How much attack damage does the AC boost from a shield prevent on average?
$begingroup$
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?
dnd-5e damage statistics armor-class shield
edited 6 hours ago
doppelgreener♦
32.4k11137231
asked 8 hours ago
AndrásAndrás
28.7k14112205
$endgroup$
add a comment |
$begingroup$
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?
dnd-5e damage statistics armor-class shield
edited 6 hours ago
doppelgreener♦
32.4k11137231
asked 8 hours ago
AndrásAndrás
28.7k14112205
$endgroup$
$begingroup$
Let us continue this discussion in chat.
$endgroup$
– NautArch
6 hours ago
add a comment |
$begingroup$
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?
dnd-5e damage statistics armor-class shield
edited 6 hours ago
doppelgreener♦
32.4k11137231
asked 8 hours ago
AndrásAndrás
28.7k14112205
$endgroup$
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?
dnd-5e damage statistics armor-class shield
dnd-5e damage statistics armor-class shield
edited 6 hours ago
doppelgreener♦
32.4k11137231
asked 8 hours ago
AndrásAndrás
28.7k14112205
edited 6 hours ago
doppelgreener♦
32.4k11137231
asked 8 hours ago
AndrásAndrás
28.7k14112205
edited 6 hours ago
doppelgreener♦
32.4k11137231
edited 6 hours ago
doppelgreener♦
32.4k11137231
edited 6 hours ago
doppelgreener♦
32.4k11137231
32.4k11137231
asked 8 hours ago
AndrásAndrás
28.7k14112205
asked 8 hours ago
AndrásAndrás
28.7k14112205
asked 8 hours ago
AndrásAndrás
28.7k14112205
28.7k14112205
$begingroup$
Let us continue this discussion in chat.
$endgroup$
– NautArch
6 hours ago
add a comment |
$begingroup$
Let us continue this discussion in chat.
$endgroup$
– NautArch
6 hours ago
$begingroup$
Let us continue this discussion in chat.
$endgroup$
– NautArch
6 hours ago
$begingroup$
Let us continue this discussion in chat.
$endgroup$
– NautArch
6 hours ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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
answered 8 hours ago
AndrásAndrás
28.7k14112205
$endgroup$
3
$begingroup$
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
8 hours ago
1
$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
8 hours 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
7 hours 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
7 hours ago
$begingroup$
Everything in this post seems to check out; one thing I would quibble with is that a 50% damage increase on a Critical hit is probably on the lower end; it's realistic for some scenarios (Dueling Fighting Style characters being the big example) but many characters have some high damage dice that get doubled by a lot on a successful crit.
$endgroup$
– Xirema
6 hours ago
|
show 1 more comment
$begingroup$
About 14%-30% in normal play
I've produced odds for the scenario where the Attacker is a Great-Weapon-Fighter using a Greataxe with a +3 Damage modifier, or 1d12+3[GWF] for a normal hit, or 2d12+3[GWF] for a critical hit. Different weapons and damage modifiers and features will skew these results, but these should represent a relatively "normal" scenario for most modes of play.
Across most of the game, a shield will reduce this Attacker's DPR by a flat 1.034, only meaningfully varying at the highest ACs, when Critical Hits represent the only significant chance to hit.
My experience with the game has taught me that at the usual range of Armor Class values that an average party will encounter (both for themselves and for enemy creatures), the "to-hit" range usually lands between 7 and 15. In this range, we can see that at the low-end, a shield reduces the Attacker's expected DPR (per attack) by about 13.592%, and at the higher end, it reduces DPR by about 29.824%.
