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How much attack damage does the AC boost from a shield prevent on average?

Are there no bonuses to two-handed weapons' damage?What is the expected average damage for an area of effect power?How do you calculate an average damage when damage is conditional on circumstances?Does the Dueling Fighting Style prevent using a shield?How much damage does Great Weapon Fighting add on average?What's the average damage increase from Elemental Adept?How much does ongoing damage add to the average damage when creating a monster?How does shield bashing work?To what extent does the Shield Master feat ignore penalties?How does shield guardian damage get transferred along a chain?How do you calculate average damage for DPR comparisons?

6

$begingroup$

Statistically, how much attack damage does the AC boost from a shield prevent on average?

dnd-5e damage statistics armor-class shield

share|improve this question

edited 12 mins ago

NautArch

59k8211393

asked 1 hour ago

AndrásAndrás

28.6k14111203

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Is the question you are asking "statistically how much damage does the AC boost from a shield prevent on average?" or something like that? Or are you thinking that shields actually reduce damage?
  $endgroup$
  – Rubiksmoose
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
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  Okay, i'll let the statisticians take a look. But to me it seems like there are two variables which makes this too broad: The to-hit modifier can drastically affect what hits, and the base AC without shield can drastically affect when you get hit. The shield isn't reducing damage, it reduces all damage if there's no hit. I'm really not understanding this. Are you really asking what a +2 AC does to your chances of being hit?
  $endgroup$
  – NautArch
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @NautArch, but it can be reduced to one variable by substracting one variable from the other
  $endgroup$
  – András
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Rubiksmoose, disprove something that I have seen here, and other places. Now I can only find the comment to my answer.
  $endgroup$
  – András
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I don't understand how a mechanic (AC) that is binary (hits/doesn't hit) affects damage delivery prevention. Others clearly do - can someone explain?
  $endgroup$
  – NautArch
  1 hour ago
  
  
  

  
  
  
  

 | 
show 11 more comments

6

$begingroup$

Statistically, how much attack damage does the AC boost from a shield prevent on average?

dnd-5e damage statistics armor-class shield

share|improve this question

edited 12 mins ago

NautArch

59k8211393

asked 1 hour ago

AndrásAndrás

28.6k14111203

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Is the question you are asking "statistically how much damage does the AC boost from a shield prevent on average?" or something like that? Or are you thinking that shields actually reduce damage?
  $endgroup$
  – Rubiksmoose
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Okay, i'll let the statisticians take a look. But to me it seems like there are two variables which makes this too broad: The to-hit modifier can drastically affect what hits, and the base AC without shield can drastically affect when you get hit. The shield isn't reducing damage, it reduces all damage if there's no hit. I'm really not understanding this. Are you really asking what a +2 AC does to your chances of being hit?
  $endgroup$
  – NautArch
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @NautArch, but it can be reduced to one variable by substracting one variable from the other
  $endgroup$
  – András
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @Rubiksmoose, disprove something that I have seen here, and other places. Now I can only find the comment to my answer.
  $endgroup$
  – András
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I don't understand how a mechanic (AC) that is binary (hits/doesn't hit) affects damage delivery prevention. Others clearly do - can someone explain?
  $endgroup$
  – NautArch
  1 hour ago
  
  
  

  
  
  
  

 | 
show 11 more comments

$begingroup$

Statistically, how much attack damage does the AC boost from a shield prevent on average?

dnd-5e damage statistics armor-class shield

share|improve this question

edited 12 mins ago

NautArch

59k8211393

asked 1 hour ago

AndrásAndrás

28.6k14111203

$endgroup$

share|improve this question

edited 12 mins ago

NautArch

59k8211393

asked 1 hour ago

AndrásAndrás

28.6k14111203

share|improve this question

edited 12 mins ago

NautArch

59k8211393

asked 1 hour ago

AndrásAndrás

28.6k14111203

edited 12 mins ago

NautArch

59k8211393

edited 12 mins ago

NautArch

59k8211393

asked 1 hour ago

AndrásAndrás

28.6k14111203

asked 1 hour ago

AndrásAndrás

28.6k14111203

1 Answer
1

active

oldest

votes

9

$begingroup$

10% is the naive answer

In actual games it is around 15-25%.

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

Calculation

Assume for simplicity that the attacker does 10 hp damage per hit, and criticals increase damage by 5 HP (50%).

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

share|improve this answer

edited 49 mins ago

answered 1 hour ago

AndrásAndrás

28.6k14111203

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In my experience, the 15-25% number sounds about right, but comparing typical enemy hit bonus and tanky player AC would make this answer even better.
  $endgroup$
  – Chris Starnes
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
  $endgroup$
  – GreySage
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Might be worth calling out how you calculate rollNeeded and that it is always a number between 2 and 20, due to the rules surrounding auto-hits and auto-misses.
  $endgroup$
  – Erik
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  My only critique is that the naive answer should assume a hit on an 11 (and may ignore crits) so I would say it should be 20%. Which is a more reasonable approximation.
  $endgroup$
  – Jesse
  34 mins ago
  

  
  
  
  

add a comment | 

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9

$begingroup$

10% is the naive answer

In actual games it is around 15-25%.

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

Calculation

Assume for simplicity that the attacker does 10 hp damage per hit, and criticals increase damage by 5 HP (50%).

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

share|improve this answer

edited 49 mins ago

answered 1 hour ago

AndrásAndrás

28.6k14111203

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In my experience, the 15-25% number sounds about right, but comparing typical enemy hit bonus and tanky player AC would make this answer even better.
  $endgroup$
  – Chris Starnes
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
  $endgroup$
  – GreySage
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Might be worth calling out how you calculate rollNeeded and that it is always a number between 2 and 20, due to the rules surrounding auto-hits and auto-misses.
  $endgroup$
  – Erik
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  My only critique is that the naive answer should assume a hit on an 11 (and may ignore crits) so I would say it should be 20%. Which is a more reasonable approximation.
  $endgroup$
  – Jesse
  34 mins ago
  

  
  
  
  

add a comment | 

9

$begingroup$

10% is the naive answer

In actual games it is around 15-25%.

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

Calculation

Assume for simplicity that the attacker does 10 hp damage per hit, and criticals increase damage by 5 HP (50%).

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

share|improve this answer

edited 49 mins ago

answered 1 hour ago

AndrásAndrás

28.6k14111203

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  In my experience, the 15-25% number sounds about right, but comparing typical enemy hit bonus and tanky player AC would make this answer even better.
  $endgroup$
  – Chris Starnes
  1 hour ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
  $endgroup$
  – GreySage
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Might be worth calling out how you calculate rollNeeded and that it is always a number between 2 and 20, due to the rules surrounding auto-hits and auto-misses.
  $endgroup$
  – Erik
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  My only critique is that the naive answer should assume a hit on an 11 (and may ignore crits) so I would say it should be 20%. Which is a more reasonable approximation.
  $endgroup$
  – Jesse
  34 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

10% is the naive answer

In actual games it is around 15-25%.

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

Calculation

Assume for simplicity that the attacker does 10 hp damage per hit, and criticals increase damage by 5 HP (50%).

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

share|improve this answer

edited 49 mins ago

answered 1 hour ago

AndrásAndrás

28.6k14111203

$endgroup$

share|improve this answer

edited 49 mins ago

answered 1 hour ago

AndrásAndrás

28.6k14111203

answered 1 hour ago

AndrásAndrás

28.6k14111203

answered 1 hour ago

AndrásAndrás

28.6k14111203