GamePress
Article byDaniel O'Brien
Table of Contents
- Behind The Numbers: Damage Formula Explained
- Scaling_Def_Down and Scaling_Res_Down
- Flat_Def_Down and Flat_Res_Down
- Arts_Dmg_Taken_Up and Phys_Dmg_Taken_Up
- Phys_Damage
- Arts_Damage
- Major Takeaways
- Short Theoretical Example
- Realistic Example
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. 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.Behind The Numbers: Damage Formula Explained
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 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: Operators with Defense Down Debuffs Meteor - Skill - Armor Breaker Meteor - Skill - Armor Breaker - Spread Pramanix - Skill - Natural Deterrent Operators with Defense Ignore Talents/Skills Franka - Talent - Thermite Blade Franka - Skill - Vorpal Edge Indra - Skill - ArmorCrusher Amiya - Skill - Chimera Nightmare - Skill - Night Phantom Cliffheart - Skill - Binding Chains Operators with Arts Resistance Down Debuffs Pramanix - Skill - Natural Deterrent Haze - Talent - Black Mist Eyjafjalla - Skill - Ignition Ifrit - Talent - Spiritual Dissolution Operators with Resistance Ignore Talents/Skills Amiya - Skill - Chimera Nightmare - Skill - Night Phantom Cliffheart - Talent - Binding ChainsScaling_Def_Down and Scaling_Res_Down
Scaling_Def_Down = 1 - [(1-20%)*(1-35%)] = .48 or 48%
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: Operators with Flat Defense Down Debuffs Meteorite - Skill - High Explosive Shell Ifrit - Skill - Pyroclasm Operators with Flat Resistance Down DebuffsFlat_Def_Down and Flat_Res_Down
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: Operators with Damage Taken Increased Saria - Skill - Calcification Skyfire - Talent - Arts Sniper Pramanix - Talent - WeakeningArts_Dmg_Taken_Up and Phys_Dmg_Taken_Up
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'sweird. So what does this formula mean in English? Start with the Defense of the enemy target. Subtract the flat Defense debuffs. Multiply by the percentage Defense debuffs. Subtract the result from the Operator’s buffed ATK stat. Multiply the result by Physical damage up modifiers.Phys_Damage
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? Start with the Resistance of the enemy target. Subtract the flat Resistance debuffs. Multiply by the percentage Resistance debuffs. Turn what is remaining into a resistance percentage Reduce the Operators attack by the resistance percentage Multiply by any Arts Damage Up modifiers.Arts_Damage
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.Major Takeaways
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 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 = 935Short Theoretical Example
Physical Damage
Arts Damage
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:Realistic Example
Arts_Damage = 1560 * [1 - ((50 + (-7))*(1 - .35)/100)]* 1.07 = 1124
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About the Author(s)
Daniel O'Brien
Arknights: Alyeska#2654
Discord:Alyeska#7717