begin{array}{|l|r|r|r|}
hline
text{Name} & text{Normal} & text{+Shield} & text{[%]}\ hline
text{To-hit = 1} & 10.183 & 9.667 & text{-5.067%}\ hline
text{To-hit = 2} & 10.183 & 9.150 & text{-10.144%}\ hline
text{To-hit = 3} & 9.667 & 8.633 & text{-10.696%}\ hline
text{To-hit = 4} & 9.150 & 8.117 & text{-11.290%}\ hline
text{To-hit = 5} & 8.633 & 7.600 & text{-11.966%}\ hline
text{To-hit = 6} & 8.117 & 7.083 & text{-12.739%}\ hline
text{To-hit = 7} & 7.600 & 6.567 & text{-13.592%}\ hline
text{To-hit = 8} & 7.083 & 6.050 & text{-14.584%}\ hline
text{To-hit = 9} & 6.567 & 5.533 & text{-15.745%}\ hline
text{To-hit = 10} & 6.050 & 5.017 & text{-17.074%}\ hline
text{To-hit = 11} & 5.533 & 4.500 & text{-18.670%}\ hline
text{To-hit = 12} & 5.017 & 3.983 & text{-20.610%}\ hline
text{To-hit = 13} & 4.500 & 3.467 & text{-22.956%}\ hline
text{To-hit = 14} & 3.983 & 2.950 & text{-25.935%}\ hline
text{To-hit = 15} & 3.467 & 2.433 & text{-29.824%}\ hline
text{To-hit = 16} & 2.950 & 1.917 & text{-35.017%}\ hline
text{To-hit = 17} & 2.433 & 1.400 & text{-42.458%}\ hline
text{To-hit = 18} & 1.917 & 0.883 & text{-53.938%}\ hline
text{To-hit = 19} & 1.400 & 0.883 & text{-36.929%}\ hline
text{To-hit = 20} & 0.883 & 0.883 & text{-0.000%}\ hline
end{array}
I'm producing these values just as a confirmation against Andras' values: I believe the small difference between our results are just the consequences of using different damage dice, and that based on my own results, their values are probably correct for their scenario.
answered 6 hours ago
XiremaXirema
21.1k263123
$endgroup$
$begingroup$
This is kind of my point (and I think you're the right user to explain this to me), but if different to-hit and ACs create differences, then don't we need to know those values in order to answer this?14-30% with your current dataset is fairly swingy.
$endgroup$
– NautArch
6 hours ago
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@András I have a program I use to generate values. There's a discussion here for this answer that describes the in-detail methodology.
$endgroup$
– Xirema
5 hours ago
1
$begingroup$
@András The table uses MathJax. You can attempt to edit the post and look at the markup to figure out how it works. Alternately, you can use the generator at tablesgenerator to create a table, though you need to change thebegin{table}begin{tabular}tags tobegin{array}to work on Stack Overflow.
$endgroup$
– Xirema
5 hours ago
$begingroup$
@Xirema thank you
$endgroup$
– András
5 hours ago
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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
answered 8 hours ago
AndrásAndrás
28.7k14112205
$endgroup$
3
$begingroup$
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
8 hours ago
1
$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
8 hours 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
7 hours 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
7 hours ago
$begingroup$
Everything in this post seems to check out; one thing I would quibble with is that a 50% damage increase on a Critical hit is probably on the lower end; it's realistic for some scenarios (Dueling Fighting Style characters being the big example) but many characters have some high damage dice that get doubled by a lot on a successful crit.
$endgroup$
– Xirema
6 hours ago
|
show 1 more 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
answered 8 hours ago
AndrásAndrás
28.7k14112205
$endgroup$
3
$begingroup$
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
8 hours ago
1
$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
8 hours 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
7 hours 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
7 hours ago
$begingroup$
Everything in this post seems to check out; one thing I would quibble with is that a 50% damage increase on a Critical hit is probably on the lower end; it's realistic for some scenarios (Dueling Fighting Style characters being the big example) but many characters have some high damage dice that get doubled by a lot on a successful crit.
