Arknights Mechanics: Behind the Numbers - Damage Formula

Ever wonder how Arknights calculates the damage done by our Operators?  By the end of this article, we hope you will have a much better idea! The formulas presented here are not of my creation.  They were shared with me by Kawa and come from the RIHQ Discord.  My goal is to share them in a concise format, explain what they mean, and list Operators that have relevant abilities.  I am not a mathematical genius, in fact numbers frighten me, so if you find any errors in my calculations or conclusions, please contact me via Discord. 

• Note: For a broader view of the entire DPS calculation, see our reference guide:

Physical and Arts damage are calculated in slightly different ways, though the inputs to the formulas are similar.  We will present each of the factors involved in determining the final values, followed by the damage formulas below.

Scaling_Def_Down and Scaling_Res_Down will be the total Defense and Arts Resistance reduction percentages, respectively, applied by Operator debuffs.

• Note: Flat (non-percentage) Def andRes Down debuffs are applied in a different way, as will be seen in later sections.

Each debuff that is applied has a multiplicative effect.  Thus, the formula looks like this:

and

Where

• each x is a different Def or Res debuff (appropriate to the respective formula),
• x is the absolute value of the debuff value listed in-game.  
  • For example, if X1 is listed in-game as -20%, then X1 in the above formula is 20%, and the formula becomes 1 -[(1-20%)]
•  n is the total number of debuffs.

An example of a Defense down debuff can be seen here in Meteor’s Skill 1 Armor Breaker:

An example of another Defense down debuff would be Pramanix’s Skill 2, Natural Deterrent.  If we assume both debuffs are present, and Pramanix’s skill is at level 1, then:

Scaling_Def_Down = 1 - [(1-20%)*(1-35%)] = .48 or 48%

• Meteor - Skill - Armor Breaker

• Meteor - Skill - Armor Breaker - Spread

• Pramanix - Skill - Natural Deterrent

• Franka - Talent - Thermite Blade

• Franka - Skill - Vorpal Edge

• Indra - Skill - ArmorCrusher

• Amiya - Skill - Chimera

• Nightmare - Skill - Night Phantom

• Cliffheart - Skill - Binding Chains

• Pramanix - Skill - Natural Deterrent

• Haze - Talent - Black Mist

• Eyjafjalla - Skill - Ignition

• Ifrit - Talent - Spiritual Dissolution

• Amiya - Skill - Chimera

• Nightmare - Skill - Night Phantom

• Cliffheart - Talent - Binding Chains

Flat_Def_Down and Flat_Res_Down will be any flat (non-percentage) reduction to Defense or Resistance.  These will be subtracted from Defense or Resistance before the Scaling_Def_Down and Scaling_Res_Down percentages are applied.  

Here is an example of a flat Defense down debuff:

• Meteorite - Skill - High Explosive Shell

• Ifrit - Skill - Pyroclasm

• Ifrit - Skill - Scorched Earth

Phys_Dmg_Taken_Up and Arts_Dmg_Taken_Up modifiers are any abilities that increase Physical or Arts damage taken.  Each modifier of this type that is applied has a multiplicative effect. Thus, the formula is:

And

Where each x is a different Arts or Physical damage taken effect for the respective formula, and n is the total number applied.

An example of an Arts damage taken increase from a skill can be seen here with Saria’s Skill 3 Calcification:

• Saria - Skill - Calcification

• Skyfire - Talent - Arts Sniper

• Pramanix - Talent - Weakening

We now have all the information we need to calculate our Physical Damage or Arts Damage, whichever our Operator inflicts.  Let’s look at Physical Damage first.

• Minimum physical damage is 5% of Final_ATK.

• Defense cannot be lowered below 0.

• Final_ATK is the ATK of the Operator after attack modifiers are applied.  The details of calculating this value can be found in our article on Final Attack and Attack Modifiers.

• Defense is the corresponding stat of the enemy the Operator is attacking.  These values are different for every enemy. Letter grades for these stats can be found in the Enemy Intelligence box for each quest after completion, and exact numbers can be found using some online resources, but numerical values are not available in-game.

• Flat_Def_Down is listed as a negative number in-game, which is why it is added in the formula.  I know. It's weird.

So what does this formula mean in English?

