The monk's Deflect Missiles feature description says (PHB, pg. 78):
Starting at 3rd level, you can use your reaction to deflect or catch the missile when you are hit by a ranged weapon attack.
I take this to mean that the player controlling the monk gets to decide whether or not to use Deflect Missiles after they know whether or not the attack hits.
It continues:
When you do so, the damage you take from the attack is reduced by 1d10 + your Dexterity modifier + your monk level.
Does the monk's player get to know the damage before they decide to use Deflect Missiles? Or is damage is rolled after they choose to use the feature?
Best Answer
You choose before you know the damage. Hitting and dealing damage are separate steps — if the ability was supposed to give the choice when damage was being resolved, it would say something like "… when you are damaged by a ranged weapon attack." Instead, it says "when you are hit". So when you're hit, but before damage is rolled (or revealed), you decide whether to deflect it or not.
Besides, it's a deflection. It wouldn't make sense to see how wounded you are first, and only then decide whether to make the missile hit you differently or not at all. The ability's use of a hit as the trigger instead of suffering damage as the trigger is in line with this intuition about how voluntary deflection ought to work.