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The rogue has the Uncanny Dodge class feature, which says this (PHB, pg. 96):

Starting at 5th level, when an attacker that you can see hits you with an attack, you can use your reaction to halve the attack's damage against you.

As pointed out in the answers to this question, if an attack has multiple damage types, you half all of it. So consider the Spiked Bone Club attack of the Grimlock (MM, pg. 175):

Spiked Bone Club. Melee Weapon Attack: +5 to hit, reach 5 ft., one target. Hit: 5 (1d4 + 3) bludgeoning damage plus 2 (1d4) piercing damage.

The Grimlock attacks the level 5 rogue and hits, and the DM rolls damage. The first d4 gives a 2, giving a total of 5 bludgeoning damage, and the other d4 gives a 3, giving a total of 3 piercing damage. The grand total is 8 damage.

Given that damage is rounded down when halved, do we:

  • round each individual total down, which in this example is (5 / 2) + (3 / 2) = 2 + 1 = 3?
  • round down the grand total, which in this example is (5 + 3) / 2 = 8 / 2 = 4?

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Uncanny Dodge halves the individual types

The wording doesn't use reference to damage types or to the concept of resistance, so you're not reducing the damage because you're resistant to it, but rather because you're quick and agile and can dodge the brunt of it.

The Jeremy Crawford Tweet that Grosscol's answer mentioned uses language that lumps the damage into "one big damage roll," which is what this feature affects. All of this would suggest that you could halve the total and be done with it, however:

Resistances/vulnerabilities are calculated last

Resistance and then vulnerability are applied after all other modifiers to damage. - (PHB 197)

This means that you have to apply Uncanny Dodge before you apply any resistances or vulnerabilities. This is impossible without abandoning rounding in any cases involving odd numbers. In order to be able to apply Uncanny Dodge before an effect that alters individual damage types, you must apply it to those individual types too!

For example:

An Ice Devil (MM 75) hits Bobby with it's Claws, dealing 9 slashing damage and 11 cold damage.

Bobby, a level 10 rogue, is wearing the Boots of the Winterlands (DMG 156) giving him resistance to cold. He also uses his Uncanny Dodge ability.

Resistance is calculated last, so we must calculate Uncanny Dodge first. If we halve the total (20) for 10 damage, what damage is halved by cold resistance? If instead we halve both individually (4 slashing, 5 cold) then we have a cold type damage value (5) to halve at the end using resistance.

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  • \$\begingroup\$ This answer deals with a closely related but different issue - in this case, we aren't dealing with resistance. In the linked question, while it's an unusual example, the resistance granted replaces any resistances the creatures would otherwise have, as multiple instances of resistance do not stack. \$\endgroup\$ – Isaac Reefman Aug 24 '18 at 6:53
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The fastest method is to halve the total damage; by the time a character has Uncanny Dodge, half a Hit Point here or there shouldn't really matter all that much.

However, this fails to take into account characters who may be resistant to some or all of the damage:

  • A flame tongue swords hitting a Tiefling or non-Bear Raging Barbarians...
  • A spiked bone club hitting a character with the DDAL Season 4 Dark Gift that provides resistance to only bludgeoning damage...
  • Etc, etc, etc...

The most consistent method would be to halve them individually. There would be no issues on characters with or without resistances. After all, by the time a character has Uncanny Dodge, half a Hit Point here or there shouldn't really matter all that much.

Which is the right way is for your table to decide. I've played in games done both ways. Personally, when I run games... I let Fantasy Grounds' automation handle resistances, and then just halve the resulting damage for Uncanny Dodge (because it isn't automated).

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Half of the Total Damage of the Attack

tl;dr all damage is consolidated per attack. Take half of the total.

Attack Damage is "One Big Roll"

JC tweet

When something in the game (Sneak Attack, Divine Smite, hex, etc.) causes your attack/spell/etc. to deal extra dice of damage, those dice are added to the damage the effect is already dealing, if any. It's one big damage roll, extra damage included.

Treating the damage of an attack as one big roll is consistent with halving the total damage of an attack. This is the correct calculation for 5e and is simpler to boot.

Separate Calculation is NOT Equal

Due to rounding down in 5e, applying half damage to two damage types that are part of the whole could result in less than half total damage. For example:

An attack does 7 piercing and 3 fire damage. Total damage 10.

  • Half of the total is 5 damage.
  • The sum of halving parts is 4 damage (half of 7 rounds to 3 and half of 3 rounds down to 1).
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The only reasonable answer is that each damage type is halved individually, because the alternative means you have to lose track of what amount of damage of each type you're doing, and 5th Edition does not support damage that has multiple types (you can't do 'piercing and fire' damage or similar) or no type. You have to be able to attach a type to the damage dealt, and mixing different types of damage before halving it would obscure that information.

That is to say, if you add it all up and divide the total by 2 (to get 8/2 = 4 in your example), you've lost track of what damage type it is (or how much of the damage dealt is each type), and that's not allowed.

When the uncanny dodge is the only thing altering your damage total, it may not look like it makes much difference, but the answer to how to halve damage needs to continue to support other effects that depend on damage type. It would be unreasonable to use one algorithm when there's no relevant damage-type-related effects than when there are; the math should not change just because a later step does or does not exist.

By halving down each damage total individually -- the "(5 / 2) + (3 / 2) = 2 + 1 = 3" version -- it's clear what's what; you have 2 bludgeoning + 1 piercing, and if you need to further modify one of those totals, it's trivial to do so.

If you just say "okay that's half of 8, so 4 damage", you can't say how much of that 4 gets modified by type resistances or vulnerabilities after that point.

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