Guide to Armor Penetration calculations

### **Introduction**

The purpose of this guide is to help you calculate how much benefit you get from x% armor penetration and consequently decide whether picking up armor penetration talents/REs and items with armor penetration ratings is worth it compared to getting other stats.

**TL:DR -> take a look at appendices showing you exactly how much value armor pen provides per percentage in different generic scenarios.**

### **General Information**

Generally speaking 100% armor penetration (ArP) obtained from talents, items and buffs does not account for 100% armor reduction, however if you manage to reduce the armor of the boss low enough with armor reduction effects applied to the boss, there is a crossover point where 100%  ArP is actually 100% armor reduction and thus the boss’ armor will be reduced to 0. Therefore it is possible for 100% ArP to account for 100% armor reduction.

In WotLK this was only possible if the boss was debuffed with a Major & Minor armor debuff & Shattering throw and the player had 100% ArP,  This was only for  the limited duration of shattering throw’s debuff. This technique is not applicable to Ascension since shattering throw only applies 5 stacks of Sunder Armor. However on Ascension we have special armor reduction debuffs from LREs, which allow us to constantly keep up the 100% armor reduction. We will see this in the calculations below.

### Armor Debuff Types

Minor: Faire Fire/Curse of Weakness/Scorpid Sting/Wasp Pet's Sting -> 5%

Major: Shattering Throw/Sunder armor/Expose armor/Nature's fervor/Worm Pet's Acid Spit -> 20%

Ascension special: Blademaster -> 10%, Demolisher -> Flat 608/371 armor (Level 70/60)

Flat Armor Debuff from items: Annihilator - 3x200 armor, Rivenspike/Bashguder - 3x200 armor , Crystal Yield - 200 armor

### Reduction effects order of operations

Flat Armor debuffs stack additively and apply first. Percentage armor debuffs stack multiplicatively and apply after the flat armor reduction, if all 3 above mentioned percentage reduction is applied then calculation is *Armor \* 0.95 \* 0.8  \* 0.9*. Armor penetration percentage from talents, buffs and from armor penetration rating stack additively. For instance 10% from battle stance + 15% from mace spec + 5% armor penetration from armor penetration rating from items would end up 30%.

Once again the order in which armor pen is calculated is:

1. Flat armor debuff is reduced from boss armor

2. Armor % debuff is reduced from boss armor

3. Personal armor penetration % is applied to a certain portion of the debuffed armor. This certain portion is called the armor cap and will be addressed later on.

### Raid Boss Armor Values

In Vanilla and The Burning Crusade there are 2 types of bosses with different armor values. These two types are bosses with or without Mana aka spell user and non spell user. Spell user bosses (e.g. Shade of Aran) will have lower armor compared to non spell users (e.g. Gruul). In WOTLK all bosses have the same armor. Lower armor TBC bosses confirmed after the armor value change on the 6th of August 2022: Shade of Aran, Lady Vashj, Leotheras the Blind, High Astromancer Solarian, Void Reaver, Kaelthas Sunstrider, Maiden of Virtue, Netherspite and Hex Lord Malachrass. Armor of world mobs and dungeon bosses can be found in Appendix F.

Link to message on ascension official discord server, also screenshot below. Further info about the impact of this change can be found here.

### Armor Constant

The armor constant is used for calculating the damage reduction you have against certain level targets, the targets have against you and is a part of the formula used to determine the maximum amount of armor you can ignore from a certain target. We will see exactly how that works later on in the guide.

In game, the character sheet displays your armor and how much damage reduction it translates to, however that's only valid against same level targets, therefore in order to reach to same amount of damage reduction against boss targets you need more armor. The damage reduction cap is 75%, in order to reach that as a level 70 character against level 73 boss targets you need 35880 armor, whereas you only need 31673 armor to reach 75% damage reduction against level 70 targets.

The armor constant at and above level 60 is calculated via the following formula:

*Armor constant = 400 + 85 \* attackerLevel + 4.5 \* 85 \* (attackerLevel-59)*

Armor constants used to calculate the damage reduction from armor of a player against a boss.

Armor constants used to calculate the damage reduction from armor of a boss against a player.

### Armor Penetration Cap/Ignorable Armor

There is a certain limit to the amount of armor you can ignore with your personal armor penetration, this limit will be referred to as the armor penetration cap/ignorable armor. The armor penetration cap is not predefined and is changing based on the armor reduction effects applied to the target. In general this cap is less than the total amount of armor the boss has therefore 100% armor penetration will not reduce your opponents armor to 0, however as mentioned above there is a crossover point where the armor cap can be equal to the armor of the boss, thus enabling armor penetration effects to completely negate the opponent's armor.

