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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
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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").

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    \$\begingroup\$ It's always a good idea to summarise the relevant information in you answer here instead of just providing links. This allows your answer to remain viable even if the links change or corrode over time. \$\endgroup\$ – Purple Monkey Jun 26 '15 at 0:28
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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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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.

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    \$\begingroup\$ As per @Duragar Ironroc's answer, Crawford has answered differently, and his answers overrule those of Mike Mearls. That means this answer is no longer correct, unfortunately. \$\endgroup\$ – xanderh Jun 25 '15 at 22:35
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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.

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    \$\begingroup\$ Actually, given the wording of the spell doesn't combine the darts when the target of the three missiles is the same, I'm pretty sure the damage rolls remain distinct. You still have three targets, just the same creature targetted three times by three missiles. This reading is consistent with both the "once per target" Mearls tweet and the existing once-per-damage-roll wording of Empowered Evocation, whereas the "all missiles at one target means one bonus" requires a rewrite of the ability (as people are complaining on twitter). \$\endgroup\$ – SevenSidedDie Sep 2 '14 at 16:42
  • \$\begingroup\$ He also seems to contradict himself since for the Warlock power Agonizing Blast he says to add it to each Eldritch Blast even if they target the same creature \$\endgroup\$ – briddums Sep 3 '14 at 19:19
  • \$\begingroup\$ @briddums The difference is that each blast from Eldritch Blast requires a separate attack roll, whereas the Magic Missiles automatically hit. \$\endgroup\$ – Dyndrilliac Jun 22 '15 at 23:41
  • \$\begingroup\$ Can you give two examples to clarify? 1. For a single target 2. For multiple targets So I can make sure I fully understand. Thanks. \$\endgroup\$ – Night Owl Jun 28 '15 at 11:00
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    \$\begingroup\$ Its like fireball, roll a D4+1 add any bonuses then each dart does that damage, regardless of number of targets. \$\endgroup\$ – Voromir Kadien Jan 7 '18 at 15:19
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You guys are overcomplicating the situation.

Magic missile is an odd cat as it is a targeted spell with some of the properties of an AoE. But the rules still function normally when you add a little logic and don't intentionally try to break the game.

For every instance of Empowered Evocation, excluding magic missile, no target will ever take that damage more than once per casting. That is clearly the RAI, the obvious implication being each target gets damaged by the spell, and then takes bonus damage.

So it plays out like this. With an Int bonus of +4, I attack 2 targets with 3 magic missiles, 2 to target A and 1 to target B. Target B takes 1d4+1+4 damage, while target A takes 2d4+2+4 damage.

Like someone else posted, despite how many missiles you strike someone with, that's still one damage roll.

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    \$\begingroup\$ This answer is needlessly aggressive and would benefit from having the language toned down a bit. Especially since it's directly contradicting the guy who designed the game. \$\endgroup\$ – Erik Apr 30 at 7:25
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    \$\begingroup\$ Welcome to rpg.se! Take the tour and visit the help center to learn how things work around here. This answer could be improved by cited some evidence or ruling. "That is clearly the RAI" is disputable as per the other answers in this post. Additionally the aggressive and accusatory tone of this post isn't great. I suggest you tone it down a bit. Thanks for participating and happy gaming. \$\endgroup\$ – linksassin Apr 30 at 7:26

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