Grod_The_Giant

2019-05-27, 10:20 AM

Spinning out of this thread (http://www.giantitp.com/forums/showthread.php?588726-The-Decline-of-Armor-in-D-amp-D), I got to thinking... it's generally agreed that it's more "realistic" for armor to reduce damage than it is to reduce your to-hit. It's also generally agreed that you can't really fit that into the D&D paradigm without totally rewriting everything. Well...that sounded like a challenge to me. One buttload of math (https://www.dropbox.com/s/cv35xelv4q86gl8/Armor%20to%20Soak.xlsx?dl=0) later, I think I've cracked it. BEHOLD:

Armor Class: A character's Armor Class (AC) is 10 plus their Dexterity modifier. If they're wearing Medium Armor, they can't apply more than a +2 bonus towards their AC; if they're wearing heavy armor, they can't add their Dexterity to AC. Shields and the Defensive fighting style still work normally.

Soak: Rather than increasing armor class, wearing armor provides Soak. Every round, your armor can absorb damage equal to its soak-- up until that point is reached, attacks don't reduce your hit points at all. The amount of soak provided depends on the type of armor you're wearing, and on your level:

Armor Type

Soak

Unarmored

None

Light Armor

1/2 level + 2

Medium Armor

Level + 1

Heavy Armor

2 * level +2

Plate Armor

2.5 * Level +2

Always round down when calculating your soak. Magic armor applies its bonus to your level when calculating soak, rather than to AC. For example, a 10th level character wearing a suit of +2 scalemail would have a Soak of 26.

Apply your soak before your Resistances, if any apply.

Monsters and Soak

Not all monsters have soak--only those whose Armor Class entry specifies natural armor. Subtract 10 + its Dexterity to determine how much natural AC it has, and give it soak based on that value. (Specifically, as if it were wearing +X armor, where X is the difference between its natural armor and the next lowest category of armor, with CR in place of its level).

Armor Points: Wearing armor grants a character Armor Points. Similar to temporary hit points, Armor Points (AP) are a buffer against damage, representing how many hits your armor can safely absorb before being disabled. Just like temporary hit points you have AP and are damaged by an attack, your AP are lost first and any leftover damage carries over to your temporary hit points (if any), then to your normal hit points. Note that AP only apply against weapon and spell attacks-- effects requiring saving throws, such as a Fireball spell, ignore them completely.

Healing can't restore AP. However, the Mending cantrip restores a number of AP equal to the caster's spellcasting ability modifier, and anyone proficient in the type of armor they're wearing can restore all their lost AP by taking one minute to quickly patch up broken straps and dents.

AP are based on your level and on the type of armor you're wearing. A character gains one AP per level per point of bonus AC granted by their armor (that is, AC above 10). For example, wearing Leather Armor would receive 1 AP/level, while someone wearing a Breastplate would gain 4 AP/level, and a suit of plate mail grants a whopping 8 AP/level.

(I know that seems like too convenient a value to be right, but I swear--I did the calculations for how much each extra point of AC is worth, based on three rounds of combat, and it comes out to almost exactly that)

AP and Monsters: Figuring out how many AP a monster has is simple. First, determine its armor bonus by subtracting 10+its Dexterity modifier from its written AC. Multiply that value by its CR to get its total AP. (For simplicity's sake, you might as well go ahead and combine their AP and HP pools--the differences are functionally irrelevant for monsters who'll only appear for a single encounter at a time).

Effect: Ideally, you'll see a real difference between heavily-armored and lightly-armored characters. A Monk or Rogue will get hit very rarely, but almost every shot will come out of their real health. A Fighter or Paladin, on the other hand, will be struck regularly--but they'll be able to absorb those shots with no ill effect.

I started by calculating how likely a monster of CR X was to hit each AC from 10-25, using the "Monster Stats by CR" table in the DMG to get my numbers1.

Then, figuring that the most common case for monsters seems to be two swings/action, I multiplied half the expected DPR2 by their chance of hitting a given AC, to determine the average DPR of each attack.

Subtracting that value from the the original expected DPR/swing gives me a number for how much a given AC reduces a monster's DPR.

Subtracting the reduction of AC 10 tells me how much extra damage reduction each point of AC is worth.

I estimated how much each kind of armor increases your AC from the base of 10, on average: light, medium, heavy, and plate (which is better enough and expensive enough it's practically a category of its own)3. I figured that light armor was a +2 boost, medium armor a +4, heavy a +6, and plate a +8--AC 12, 14, 16, and 18.