The Armor Penetration Cap is calculated by a minimum function defined as:

*Armor Penetration Cap = MIN[ ( Armor Constant based on level defined above + Armor) / 3 , Armor ]*

An example scenario at Level 70 for the armor penetration cap would like like this:

LvL 73 non mana user boss with 6390 armor and LvL 70 attacker with armor constant 10557.5

Armor Penetration Cap = MIN[ ( 10557.5 + 6390) / 3 , 6390 ] = MIN[ 5649.17, 6390] -> Chose the lowest/minimum value out of the available options -> the chosen value is 5649.17 therefore the armor penetration cap is 5649.17.

### **Damage Reduction & Damage Applied**

The Damage Reduction (DR) from armor and Damage applied (DA) can be calculated using the formulas below:

*Damage Reduction = Armor / (Armor + Armor Constant)*

*Damage applied = 1 - Damage reduction*

An example scenario at Level 70 for the damage reduction calculation would like like this:

Level 73 non mana user boss with 6390 armor and armor constant 11960.

Level 70 attacker with 20k armor and armor constant 10557.5.

Damage reduction of boss against the player = 6390/ ( 6390 + 10557.5) = 0.3770 -> 37.70% damage reduction

Damage applied of player to the boss = 1 - 0.3770 = 0.623 -> 62.3% damage applied

Damage reduction of the player against the boss = 20000/(20000 + 11960) = 0.6258 -> 62.58% damage reduction

Damage applied of the boss to the player = 1 - 0.6258 = 0.3742 -> 37.42%

### **Calculation Examples**

#### Level 73 Mana user boss and Level 70 attacker ArP calculation example

***Step 1.*** Calculate reduction from Major (20%) and Minor (5%) armor debuff, if we consider the special 10% debuff introduced by LREs such as Blademaster, should also be calculated here:

The base damage reduction of the boss without any modifiers is:

DR = 5545 /(5545+10557.5) = 0.3444 -> 34.44% damage reduction

DA = 1-0.3444 = 0.6556 - > 65.56% damage applied

After the application of a Major and Minor armor debuff, the following will happen

5545 \* 0.8 \* 0.95 =~ 4214 armor -> 28.53% damage reduction -> 71.47% damage applied

Calculate % damage increase by dividing the new damage applied value with the old damage applied value and subtract one from the result to get the percentage damage increase.

Therefore the value of a Major and Minor armor debuff on a mana user boss is  71.47 / 65.56 = 1.0901 - 1= 0.901 -> 9.01% physical damage increase.

***Step 2.*** Calculate the Armor cap with the formula and armor constant defined in the armor cap section, and the armor value which has been reduced by the debuffs :

Armor cap = MIN[(4214 + 10557.5)/3, 4214] = MIN[ 4924, 4214] = 4214

The armor cap here is 4214 which is the full armor of the boss, therefore in this case if you have 100% ArP the boss' armor will be completely negated.

Step 3. Take the armor cap value defined in step 2, calculate your current  ArP % from your char sheet, talents and buffs, these stack additively as mentioned previously.

Taking 50% ArP as an example, multiply the ignorable armor by the % armor pen you have and then subtract it from the boss armor.

The calculation is as follows:

4214 - (4214 \* 0.5) = 2107 armor which is 16.64% damage reduction -> 83.36% damage applied

Therefore 50% ArP equals 83.36 / 71.47 = 1.1664 -> 16.64% physical damage increase

100% ArP means that the damage applied goes from 71.47 to 100% -> 100 / 71.47 = 1.3992 - 1 = 0.3992 -> 39.92% physical damage increase.

#### **Level 73 Non Mana user boss and Level 70 attacker ArP calculation example**

***Step 1.*** Calculate reduction from Major (20%) and Minor (5%) armor debuff, if we consider the special 10% debuff introduced by LREs such as Blademaster, should also be calculated here:

The base damage reduction of the boss without any modifiers is:

Damage reduction = 6390/ ( 6390 + 10557.5) = 0.3770 -> 37.70% damage reduction

Damage applied = 1 - 0.3770 = 0.623 -> 62.3% damage applied

After the application of a Major and Minor armor debuff, the following will happen

6390 \* 0.8 \* 0.95 =~ 4856 armor = 31.5% damage reduction -> 68.5% damage applied

Calculate % damage increase by dividing the new damage applied value with the old damage applied value and subtract one from the result to get the percentage damage increase.

Therefore the value of a Major and Minor armor debuff on a non mana user boss is  68.5 / 62.3 = 1.0995 - 1= 0.0995 -> 9.95% physical damage increase.