$endgroup$
– Xirema
6 hours ago
|
show 1 more 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
answered 8 hours ago
AndrásAndrás
28.7k14112205
$endgroup$
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
answered 8 hours ago
AndrásAndrás
28.7k14112205
edited 7 hours ago
answered 8 hours ago
AndrásAndrás
28.7k14112205
answered 8 hours ago
AndrásAndrás
28.7k14112205
answered 8 hours ago
AndrásAndrás
28.7k14112205
28.7k14112205
3
$begingroup$
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
8 hours ago
1
$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
8 hours 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
7 hours 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
7 hours ago
$begingroup$
Everything in this post seems to check out; one thing I would quibble with is that a 50% damage increase on a Critical hit is probably on the lower end; it's realistic for some scenarios (Dueling Fighting Style characters being the big example) but many characters have some high damage dice that get doubled by a lot on a successful crit.
$endgroup$
– Xirema
6 hours ago
|
show 1 more comment
3
$begingroup$
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
8 hours ago
1
$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
8 hours 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
7 hours 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
7 hours ago
$begingroup$
Everything in this post seems to check out; one thing I would quibble with is that a 50% damage increase on a Critical hit is probably on the lower end; it's realistic for some scenarios (Dueling Fighting Style characters being the big example) but many characters have some high damage dice that get doubled by a lot on a successful crit.
$endgroup$
– Xirema
6 hours ago
3
3
$begingroup$
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
8 hours ago
$begingroup$
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
8 hours ago
1
1
$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
8 hours ago
$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
8 hours 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
7 hours 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
7 hours 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
7 hours 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
7 hours ago
$begingroup$
Everything in this post seems to check out; one thing I would quibble with is that a 50% damage increase on a Critical hit is probably on the lower end; it's realistic for some scenarios (Dueling Fighting Style characters being the big example) but many characters have some high damage dice that get doubled by a lot on a successful crit.
$endgroup$
– Xirema
6 hours ago
$begingroup$
Everything in this post seems to check out; one thing I would quibble with is that a 50% damage increase on a Critical hit is probably on the lower end; it's realistic for some scenarios (Dueling Fighting Style characters being the big example) but many characters have some high damage dice that get doubled by a lot on a successful crit.
$endgroup$
– Xirema
6 hours ago
|
show 1 more comment
$begingroup$
About 14%-30% in normal play
I've produced odds for the scenario where the Attacker is a Great-Weapon-Fighter using a Greataxe with a +3 Damage modifier, or 1d12+3[GWF] for a normal hit, or 2d12+3[GWF] for a critical hit. Different weapons and damage modifiers and features will skew these results, but these should represent a relatively "normal" scenario for most modes of play.
Across most of the game, a shield will reduce this Attacker's DPR by a flat 1.034, only meaningfully varying at the highest ACs, when Critical Hits represent the only significant chance to hit.
My experience with the game has taught me that at the usual range of Armor Class values that an average party will encounter (both for themselves and for enemy creatures), the "to-hit" range usually lands between 7 and 15. In this range, we can see that at the low-end, a shield reduces the Attacker's expected DPR (per attack) by about 13.592%, and at the higher end, it reduces DPR by about 29.824%.
