[RPG] How does the Evocation wizard’s Empowered Evocation feature work with the Magic Missile spell

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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

Best Answer

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.

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