***Step 2.*** Calculate the Armor cap with the formula and armor constant defined in the armor cap section, and the armor value which has been reduced by the debuffs :

Armor cap = MIN[(4856 + 10557.5)/3, 4856] = MIN[ 5138 , 4856] = 4856

The armor cap here is 4856 which is the full armor of the boss, therefore in this case if you have 100% ArP the boss' armor will be completely negated.

The below section is not applicable anymore after the armor nerfs hence the strikethrough. Due to the armor nerfs on level 70 (still applicable on level 60 though) even non mana user bosses will have their armor reduced without any additional armor reduction effects, therefore these provide no extra value if 100% armor penetration is achieved. The old calculation can be found in the Archive section. Leaving it here as an example for how these additional resources were needed previously to achieve real 100% armor pen (meaning that the boss' armor would be reduced to 0).

*~~Therefore, the armor cap is 5465, whereas the boss has 5781 armor, so even if you get 100% ArP, the boss will still have 5781 - 5446 = 335 armor => 3.08% damage reduction and thus your damage applied will cap out at 1 - 0.0307 = 0.9693 -> 96.92%.~~*

*~~Calculating  the additional 10% armor reduction applied by Blademaster would be 5840 \* 0.9 = 5256; MIN[(5256 + 10557.5)/3, 5256] = 5256. The ignorable armor is equal to the boss armor therefore this shows 100% ArP will negate the bosses armor to 0% when the debuff from Blademaster is up.~~*

*~~Calculating the additional flat reduction applied by Demolisher would be (7607 - 608) \* 0. 8 \* 0.95 = 5319; MIN[(5319 + 10557.5)/3, 5319] = 5292. The ignorable armor is 5292 whereas the boss armor is 5319, therefore in this case with 100% ArP the boss will still have 5319 - 5292 = 27 armor left, which equals to 0.25% damage reduction.~~*

**Step 3.** Take the armor cap value defined in step 2, calculate your current  ArP % from your char sheet, talents and buffs, these stack additively as mentioned previously.

Taking 30% ArP as an example, multiply the ignorable armor by the % armor pen you have and then subtract it from the boss armor.

The calculation is as follows:

4856 - (4856 \* 0.3) = ~3399 armor = 24.35% damage reduction -> 75.65% damage applied.

Therefore 30% ArP -> 75.65 / 68.5 = 1.1111 - 1 = 0.1044 -> 10.44% physical damage increase.

100% ArP means the damage applied goes from 68.5% to 100% -> 100 / 68.5= 1.4599 - 1 = 0.4599 -> 45.99% physical damage increase.

### Appendices

#### Appendix A - Level 63 mana user boss against Level 60 attacker ArP Damage Increase Table

This table assumes the boss has Major and Minor armor debuffs.

#### Appendix B - Level 63 non mana user boss against Level 60 attacker ArP Damage Increase Table

This table assumes the boss has Major and Minor armor debuffs.

#### Appendix C - Level 73 mana user boss against Level 70 attacker ArP Damage Increase Table

This table assumes the boss has Major and Minor armor debuffs.

#### Appendix D - Level 73 non mana user boss against Level 70 attacker ArP Damage Increase Table

This table assumes the boss has Major and Minor armor debuffs.

#### Appendix E - Level 83 boss against Level 80 attacker ArP Damage Increase Table

This table assumes the boss has Major and Minor armor debuffs.

#### Appendix F - Creature Armor Table based on Level & Type

This armor table applies to all creatures except raid bosses, so the table applies to dungeon bosses. Raid boss armor values are documented above. Lower armor is mana user, higher armor non mana user.

### Archive

***This section contains calculations before the armor change of 2022 August 6.***

#### OLD - Level 73 Mana user boss and Level 70 attacker ArP calculation example

***Step 1.*** Calculate reduction from Major (20%) and Minor (5%) armor debuff, if we consider the special 10% debuff introduced by LREs such as Blademaster, should also be calculated here:

The base damage reduction of the boss without any modifiers is:

DR = 6131 / (6131+10557.5) = 0.3673% -> 36.73% damage reduction

DA = (1 - 0.3673) = 0.6327 - > 63.27% damage applied

After the application of a Major and Minor armor debuff, the following will happen

6131 \* 0.8 \* 0.95 =~ 4660 armor -> 30.62% damage reduction -> 69.38% damage applied

Calculate % damage increase by dividing the new damage applied value with the old damage applied value and subtract one from the result to get the percentage damage increase.

Therefore the value of a Major and Minor armor debuff on a mana user boss is  69.38 / 63.27 = 1.0965 - 1= 0.965 -> 9.65% physical damage increase.

