# dnd-5e – Average Attack Damage Prevented by AC Boost from a Shield

armor-classdamagednd-5eshieldstatistics

Statistically, how much attack damage does the AC boost from a shield prevent on average? I've seen claims it results in a 10% reduction in damage taken, is that accurate?

# 10% is the naive answer

The +2 bonus to AC is 10% of the d20 roll, but it is more complicated than that:

• If the enemy can only hit you on a natural 20, adding a shield does not do anything
• If without a shield the enemy hits you 50% of the time, it becomes 40% with one. The difference is about 20%1.
• If the enemy only misses on 1, dropping the shield does nothing

In actual games it is around 15-25%.

## Calculation

Assume for simplicity that the attacker does 10 hp damage per hit, and criticals increase damage by 5 HP (50%)2.
The DPR against a shieldless opponent is $$\frac{(21 - rollNeeded) * 10 + 5}{20} {}$$
The DPR against a shielded opponent is $$\frac{(21 - rollNeeded - 2) * 10 + 5}{20} {}$$ rollNeeded = (your AC) - (opponent's to hit). It is always between 2 and 20.

### Table

Substract your typical enemy's to hit from your AC, and find how much a shield would help.
For example you want to decide between dual wielding and sword-and-board for a new Fighter. As starting equipment you can get Chain mail (AC 16), and you expect many Goblins (+4 to hit). You get 12 -> 21.05% less damage received with a shield!

### Graph

1) Criticals complicate things
2) Assuming no magic items and a +5 ability, a critical increases Greatsword[GWF] by 62%, Longsword[Dueling] by 39%. Sneak Attacks gain about 88% at level 19. 50% is just an approximation, but changing it does not influence the end result significantly