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I have a character playing a multiclass Barbarian/Monk. Does the resistance from rage combine with Deflect Missiles to negate the damage and make the reaction attack?

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Yes, they combine...

Barbarian rage (PHB p.48) uses the Resistance mechanic (PHB p.197), while the monk's deflect missiles ability (PHB p.78) uses a flat (if dice-based) damage reduction. So the two can both work to reduce the amount of incoming damage.

... but probably not well enough for the reaction attack.

However, resistance acts last. So assuming you're hit for 20 damage, you're not resisting it down to 10 and then trying to deflect the 10, which is doable; you're trying to deflect the 20, which is less so, and then resisting whatever's left down to half of itself. If you don't cut it to zero with the first step, you won't with the second, because the only number that gives you zero when you halve it is already zero.

(Arguably, if you reduced the damage to 1, resistance would then reduce that to 1/2 which does round down to 0, which could be interpreted as "reducing the damage to zero" depending on your DM. But this already requires you to miss it by only one point, so it's a pretty slim edge case.)

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Yes, but ...

The reduction from the monk feature is applied first; then the barbarian resistance is applied. So, if you reduce the damage to 0 you can catch and use the missile but if the damage becomes 0 from 1 using barbarian resistance, you can’t.

This is because deflect missiles is triggered by being hit while barbarian resistance happens when you take damage.

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    \$\begingroup\$ although I would say it would be awesome to see a barbarian pull an arrow out of his side and then throw it back. \$\endgroup\$ – Daniel Jan 15 '18 at 4:41
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So, I wondered this question myself. I found this thread directly after reading the DMG definition of a reaction, which made me realize the other answers, by RAW, are totally wrong. Because Deflect Missiles is a reaction. As such, it can only occur after it's trigger has been resolved, which in this case is a hit. To resolve a hit, one must roll and deal damage. Ergo, because Deflect Missiles is a reaction, Resistance would apply and resolve before deflect missles attempts to reduce it further

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    \$\begingroup\$ Can you add some rules citations to back up your claim that deflection would happen after applying resistance but before taking the damage? The "trigger" you mention is "being hit by an attack", so by the normal rules of a reaction, it would only do something after you take the damage, at which point reducing that damage becomes pointless. \$\endgroup\$ – Erik Sep 4 '20 at 11:09
  • \$\begingroup\$ Phb. 78 - Deflect Missiles; "...you can use your reaction to deflect or catch the missile when you are HIT by a ranged weapon attack. When you do so, the DAMAGE YOU TAKE from the attack is reduced.." and DMG. 252 - Adjudicating Reaction Timing; "For example, the opportunity attack and the shield spell are clear about the fact that they interrupt their triggers, If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, aas in the Ready action." \$\endgroup\$ – ogtrapcard Sep 4 '20 at 12:46
  • \$\begingroup\$ the hit occurs, damage is rolled, resistance is applied because the attack has to HIT before the reaction can be used. Deflect Missiles occurs after the damage of the missile is determined, not before. \$\endgroup\$ – ogtrapcard Sep 4 '20 at 12:56
  • \$\begingroup\$ @ogtrapcard Please edit your answer to include these details. Comments are temporary and may be removed after some time; information that needs to be kept should be edited into the answer post. \$\endgroup\$ – doppelgreener Sep 4 '20 at 13:00
  • \$\begingroup\$ This would seem to contradict the answer to this question. You might think about addressing that in your edit, too. \$\endgroup\$ – Rykara Sep 4 '20 at 15:07

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