begin{array}{|l|r|r|r|}
hline
text{Name} & text{Normal} & text{+Shield} & text{[%]}\ hline
text{To-hit = 1} & 10.183 & 9.667 & text{-5.067%}\ hline
text{To-hit = 2} & 10.183 & 9.150 & text{-10.144%}\ hline
text{To-hit = 3} & 9.667 & 8.633 & text{-10.696%}\ hline
text{To-hit = 4} & 9.150 & 8.117 & text{-11.290%}\ hline
text{To-hit = 5} & 8.633 & 7.600 & text{-11.966%}\ hline
text{To-hit = 6} & 8.117 & 7.083 & text{-12.739%}\ hline
text{To-hit = 7} & 7.600 & 6.567 & text{-13.592%}\ hline
text{To-hit = 8} & 7.083 & 6.050 & text{-14.584%}\ hline
text{To-hit = 9} & 6.567 & 5.533 & text{-15.745%}\ hline
text{To-hit = 10} & 6.050 & 5.017 & text{-17.074%}\ hline
text{To-hit = 11} & 5.533 & 4.500 & text{-18.670%}\ hline
text{To-hit = 12} & 5.017 & 3.983 & text{-20.610%}\ hline
text{To-hit = 13} & 4.500 & 3.467 & text{-22.956%}\ hline
text{To-hit = 14} & 3.983 & 2.950 & text{-25.935%}\ hline
text{To-hit = 15} & 3.467 & 2.433 & text{-29.824%}\ hline
text{To-hit = 16} & 2.950 & 1.917 & text{-35.017%}\ hline
text{To-hit = 17} & 2.433 & 1.400 & text{-42.458%}\ hline
text{To-hit = 18} & 1.917 & 0.883 & text{-53.938%}\ hline
text{To-hit = 19} & 1.400 & 0.883 & text{-36.929%}\ hline
text{To-hit = 20} & 0.883 & 0.883 & text{-0.000%}\ hline
end{array}
I'm producing these values just as a confirmation against Andras' values: I believe the small difference between our results are just the consequences of using different damage dice, and that based on my own results, their values are probably correct for their scenario.
answered 6 hours ago
XiremaXirema
21.1k263123
$endgroup$
$begingroup$
This is kind of my point (and I think you're the right user to explain this to me), but if different to-hit and ACs create differences, then don't we need to know those values in order to answer this?14-30% with your current dataset is fairly swingy.
$endgroup$
– NautArch
6 hours ago
$begingroup$
@András I have a program I use to generate values. There's a discussion here for this answer that describes the in-detail methodology.
$endgroup$
– Xirema
5 hours ago
1
$begingroup$
@András The table uses MathJax. You can attempt to edit the post and look at the markup to figure out how it works. Alternately, you can use the generator at tablesgenerator to create a table, though you need to change thebegin{table}begin{tabular}tags tobegin{array}to work on Stack Overflow.
$endgroup$
– Xirema
5 hours ago
$begingroup$
@Xirema thank you
$endgroup$
– András
5 hours ago
add a comment |
$begingroup$
About 14%-30% in normal play
I've produced odds for the scenario where the Attacker is a Great-Weapon-Fighter using a Greataxe with a +3 Damage modifier, or 1d12+3[GWF] for a normal hit, or 2d12+3[GWF] for a critical hit. Different weapons and damage modifiers and features will skew these results, but these should represent a relatively "normal" scenario for most modes of play.
Across most of the game, a shield will reduce this Attacker's DPR by a flat 1.034, only meaningfully varying at the highest ACs, when Critical Hits represent the only significant chance to hit.
My experience with the game has taught me that at the usual range of Armor Class values that an average party will encounter (both for themselves and for enemy creatures), the "to-hit" range usually lands between 7 and 15. In this range, we can see that at the low-end, a shield reduces the Attacker's expected DPR (per attack) by about 13.592%, and at the higher end, it reduces DPR by about 29.824%.
