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# Arknights: Damage Formulas Pocket Reference

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Article by Daniel O'Brien

## Knowing Is Half the Battle!

(the other half is the battle with Sanity)

In this reference document we will present what are generally believed to be the damage formulas for Arknights in a concise format and offer links to more in-depth information and examples of the formulas presented.  The formulas presented here are not of my creation.  They were shared with me by Kawa and, to my knowledge, 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.

## Attacks Per Second Formula

Where,

• Attack_Interval = Operators Base Attack Interval, the measure of how long it takes to do one attack (Seconds per Attack)

• Attack_Interval_Modifer = Change to Base Attack Interval applied by the Operator’s own Skill.  Will say modifies “Attack Interval”.

• Attack_Speed_Modifiers = the summation of all +ASPD modifiers

For more details on what these variables mean and how to find them, see our detailed article:

English Description of Attack Per Second Formula
• First, Increase/decrease the normal Attack Interval by any Attack Interval change from an active Skill.

• Second, increase the attacking rate by a percentage equal to the summation of all the ASPD buffs.

Operators That Provide ASPD Buffs
Major Takeaways
• The Attack Interval modifier is a flat increase/decrease to the attack interval.  Thus, any given value change will have a larger effect on faster attackers than slower ones.

• Attack Speed increases are percentile, and thus represent an equal percent increase in damage for any Operator.

## Final_ATK (Attack Modifiers)

Where,

• Base_Attack = ATK stat of the Operator

• Base_ATK_Buff = the summation of all ATK percentage increases

• Sora_SK2_Buff = the ATK added by Sora’s Skill 2

• Attack_Multiplier_Buff = ATK percentage increase or decrease associated with any Talents or Skills that say things like “Increases ATK to X%” or “ X% of ATK”. Multiple buffs of this type are multiplicative with each other.

For more details on what these variables mean and how to find them, see our detailed article:

English Description of Final_Attack (Attack Modifiers) Formula

• Apply any Base ATK buffs (ATK % with a +).

• Add the ATK from Sora’s Skill 2 if it applies

• Apply the ATK multiplier buff (ATK % without a +)

Operators that Provide Base_ATK_Buff to Other Operators
Major Takeaways
• Same-type Base ATK buffs are additive with each other, where ATK multiplier buffs are multiplicative with each other and Base ATK buffs.  This means, all else equal, additional ATK Multiplier buffs will provide better overall performance than additional Base ATK buffs because of the nature of diminishing relative gain of additive buffs.

• Sora’s Skill 2 is additive with base ATK buffs, but multiplicative with ATK multiplier buffs.  Thus, in general, she will be more effective at improving the latter.

## Phys_Damage Formula

Where,

• Final_Attack = as described in section above

• Defense = the target’s Defense value

• Flat_Def_Down = any flat (non-percentage) reduction to Defense. Note: Flat_Def_Down is listed in-game as a negative number, which is why in the formula it is added to Defense and not subtracted from it.   For more details, see the detailed Damage formula article linked below.

• Scaling_Def_Down = total Defense reduction percentages applied by debuffs

• Phys_Dmg_Taken_Up = abilities that increase Physical damage take

• Minimum Physical Damage is 5% of Final_Attack.

For more details on what these variables mean and how to find them, see our detailed article:

English Description of Phys_Damage Formula

• Subtract the flat Defense debuffs.

• Multiply by the percentage Defense debuffs.

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

• Multiply by Physical damage up modifiers

Operators with Defense Down Debuffs
Operators with Defense Ignore Talents/Skills
Operators with Flat Defense Down Debuffs
Operators With Physical Damage Taken Increased
Major Takeaways

Included with Arts_Damage Takeaways below.

## Arts_Damage Formula

Where,

• Final_Attack = as described in section above

• Resistance = the target’s Resistance value

• Flat_Res_Down = any flat (non-percentage) reduction to Resistance. Note: Flat_Res_Down is listed in-game as a negative number, which is why in the formula it is added to Resistance and not subtracted from it.   For more details, see the detailed Damage formula article linked below.

• Scaling_Res_Down = total Resistance reduction percentages applied by debuffs

• Arts_Dmg_Taken_Up = abilities that increase Arts damage taken

For more details on what these variables mean and how to find them, see our detailed article:

English Description of Arts_Damage Formula

• Subtract the flat Resistance debuffs.

• Multiply by the percentage Resistance debuffs.

• Turn what is remaining into a resistance percentage.

•  Reduce the buffed attack by the resistance percentage.

• Multiply by Arts Damage Up modifiers.

Operators with Arts Resistance Down Debuffs
Operators with Resistance Ignore Talents/Skills
Operators with Flat Resistance Down Debuffs
Operators with Arts Damage Taken Increased
Major Takeaways
• 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 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

## Total DPS and HPS

• For Arts Damage attacker: Attacks_Per_Second * Arts_Damage

• For Physical Damage attacker: Attacks_Per_Second * Phys_Damage

• For healer: Attacks_Per_Second * Arts_Damage

• (healing is Medic damage to friendly Operators

Where

• Attacks_Per_Second = as shown in Section above.

• Arts_Damage = as shown in Section above.

• Phys_Damage = as shown in Section above.

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