Which is better, AC 17 and disadvantage on attacks against you, or AC 19?

Question

I am playing in an Epic tier PvP. I have the option of a +2 studded leather, with max Dex, for AC 19, or normal studded leather and a cloak of displacement. Since everybody has +3 weapons, all the attack modifiers will be +14.

I am aware of this question (Mathematically, is a +2 bonus to AC better than attackers having disadvantage?), but I am looking for even more specific to my situation.

The PvP is a free for all. I have no other consistent sources of disadvantage. My class is Swashbuckler Rogue, so I hope to avoid being hit.

Answer 1

Purely by the chance to hit, it's almost equal.

+14 attack vs. AC 17 requires at least a 3 to hit, which is a 90% chance, so the chance to hit with disadvantage is 81%.

+14 attack vs. AC 19 requires at least a 5, which is an 80% chance.

However, the chance to crit is 5% against AC 19, and effectively zero if you have the cloak on. Since a crit is basically an extra hit worth of damage, the effective hit rate (number of hits worth of damage per attack) is 85% against AC 19.

AC 19 is better if you have some other way to give them disadvantage.

Because, duh.

AC 19 is better if they're going to attack you twice per round.

With the cloak on, there's an 81% chance the first attack hits, and if it does, the second attack has a 90% chance instead of 81%. On average, you get hit 85% of the time, which is as bad as AC 19's crit-adjusted rate. Adding more attacks per round just makes this worse.

AC 17 with the cloak is better if you're fighting a rogue or paladin.

First, as noted above, the cloak prevents crits most of the time. You don't want a paladin to crit; they'll Divine Smite you for a ton of damage.

Second is Sneak Attack. If a 20th-level rogue gets the drop on you, they will probably hit you either way, but the cloak will save you from their extra 10d6 damage. Saving you from a devastating first strike is exactly what the cloak does best.

Answer 2

Looking at AnyDice:

• Attacking +14 with Disadvantage v. AC 17: Hits 81%, Misses 19%.

• Attacking +14 v. AC 19: Hits 80%, Misses 20%

They're really close, but you're very slightly better off with AC 19 on attack rolls.

With a margin that thin, though, if those were the only two choices, I'd go with the cloak, if only because it looks cool and has a chance to make your opponents overestimate how hard you are to hit.