***Step 2.*** Calculate the Armor cap with the formula and armor constant defined in the armor cap section, and the armor value which has been reduced by the debuffs :

Armor cap = MIN[(4660 + 10557.5)/3, 4660] = MIN[ 5072.5 , 4660] = 4660

The armor cap here is 4660 which is the full armor of the boss, therefore in this case if you have 100% ArP the boss' armor will be completely negated.

**Step 3.** Take the armor cap value defined in step 2, calculate your current  ArP % from your char sheet, talents and buffs, these stack additively as mentioned previously.

Taking 50% ArP as an example, multiply the ignorable armor by the % armor pen you have and then subtract it from the boss armor.

The calculation is as follows:

4660 - (4660 \* 0.5) = 2330 armor which is 18.08% damage reduction -> 81.92% damage applied

Therefore 50% ArP -> 81.92 / 69.38 -> 1.1808 -> 18.08% physical damage increase

100% ArP means that the damage applied goes from 69.4% to 100% -> 100 / 69.38 = 1.4413 - 1 = 0.4413 -> 44.13%  physical damage increase.

#### OLD - **Level 73 Non Mana user boss and Level 70 attacker ArP calculation example**

***Step 1.*** Calculate reduction from Major (20%) and Minor (5%) armor debuff, if we consider the special 10% debuff introduced by LREs such as Blademaster, should also be calculated here:

The base damage reduction of the boss without any modifiers is:

Damage reduction = 7607 / ( 7607 + 10557.5) = 0.4187 -> 41.87% damage reduction

Damage applied = 1 - 0.4187 = 0.5813 -> 58.13% damage applied

After the application of a Major and Minor armor debuff, the following will happen

7607 \* 0.8 \* 0.95 =~ 5781 armor = 35.38% damage reduction -> 64.62% damage applied

Calculate % damage increase by dividing the new damage applied value with the old damage applied value and subtract one from the result to get the percentage damage increase.

Therefore the value of a Major and Minor armor debuff on a non mana user boss is  64.62 / 58.13 = 1.1116 - 1= 0.1116 -> 11.16% physical damage increase.

***Step 2.*** Calculate the Armor cap with the formula and armor constant defined in the armor cap section, and the armor value which has been reduced by the debuffs :

Armor cap = MIN[(5781 + 10557.5)/3, 5781] = MIN[ 5446 , 5781] = 5446

Therefore the the armor cap is 5465, whereas the boss has 5781 armor, so even if you get 100% arp, the boss will still have 5781 - 5446 = 335 armor => 3.08% damage reduction and thus your damage applied will cap out at 1 - 0.0307 = 0.9693 -> 96.92%.

*Calculating  the additional 10% armor reduction applied by Blademaster would be 5840 \* 0.9 = 5256; MIN[(5256 + 10557.5)/3, 5256] = 5256. The ignorable armor is equal to the boss armor therefore this shows 100% ArP will negate the bosses armor to 0% when the debuff from Blademaster is up.*

*Calculating the additional flat reduction applied by Demolisher would be (7607 - 608) \* 0. 8 \* 0.95 = 5319; MIN[(5319 + 10557.5)/3, 5319] = 5292. The ignorable armor is 5292 whereas the boss armor is 5319, therefore in this case with 100% ArP the boss will still have 5319 - 5292 = 27 armor left, which equals to 0.25% damage reduction.*

**Step 3.** Take the armor cap value defined in step 2, calculate your current  ArP % from your char sheet, talents and buffs, these stack additively as mentioned previously.

Taking 30% ArP as an example, multiply the ignorable armor by the % armor pen you have and then subtract it from the boss armor.

The calculation is as follows:

5781 - (5446 \* 0.3) = ~4147 armor = 28.20% damage reduction -> 71.8% damage applied.

Therefore 30% ArP -> 71.8 / 64.62 = 1.1111 - 1 = 0.1111 -> 11.11% physical damage increase.

100% ArP means the damage applied goes from 64.62% to 96.92% -> 96.92 / 64.62 = 1.4998 - 1 = 0.4998 -> 49.98%  physical damage increase.

#### Impact of Base Armor Reduction for Level 73 Bosses - 6th of August 2022

Even though the armor reduction of bosses at level 73 is a buff to physical based builds, it reduced the value of armor penetration overall since the amount of armor is less therefore the amount of armor to be reduced is also less which means less damage increase to be gained. This means that some builds might need to reconsider their choices and pick other talents instead of armor pen talents, however this needs to be evaluated on a case-by-case basis.

Damage to be gained before and after armor reductions via armor penetration. Assuming minor and major debuff on the target.

 Non Mana User