begin{array}{|l|r|r|r|}
hline
text{Name} & text{Normal} & text{+Shield} & text{[%]}\ hline
text{To-hit = 1} & 10.183 & 9.667 & text{-5.067%}\ hline
text{To-hit = 2} & 10.183 & 9.150 & text{-10.144%}\ hline
text{To-hit = 3} & 9.667 & 8.633 & text{-10.696%}\ hline
text{To-hit = 4} & 9.150 & 8.117 & text{-11.290%}\ hline
text{To-hit = 5} & 8.633 & 7.600 & text{-11.966%}\ hline
text{To-hit = 6} & 8.117 & 7.083 & text{-12.739%}\ hline
text{To-hit = 7} & 7.600 & 6.567 & text{-13.592%}\ hline
text{To-hit = 8} & 7.083 & 6.050 & text{-14.584%}\ hline
text{To-hit = 9} & 6.567 & 5.533 & text{-15.745%}\ hline
text{To-hit = 10} & 6.050 & 5.017 & text{-17.074%}\ hline
text{To-hit = 11} & 5.533 & 4.500 & text{-18.670%}\ hline
text{To-hit = 12} & 5.017 & 3.983 & text{-20.610%}\ hline
text{To-hit = 13} & 4.500 & 3.467 & text{-22.956%}\ hline
text{To-hit = 14} & 3.983 & 2.950 & text{-25.935%}\ hline
text{To-hit = 15} & 3.467 & 2.433 & text{-29.824%}\ hline
text{To-hit = 16} & 2.950 & 1.917 & text{-35.017%}\ hline
text{To-hit = 17} & 2.433 & 1.400 & text{-42.458%}\ hline
text{To-hit = 18} & 1.917 & 0.883 & text{-53.938%}\ hline
text{To-hit = 19} & 1.400 & 0.883 & text{-36.929%}\ hline
text{To-hit = 20} & 0.883 & 0.883 & text{-0.000%}\ hline
end{array}
I'm producing these values just as a confirmation against Andras' values: I believe the small difference between our results are just the consequences of using different damage dice, and that based on my own results, their values are probably correct for their scenario.
answered 6 hours ago
XiremaXirema
21.1k263123
$endgroup$
$begingroup$
This is kind of my point (and I think you're the right user to explain this to me), but if different to-hit and ACs create differences, then don't we need to know those values in order to answer this?14-30% with your current dataset is fairly swingy.
$endgroup$
– NautArch
6 hours ago
$begingroup$
@András I have a program I use to generate values. There's a discussion here for this answer that describes the in-detail methodology.
$endgroup$
– Xirema
5 hours ago
1
$begingroup$
@András The table uses MathJax. You can attempt to edit the post and look at the markup to figure out how it works. Alternately, you can use the generator at tablesgenerator to create a table, though you need to change thebegin{table}begin{tabular}tags tobegin{array}to work on Stack Overflow.
$endgroup$
– Xirema
5 hours ago
$begingroup$
@Xirema thank you
$endgroup$
– András
5 hours ago
add a comment |
$begingroup$
About 14%-30% in normal play
I've produced odds for the scenario where the Attacker is a Great-Weapon-Fighter using a Greataxe with a +3 Damage modifier, or 1d12+3[GWF] for a normal hit, or 2d12+3[GWF] for a critical hit. Different weapons and damage modifiers and features will skew these results, but these should represent a relatively "normal" scenario for most modes of play.
Across most of the game, a shield will reduce this Attacker's DPR by a flat 1.034, only meaningfully varying at the highest ACs, when Critical Hits represent the only significant chance to hit.
My experience with the game has taught me that at the usual range of Armor Class values that an average party will encounter (both for themselves and for enemy creatures), the "to-hit" range usually lands between 7 and 15. In this range, we can see that at the low-end, a shield reduces the Attacker's expected DPR (per attack) by about 13.592%, and at the higher end, it reduces DPR by about 29.824%.