1. Start with the Defense of the enemy target.

2. Subtract the flat Defense debuffs.

3. Multiply by the percentage Defense debuffs.

4. Subtract the result from the Operator’s buffed ATK stat.

5. Multiply the result by Physical damage up modifiers.

Arts damage works a little differently.  Here is the formula:

• Resistance cannot be lowered below 0.

• Final_ATK is the ATK of the Operator after attack modifiers are applied.  The details of calculating this value can be found in our article on Final Attack and Attack Modifiers.

• Resistance is the corresponding stat of the enemy the Operator is attacking.  These values are different for every enemy. Letter grades for these stats can be found in the Enemy Intelligence box for each quest after completion, and exact numbers can be found using some online resources, but numerical values are not available in-game.

So what does this formula mean in English?

1. Start with the Resistance of the enemy target.

2. Subtract the flat Resistance debuffs.

3. Multiply by the percentage Resistance debuffs.

4. Turn what is remaining into a resistance percentage

5.  Reduce the Operators attack by the resistance percentage

6. Multiply by any Arts Damage Up modifiers.

• Physical Damage is a straight subtraction of modified Defense from modified Attack.

• Arts damage is the modified ATK reduced by the modified Resistance as a percentage.

• Percentage Defense or Resistance reduction modifiers won’t increase damage much against low Defense or Resistance enemies, but become more effective as Defense or Resistance increases.

• Flat Defense reduction is basically +damage. 

• Flat Defense or Flat Resistance reduction will be relatively more effective than percent Defense or Resistance reduction at low Defense or Resistance levels, and less at higher levels.

• Percentage Defense or Resistance down debuffs and Physical or Arts Damage Taken Increases are multiplicative to each other, which means each one you add makes all the others more effective.

• The higher the ATK amount, the more effective a given percent increase will be.

• If ATK is less than Defense, increasing ATK may not result in a damage improvement if the resulting ATK is still less than Defense.  Not so for Arts Damage, as a % increase in Attack creates a % increase in damage.

• Percentage increases in ATK or decreases in DEF may result in higher or lower corresponding damage increase percentage, depending on actual values, where for Arts damage, percentage increases in ATK or decreases to RES lead to similar changes in damage.

Physical Damage

Physical damage Operator Final Attack = 1000

Scaling Defense Down Debuffs = .50

Flat Defense Down Debuff = -200

Physical damage Taken up buff = 1.1

Enemy Defense = 500

Physical Damage = [1000 - (500 + -200)*(.5)]*1.1 = [1000 - 150]*1.1 = 935

Arts Damage

Artsl damage Operator Final Attack = 1000

Scaling Arts Down Debuffs = .50

Flat Arts Down Debuff = -10

Arts damage Taken up buff = 1.1

Enemy Resistance = 40

Arts Damage = 1000 * [1 - ((40 + - 10) * (1 - .5) /100)]* 1.1 = 1000 * .85 * 1.1 = 935

We will now show a real example of a damage formula application.

We’ll use the example of from the earlier section and say that the enemy has the following debuffs applied:

• Meteor’s Skill 1 Armor Breaker Level 1

• Pramanix’s Skill 2, Natural Deterrent Level 1

This gives us:

Scaling_Def_Down = 1 - [(1 - 20%)*(1-35%) = .48

Scaling_Res_Down = 1 - [(1-.35)] = .35      

For Flat reductions we’ll assume the following are applied:

• Meteorite - Skill - High Explosive Shell Level 1

• Ifrit - Skill - Scorched Earth Level 1

This gives us:

Flat_Def_Down = -130

Flat_Res_Down = -7

For Damage Taken Increases, we’ll assume we have:

• Skyfire - Talent - Arts Sniper

This gives us:

Phys_Dmg_Taken_Up = 1

Arts_Dmg_Taken_Up = 1.07

For Operator ATK, we’ll use the example from the article describing Final Attack to give us:

Final_ATK = 1,560

For enemy Stats we’ll say:

Defense = 500

Resistance = 50

If we assume the Operator does physical damage, our damage formula becomes:

Phys_Damage = [1560- (500 + (-130))*(1 - .48)]*1 = 1368

If we assume the Operator does Arts damage, our damage formula becomes:

Arts_Damage = 1560 * [1 - ((50 + (-7))*(1 - .35)/100)]* 1.07 = 1124