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












13












$begingroup$


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







share|improve this question











$endgroup$












  • $begingroup$
    Let us continue this discussion in chat.
    $endgroup$
    – NautArch
    11 hours ago
















13












$begingroup$


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







share|improve this question











$endgroup$












  • $begingroup$
    Let us continue this discussion in chat.
    $endgroup$
    – NautArch
    11 hours ago














13












13








13


1



$begingroup$


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







share|improve this question











$endgroup$




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






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 11 hours ago









doppelgreener♦

32.4k11137231




32.4k11137231










asked 13 hours ago









AndrásAndrás

28.7k14112206




28.7k14112206












  • $begingroup$
    Let us continue this discussion in chat.
    $endgroup$
    – NautArch
    11 hours ago


















  • $begingroup$
    Let us continue this discussion in chat.
    $endgroup$
    – NautArch
    11 hours ago
















$begingroup$
Let us continue this discussion in chat.
$endgroup$
– NautArch
11 hours ago




$begingroup$
Let us continue this discussion in chat.
$endgroup$
– NautArch
11 hours ago










2 Answers
2






active

oldest

votes


















28












$begingroup$

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!
enter image description here



Graph



enter image description here




1) Criticals complicate things






share|improve this answer











$endgroup$









  • 4




    $begingroup$
    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
    13 hours ago






  • 1




    $begingroup$
    Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
    $endgroup$
    – GreySage
    13 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
    13 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
    12 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
    11 hours ago



















6












$begingroup$

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.






share|improve this answer









$endgroup$













  • $begingroup$
    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
    11 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
    11 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 the begin{table}begin{tabular} tags to begin{array} to work on Stack Overflow.
    $endgroup$
    – Xirema
    10 hours ago












  • $begingroup$
    @Xirema thank you
    $endgroup$
    – András
    10 hours ago











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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









28












$begingroup$

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!
enter image description here



Graph



enter image description here




1) Criticals complicate things






share|improve this answer











$endgroup$









  • 4




    $begingroup$
    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
    13 hours ago






  • 1




    $begingroup$
    Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
    $endgroup$
    – GreySage
    13 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
    13 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
    12 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
    11 hours ago
















28












$begingroup$

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!
enter image description here



Graph



enter image description here




1) Criticals complicate things






share|improve this answer











$endgroup$









  • 4




    $begingroup$
    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
    13 hours ago






  • 1




    $begingroup$
    Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
    $endgroup$
    – GreySage
    13 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
    13 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
    12 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
    11 hours ago














28












28








28





$begingroup$

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!
enter image description here



Graph



enter image description here




1) Criticals complicate things






share|improve this answer











$endgroup$



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!
enter image description here



Graph



enter image description here




1) Criticals complicate things







share|improve this answer














share|improve this answer



share|improve this answer








edited 13 hours ago

























answered 13 hours ago









AndrásAndrás

28.7k14112206




28.7k14112206








  • 4




    $begingroup$
    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
    13 hours ago






  • 1




    $begingroup$
    Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
    $endgroup$
    – GreySage
    13 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
    13 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
    12 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
    11 hours ago














  • 4




    $begingroup$
    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
    13 hours ago






  • 1




    $begingroup$
    Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
    $endgroup$
    – GreySage
    13 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
    13 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
    12 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
    11 hours ago








4




4




$begingroup$
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
13 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
13 hours ago




1




1




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






$begingroup$
Really nice answer. Interesting how it goes all the way up to 57%, then drops to 0.
$endgroup$
– GreySage
13 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
13 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
13 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
12 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
12 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
11 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
11 hours ago













6












$begingroup$

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.






share|improve this answer









$endgroup$













  • $begingroup$
    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
    11 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
    11 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 the begin{table}begin{tabular} tags to begin{array} to work on Stack Overflow.
    $endgroup$
    – Xirema
    10 hours ago












  • $begingroup$
    @Xirema thank you
    $endgroup$
    – András
    10 hours ago
















6












$begingroup$

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.






share|improve this answer









$endgroup$













  • $begingroup$
    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
    11 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
    11 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 the begin{table}begin{tabular} tags to begin{array} to work on Stack Overflow.
    $endgroup$
    – Xirema
    10 hours ago












  • $begingroup$
    @Xirema thank you
    $endgroup$
    – András
    10 hours ago














6












6








6





$begingroup$

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.






share|improve this answer









$endgroup$



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.







share|improve this answer












share|improve this answer



share|improve this answer










answered 11 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
    11 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
    11 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 the begin{table}begin{tabular} tags to begin{array} to work on Stack Overflow.
    $endgroup$
    – Xirema
    10 hours ago












  • $begingroup$
    @Xirema thank you
    $endgroup$
    – András
    10 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
    11 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
    11 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 the begin{table}begin{tabular} tags to begin{array} to work on Stack Overflow.
    $endgroup$
    – Xirema
    10 hours ago












  • $begingroup$
    @Xirema thank you
    $endgroup$
    – András
    10 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
11 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
11 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
11 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
11 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
10 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
10 hours ago














$begingroup$
@Xirema thank you
$endgroup$
– András
10 hours ago




$begingroup$
@Xirema thank you
$endgroup$
– András
10 hours ago


















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