begin{array}{|l|r|r|r|}
hline
text{Name} & text{Normal} & text{+Shield} & text{[%]}\ hline
text{To-hit = 1} & 10.183 & 9.667 & text{-5.067%}\ hline
text{To-hit = 2} & 10.183 & 9.150 & text{-10.144%}\ hline
text{To-hit = 3} & 9.667 & 8.633 & text{-10.696%}\ hline
text{To-hit = 4} & 9.150 & 8.117 & text{-11.290%}\ hline
text{To-hit = 5} & 8.633 & 7.600 & text{-11.966%}\ hline
text{To-hit = 6} & 8.117 & 7.083 & text{-12.739%}\ hline
text{To-hit = 7} & 7.600 & 6.567 & text{-13.592%}\ hline
text{To-hit = 8} & 7.083 & 6.050 & text{-14.584%}\ hline
text{To-hit = 9} & 6.567 & 5.533 & text{-15.745%}\ hline
text{To-hit = 10} & 6.050 & 5.017 & text{-17.074%}\ hline
text{To-hit = 11} & 5.533 & 4.500 & text{-18.670%}\ hline
text{To-hit = 12} & 5.017 & 3.983 & text{-20.610%}\ hline
text{To-hit = 13} & 4.500 & 3.467 & text{-22.956%}\ hline
text{To-hit = 14} & 3.983 & 2.950 & text{-25.935%}\ hline
text{To-hit = 15} & 3.467 & 2.433 & text{-29.824%}\ hline
text{To-hit = 16} & 2.950 & 1.917 & text{-35.017%}\ hline
text{To-hit = 17} & 2.433 & 1.400 & text{-42.458%}\ hline
text{To-hit = 18} & 1.917 & 0.883 & text{-53.938%}\ hline
text{To-hit = 19} & 1.400 & 0.883 & text{-36.929%}\ hline
text{To-hit = 20} & 0.883 & 0.883 & text{-0.000%}\ hline
end{array}
I'm producing these values just as a confirmation against Andras' values: I believe the small difference between our results are just the consequences of using different damage dice, and that based on my own results, their values are probably correct for their scenario.
answered 6 hours ago
XiremaXirema
21.1k263123
$endgroup$
About 14%-30% in normal play
I've produced odds for the scenario where the Attacker is a Great-Weapon-Fighter using a Greataxe with a +3 Damage modifier, or 1d12+3[GWF] for a normal hit, or 2d12+3[GWF] for a critical hit. Different weapons and damage modifiers and features will skew these results, but these should represent a relatively "normal" scenario for most modes of play.
Across most of the game, a shield will reduce this Attacker's DPR by a flat 1.034, only meaningfully varying at the highest ACs, when Critical Hits represent the only significant chance to hit.
My experience with the game has taught me that at the usual range of Armor Class values that an average party will encounter (both for themselves and for enemy creatures), the "to-hit" range usually lands between 7 and 15. In this range, we can see that at the low-end, a shield reduces the Attacker's expected DPR (per attack) by about 13.592%, and at the higher end, it reduces DPR by about 29.824%.
begin{array}{|l|r|r|r|}
hline
text{Name} & text{Normal} & text{+Shield} & text{[%]}\ hline
text{To-hit = 1} & 10.183 & 9.667 & text{-5.067%}\ hline
text{To-hit = 2} & 10.183 & 9.150 & text{-10.144%}\ hline
text{To-hit = 3} & 9.667 & 8.633 & text{-10.696%}\ hline
text{To-hit = 4} & 9.150 & 8.117 & text{-11.290%}\ hline
text{To-hit = 5} & 8.633 & 7.600 & text{-11.966%}\ hline
text{To-hit = 6} & 8.117 & 7.083 & text{-12.739%}\ hline
text{To-hit = 7} & 7.600 & 6.567 & text{-13.592%}\ hline
text{To-hit = 8} & 7.083 & 6.050 & text{-14.584%}\ hline
text{To-hit = 9} & 6.567 & 5.533 & text{-15.745%}\ hline
text{To-hit = 10} & 6.050 & 5.017 & text{-17.074%}\ hline
text{To-hit = 11} & 5.533 & 4.500 & text{-18.670%}\ hline
text{To-hit = 12} & 5.017 & 3.983 & text{-20.610%}\ hline
text{To-hit = 13} & 4.500 & 3.467 & text{-22.956%}\ hline
text{To-hit = 14} & 3.983 & 2.950 & text{-25.935%}\ hline
text{To-hit = 15} & 3.467 & 2.433 & text{-29.824%}\ hline
text{To-hit = 16} & 2.950 & 1.917 & text{-35.017%}\ hline
text{To-hit = 17} & 2.433 & 1.400 & text{-42.458%}\ hline
text{To-hit = 18} & 1.917 & 0.883 & text{-53.938%}\ hline
text{To-hit = 19} & 1.400 & 0.883 & text{-36.929%}\ hline
text{To-hit = 20} & 0.883 & 0.883 & text{-0.000%}\ hline
end{array}
I'm producing these values just as a confirmation against Andras' values: I believe the small difference between our results are just the consequences of using different damage dice, and that based on my own results, their values are probably correct for their scenario.
