:

1. Add int bonus to each roll: 3d4 + 12
2. Add int bonus to the total damage: 3d4 + 6

Answer 1

I don't think this has been answered simply.

Jeremy Crawford has said the following about the Magic Missile spell:

It's one damage roll, just like fireball, but that roll can damage the same target more than once.

The specific rule this is taken from is (PHB p.196):

If a spell or other effect deals damage to more than one target at the same time, roll the damage once for all of them.

And the Magic Missile spell (PHB p.257) states that the missiles strike more than one target at the same time:

The darts all strike simultaneously

Thus the process is:

1. Assign a target for each magic missile created by the spell, you may target one creature more than once
2. Roll damage for the spell of 1d4+1 + [bonus]
3. Apply this damage to the target(s) once for each missile created
4. The missiles hit simultaneously and are each a separate source of damage for damage resistance or concentration rolls etc.

Thus any spell damage bonus from an ability such as Empowered Evocation (PHB p.177) applies once to the damage roll, but that damage roll is applied for each missile.

Answer 2

Jeremy Crawford has tweeted on this and according to him it is added to each bolt no matter how many targets. This is because you don't roll damage for each missile separately but only once for all the missiles and the sum total of that roll is then applied to each missile (as also explained on page 196 of the PHB).

So regardless of what spell level you cast Magic Missile at and how many targets you have, your one damage roll including Empowered Evocation would only be 1d4 + 1 + int mod (neglecting any other possible damage increases for the moment) and each missile would deal the total of that roll.

JC: Empowered Evocation does benefit magic missile's damage roll.

Q: So Scorching Ray gets +X 1 time per cast,but Magic Missile gets +X on every bolt?

JC: Correct. Magic missile is an oddball, in that it functions a bit like an area-damage spell ("strike simultaneously").

Answer 3

D&D 5e co-creator Mike Mearls unofficially answered this on Twitter: you add the bonus once per target. So if you target all the missiles at the same creature, you add the bonus just once; if you target them at different creatures you get the bonus on each target hit.

Answer 4

The damage is rolled once and all bonuses applied. The missiles can then target who they wish, dealing equal damage.
In the example: +3 INT bonus, roll 1d4, let’s say resulting in a roll of 2. 2 +1 +3 (INDt bonus) = 6, which would result in 18 damage if targeting one character.
Crawford states

it’s one damage roll just like fireball, but the roll can damage the same target more than once.

Answer 5

In your first scenario, the first circumstance is correct. In your second, the second is correct.

The difference here (as supported by Mr. Mearls' tweet linked in Johan's answer) is in how "damage roll" is implicitly defined.

In the first scenario, targeting 3 targets, there are 3 separate damage rolls (if you cast magic missile at higher levels against more targets, there are even more rolls). Since you roll the damage individually for each target.

However, there is only a single damage roll when you roll against one target, and as such you only attack the one creature.

In other words, the missiles aren't considered multiple attacks with discrete damage rolls unless they are targeted at several different targets.