I ran some linear regressions against my chosen values, comparing damage negated to AC, and simplified the resulting formulas to something usable.

Assumptions

1: To keep from making things too complicated, I did all my math for players of level X fighting a monster of CR X. I'm not sure how badly things start to warp if you move away from that, but that's a baseline medium encounter, and this gets exponentially more complicated if I do anything else, so...

2: DMG page 278 says to calculate DPR by taking the average damage of each attack, but says nothing about the chance to hit. Thus, I'm assuming that the DPR column of the table is assuming all attacks hit, and so it makes a good stand-in for damage/attack.

3: Specifically, I figured these against a base AC of 10+Dex, capped a +2 for medium armor and a flat 10 for heavy armor.

Armor Class: A character's Armor Class (AC) is 10 plus their Dexterity modifier. If they're wearing Medium Armor, they can't apply more than a +2 bonus towards their AC; if they're wearing heavy armor, they can't add their Dexterity to AC. Shields and the Defensive fighting style still work normally.

Soak: Wearing armor reduces all damage you take, by a value based on your level. The heavier the armor, the more soak it provides:

Armor Type

Soak

Unarmored

None

Light Armor

1/4 level

Medium Armor

1/2 level + 1

Heavy Armor

3/4 level +2

Plate Armor

Level +2

Always round down when calculating your soak. Magic armor applies its AC bonus towards your soak instead of your AC. Apply your soak before your Resistances, if any apply.

Attacking with Advantage

If you have advantage on your attack roll, you can choose to forfeit the extra die roll. If you do, your opponent's soak is halved against your attack.

Monsters and Soak

Not all monsters have soak--only those whose Armor Class entry specifies natural armor. Subtract 10 + its Dexterity to determine how much natural AC it has, and give it soak based on that value. (Specifically, as if it were wearing +X armor, where X is the difference between its natural armor and the next lowest category of armor, with CR in place of its level)

Natural Armor Bonus

Soak

1

1

2

1/4 CR (min 1)

3

1/4 CR +1

4

1/2 CR +1

5

1/2 CR +2

6

3/4 CR +2

7

3/4 CR +3

8

CR +2

9

CR +3

10

CR +4

11

CR +5

12

CR +6

13

CR +7

14

CR +8

15

CR +9

The Barbarian's Unarmored Defense instead grants them soak as if they were wearing medium armor.

The Monk's Unarmored Defense works normally-- they get no soak, but exceptionally high AC.

Mage Armor and the Lizardfolk's Natural Armor give you soak as though you were wearing +1 light armor.

Barkskin and the Tortle's Natural Armor give you soak as though you were wearing heavy armor.

Armor Class: A character's Armor Class (AC) is 10 plus their Dexterity modifier. If they're wearing Medium Armor, they can't apply more than a +2 bonus towards their AC; if they're wearing heavy armor, they can't add their Dexterity to AC. Shields and the Defensive fighting style still work normally.

Soak: Rather than increasing armor class, wearing armor provides Soak. Every round, your armor can absorb damage equal to its soak-- up until that point is reached, attacks don't reduce your hit points at all. The amount of soak provided depends on the type of armor you're wearing, and on your level:

Armor Type

Soak

Unarmored

None

Light Armor

1/2 level + 2

Medium Armor

Level + 1

Heavy Armor

2 * level +2

Plate Armor

2.5 * Level +2

Always round down when calculating your soak. Magic armor applies its bonus to your level when calculating soak, rather than to AC. For example, a 10th level character wearing a suit of +2 scalemail would have a Soak of 26.

Apply your soak before your Resistances, if any apply.

Monsters and Soak

Not all monsters have soak--only those whose Armor Class entry specifies natural armor. Subtract 10 + its Dexterity to determine how much natural AC it has, and give it soak based on that value. (Specifically, as if it were wearing +X armor, where X is the difference between its natural armor and the next lowest category of armor, with CR in place of its level).

Armor Points: Wearing armor grants a character Armor Points. Similar to temporary hit points, Armor Points (AP) are a buffer against damage, representing how many hits your armor can safely absorb before being disabled. Just like temporary hit points you have AP and are damaged by an attack, your AP are lost first and any leftover damage carries over to your temporary hit points (if any), then to your normal hit points. Note that AP only apply against weapon and spell attacks-- effects requiring saving throws, such as a Fireball spell, ignore them completely.

Healing can't restore AP. However, the Mending cantrip restores a number of AP equal to the caster's spellcasting ability modifier, and anyone proficient in the type of armor they're wearing can restore all their lost AP by taking one minute to quickly patch up broken straps and dents.