answered 6 hours ago
XiremaXirema
21.1k263123
answered 6 hours ago
XiremaXirema
21.1k263123
answered 6 hours ago
XiremaXirema
21.1k263123
answered 6 hours ago
XiremaXirema
21.1k263123
21.1k263123
$begingroup$
This is kind of my point (and I think you're the right user to explain this to me), but if different to-hit and ACs create differences, then don't we need to know those values in order to answer this?14-30% with your current dataset is fairly swingy.
$endgroup$
– NautArch
6 hours ago
$begingroup$
@András I have a program I use to generate values. There's a discussion here for this answer that describes the in-detail methodology.
$endgroup$
– Xirema
5 hours ago
1
$begingroup$
@András The table uses MathJax. You can attempt to edit the post and look at the markup to figure out how it works. Alternately, you can use the generator at tablesgenerator to create a table, though you need to change thebegin{table}begin{tabular}tags tobegin{array}to work on Stack Overflow.
$endgroup$
– Xirema
5 hours ago
$begingroup$
@Xirema thank you
$endgroup$
– András
5 hours ago
add a comment |
$begingroup$
This is kind of my point (and I think you're the right user to explain this to me), but if different to-hit and ACs create differences, then don't we need to know those values in order to answer this?14-30% with your current dataset is fairly swingy.
$endgroup$
– NautArch
6 hours ago
$begingroup$
@András I have a program I use to generate values. There's a discussion here for this answer that describes the in-detail methodology.
$endgroup$
– Xirema
5 hours ago
1
$begingroup$
@András The table uses MathJax. You can attempt to edit the post and look at the markup to figure out how it works. Alternately, you can use the generator at tablesgenerator to create a table, though you need to change thebegin{table}begin{tabular}tags tobegin{array}to work on Stack Overflow.
$endgroup$
– Xirema
5 hours ago
$begingroup$
@Xirema thank you
$endgroup$
– András
5 hours ago
$begingroup$
This is kind of my point (and I think you're the right user to explain this to me), but if different to-hit and ACs create differences, then don't we need to know those values in order to answer this?14-30% with your current dataset is fairly swingy.
$endgroup$
– NautArch
6 hours ago
$begingroup$
This is kind of my point (and I think you're the right user to explain this to me), but if different to-hit and ACs create differences, then don't we need to know those values in order to answer this?14-30% with your current dataset is fairly swingy.
$endgroup$
– NautArch
6 hours ago
$begingroup$
@András I have a program I use to generate values. There's a discussion here for this answer that describes the in-detail methodology.
$endgroup$
– Xirema
5 hours ago
$begingroup$
@András I have a program I use to generate values. There's a discussion here for this answer that describes the in-detail methodology.
$endgroup$
– Xirema
5 hours ago
1
1
$begingroup$
@András The table uses MathJax. You can attempt to edit the post and look at the markup to figure out how it works. Alternately, you can use the generator at tablesgenerator to create a table, though you need to change the
begin{table}begin{tabular} tags to begin{array} to work on Stack Overflow.$endgroup$
– Xirema
5 hours ago
$begingroup$
@András The table uses MathJax. You can attempt to edit the post and look at the markup to figure out how it works. Alternately, you can use the generator at tablesgenerator to create a table, though you need to change the
begin{table}begin{tabular} tags to begin{array} to work on Stack Overflow.$endgroup$
– Xirema
5 hours ago
$begingroup$
@Xirema thank you
$endgroup$
– András
5 hours ago
$begingroup$
@Xirema thank you
$endgroup$
– András
5 hours ago
add a comment |
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Let us continue this discussion in chat.
$endgroup$
– NautArch
6 hours ago