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I play in a 5e game, and a monk was getting shot in the back of the head. One of the monk's abilities is Deflect Missiles: "Starting at 3rd level you can use your reaction to deflect or catch the missile when you are hit by a ranged weapon attack." (PHB53 p.78, emphasis mine.)
We argued that it doesn't say “see” in the book, but wouldn't he have to see it to know the attack is coming?
Can a monk deflect an incoming missile even if he can't see it?
No, the monk need not see the incoming missile.
...you can use your reaction to deflect or catch the missile when you are hit by a ranged attack. (PHB p.78, emphasis mine)
As you say, nothing to indicate the monk must see the incoming missile. Call it spidey-sense, or hearing it whistle through the last intervening foot, the monk can at the moment of impact choose to deflect/catch the missile.
An intentional feature of combat in D&D 5E is that you don't have facing unless you use the optional rules in the DMG. That means that "a shot to the back of the head" is more granularity than the rules cover. The six second turn in combat by necessity encompasses a variety of movement, glancing, striking, swinging, grabbing, shifting body position, and more not being described in that depth of detail ... as was done in some previous editions.
Characters don't have a facing when it comes to combat rules so you shouldn't use concepts like "which way was the monk facing". However where it is important is when someone attacks from advantage where the monk is ruled as unaware of the attack (a rogue attacking from Hidden for instance). The monk in this situation is indeed still able to use the ability as the wording is "when you are hit" with no reference to having to be able to see etc. This fits well with the whole Monk archetype the character class is based on. You could blindfold a monk, stick wax in their ears and they would still be able to do this.