AP are based on your level and on the type of armor you're wearing. A character gains one AP per level per point of bonus AC granted by their armor (that is, AC above 10). For example, wearing Leather Armor would receive 1 AP/level, while someone wearing a Breastplate would gain 4 AP/level, and a suit of plate mail grants a whopping 8 AP/level.

(I know that seems like too convenient a value to be right, but I swear--I did the calculations for how much each extra point of AC is worth, based on three rounds of combat, and it comes out to almost exactly that)

AP and Monsters: Figuring out how many AP a monster has is simple. First, determine its armor bonus by subtracting 10+its Dexterity modifier from its written AC. Multiply that value by its CR to get its total AP. (For simplicity's sake, you might as well go ahead and combine their AP and HP pools--the differences are functionally irrelevant for monsters who'll only appear for a single encounter at a time).

Effect: Ideally, you'll see a real difference between heavily-armored and lightly-armored characters. A Monk or Rogue will get hit very rarely, but almost every shot will come out of their real health. A Fighter or Paladin, on the other hand, will be struck regularly--but they'll be able to absorb those shots with no ill effect.

I started by calculating how likely a monster of CR X was to hit each AC from 10-25, using the "Monster Stats by CR" table in the DMG to get my numbers1.

Then, figuring that the most common case for monsters seems to be two swings/action, I multiplied half the expected DPR2 by their chance of hitting a given AC, to determine the average DPR of each attack.

Subtracting that value from the the original expected DPR/swing gives me a number for how much a given AC reduces a monster's DPR.

Subtracting the reduction of AC 10 tells me how much extra damage reduction each point of AC is worth.

I estimated how much each kind of armor increases your AC from the base of 10, on average: light, medium, heavy, and plate (which is better enough and expensive enough it's practically a category of its own)3. I figured that light armor was a +2 boost, medium armor a +4, heavy a +6, and plate a +8--AC 12, 14, 16, and 18.

I ran some linear regressions against my chosen values, comparing damage negated to AC, and simplified the resulting formulas to something usable.

Assumptions

1: To keep from making things too complicated, I did all my math for players of level X fighting a monster of CR X. I'm not sure how badly things start to warp if you move away from that, but that's a baseline medium encounter, and this gets exponentially more complicated if I do anything else, so...

2: DMG page 278 says to calculate DPR by taking the average damage of each attack, but says nothing about the chance to hit. Thus, I'm assuming that the DPR column of the table is assuming all attacks hit, and so it makes a good stand-in for damage/attack.

3: Specifically, I figured these against a base AC of 10+Dex, capped a +2 for medium armor and a flat 10 for heavy armor.

Armor Class: A character's Armor Class (AC) is 10 plus their Dexterity modifier. If they're wearing Medium Armor, they can't apply more than a +2 bonus towards their AC; if they're wearing heavy armor, they can't add their Dexterity to AC. Shields and the Defensive fighting style still work normally.

Soak: Wearing armor reduces all damage you take, by a value based on your level. The heavier the armor, the more soak it provides:

Armor Type

Soak

Unarmored

None

Light Armor

1/4 level

Medium Armor

1/2 level + 1

Heavy Armor

3/4 level +2

Plate Armor

Level +2

Always round down when calculating your soak. Magic armor applies its AC bonus towards your soak instead of your AC. Apply your soak before your Resistances, if any apply.

Attacking with Advantage

If you have advantage on your attack roll, you can choose to forfeit the extra die roll. If you do, your opponent's soak is halved against your attack.

Monsters and Soak

Not all monsters have soak--only those whose Armor Class entry specifies natural armor. Subtract 10 + its Dexterity to determine how much natural AC it has, and give it soak based on that value. (Specifically, as if it were wearing +X armor, where X is the difference between its natural armor and the next lowest category of armor, with CR in place of its level)

Natural Armor Bonus

Soak

1

1

2

1/4 CR (min 1)

3

1/4 CR +1

4

1/2 CR +1

5

1/2 CR +2

6

3/4 CR +2

7

3/4 CR +3

8

CR +2

9

CR +3

10

CR +4

11

CR +5

12

CR +6

13

CR +7

14

CR +8

15

CR +9

The Barbarian's Unarmored Defense instead grants them soak as if they were wearing medium armor.

The Monk's Unarmored Defense works normally-- they get no soak, but exceptionally high AC.

Mage Armor and the Lizardfolk's Natural Armor give you soak as though you were wearing +1 light armor.

Barkskin and the Tortle's Natural Armor give you soak as though you were wearing heavy armor.