Damage Formula (PSO2)

Information here was translated directly from [https://pso2.swiki.jp/index.php?ダメージ計算] and will require some level of proofreading.

Damage Composition and Variance

Damage Composition

PSO2's damage is divided into the following:

• Player Damage (Base Stats, Mag Stats, Special Abilities, etc.)
• Weapon Element Damage
• Weapon Damage

In the case of Techniques, "Weapon Element damage" is not applicable.

Damage variance only applies to Weapon Damage. For this reason, there is no damage variance when attacking without a weapon equipped (AKA bare-handed). The minimum value of Weapon Damage always ranges between 10% and 90%. When under conditions which are too good or too bad outside the range of 10-90%, the resulting minimum Weapon Damage will always be capped within 10%-90%. A critical hit removes this variance, resulting in 100% of Weapon Damage being applied.

Maximum damage on a critical hit (Criticals are shown as blue numbers in-game):

Player Damage

Weapon Element Damage

Weapon Damage 100%

Non-critical damage under the best conditions:

Player Damage

Weapon Element Damage

Minimum Weapon Damage 90%

Variance

Non-critical damage under the worst conditions:

Player Damage

Weapon Element Damage

Min. 10%

Variance

As shown above, the damage variance only applies to Weapon Damage, thus it is less evident when observing only the total damage. Since Techniques do not have Weapon Element Damage, it is slightly easier to notice the damage variance compared to other types of attacks.

It should also be noted that Summoner Pets have a wide damage variance. The exact reasoning is unknown, but it's presumed they follow the non-rare OT damage formula. More on that later in this page.

Damage Variance

The above section can be summarized as the following table:

Maximum Damage
Player Damage	Weapon Element Damage	Weapon Damage 100%
		Minimum Weapon Damage	Damage Variance

To determine the minimum weapon damage, there are two broad categories.

• Rare weapons ( and above) → fixed 90%
  • Note that while it was previously possible to have less than 90%, it is no longer the case currently.
  • The Invade OTs and Val series have the minimum weapon damage formula similar to that of "Non-rare Crafted Weapons".

• Non-rare, crafted weapons, Invade OTs, Val series → calculated based on the difference in DEX between the player and the enemy, weapon rarity, and weapon grind.
  • Silver tier or higher crafts, Invade OTs, Val series → calculated minimum weapon damage has a large modifier, resulting in generally higher minimum weapon damage.
  • Crafts that are below Silver tier, common, uncommon, Red and Blue weapons, non-primary ATK stats (e.g. Vibrace weapon's T-ATK) → calculated minimum weapon damage has a small modifier, resulting in generally less minimum weapon damage.

In the case of non-rare, the value of minimum weapon damage is not dependent on weapon attack. If we were to compare between a weapon with 500 attack and another weapon with 1000 attack, under the same surrounding conditions (same difference in DEX between the player and the enemy, same weapon rarity, same level of weapon grind), the calculated minimum weapon damage of both weapons would still be the same.

See Minimum Damage for more details on minimum weapon damage calculation.

Damage Calculation Formula

Notice: The calculation formula is based off of information that can be verified in-game, not from any official sources.

Damage Type Reference

When calculating damage, there is an implied understanding to what the damage type an attack is. There are many different attacks with varying properties affecting how damage is calculated.

Key:

Attack Power

The ATK stat from which the damage is calculated. Increasing the specified ATK stat will increase damage. Other ATK stats have no effect.

Defense Power

The enemy's DEF stat against which the damage is calculated. The higher the specified DEF stat, the less damage can be dealt to the enemy. Similarly, other DEF stats have no effect.

Weapon Element Damage

The ATK stat from which the Weapon Element Damage is calculated. This is dealt as elemental damage and is affected by elemental Part Boost multiplier. For example, when attacking an enemy with fire weakness with a fire element weapon, the Weapon Element Damage is increased by the enemy's fire Part Boost multiplier.

Part Boost

The specific type of Part Boost multiplier used. This differs for each part on the body of the enemy hit by the attack. If the Part Boost is specified as "Ranged", the damage will be affected by headshot multiplier when attacking the head of an enemy. If the Part Boost is specified as "Elemental Attribute", the damage is considered as elemental attribute damage and is affected by elemental Part Boost multiplier. Note that this is independent from Weapon Element Damage which is always affected by elemental Part Boost multiplier.

Final Attack Type

The final damage type of the attack. This is used to determine the effects of class skills, Skill Rings, Potentials, etc. For example, if the Final Attack Type is "Ranged", the damage will be boosted by Ranger's skill "Weak Hit Advance".

Base

Method of Attack	Attack Power	Defense Power	Weapon Element Damage	Part Boost	Final Attack Type	Notes
Normal Strike Attack	S-ATK	S-DEF	S-ATK	Striking	Striking
Normal Ranged Attack	R-ATK	R-DEF	R-ATK	Ranged	Ranged
Technique	T-ATK	T-DEF	None	Elemental Attribute	Tech
Bare hands	S-ATK	S-DEF	S-ATK	Striking	Striking
Talis Attack	T-ATK	T-DEF	T-ATK	Tech	Striking
Takt Normals	T-ATK	T-DEF	None	Tech	Tech	Attack Advance not applicable
Jet Boots (Without Switch Strike)	T-ATK	T-DEF	T-ATK	Striking	Striking
Jet Boots (With Switch Strike)	S-ATK	S-DEF	S-ATK	Striking	Striking
Pets (Without Switch Strike)	T-ATK	T-DEF	T-ATK	Tech	Tech	Pets stats are used in lieu of weapons, not the stats of the Takt.
Pets (With Switch Strike)	S-ATK	S-DEF	S-ATK	Tech	Tech	Pets stats are used in lieu of weapons, not the stats of the Takt.
Pets (With Switch Shoot)	R-ATK	R-DEF	R-ATK	Tech	Tech	Pets stats are used in lieu of weapons, not the stats of the Takt.
Phantom Rod Normals	T-ATK	T-DEF	T-ATK	Striking	Striking	Unlike other classes' rod attacks, Phantom's does not scale from S-ATK.

Class Skills & Others

Method of Attack	Attack Power	Defense Power	Weapon Element Damage	Part Boost	Final Attack Type	Notes
Guard Arts	S-ATK	S-DEF	None	Striking	None
DS Whirlwind	S-ATK	S-DEF	S-ATK	Striking	Striking
Katana Counter Edge	S-ATK	S-DEF	S-ATK	Striking	Striking
Braver Combat Finish	S-ATK	S-DEF	S-ATK	Striking	Striking
Snatch Step	S-ATK	S-DEF	S-ATK	Striking	Striking
DB Photon Blades	S-ATK	S-DEF	S-ATK	Striking	Striking
Hero Sword Weapon Action	S-ATK	S-DEF	S-ATK	Striking	Striking
Ranger Tools (Traps, Bullets, Bombs)	R-ATK	R-DEF	None	Ranged	None	Standing Snipe & Moving Snipe not applicable
S-Roll Arts	R-ATK	R-DEF	R-ATK	Ranged	Ranged
Phantom Marker Detonation (Rifle)	R-ATK	R-DEF	R-ATK	Ranged	Striking
Rod Shoot	T-ATK	T-DEF	T-ATK	Tech	Striking Damage
Tech Explosion (Wand Gear)	T-ATK	T-DEF	T-ATK	Elemental Attribute	Striking
Ignition Skills	T-ATK	T-DEF	None	Tech	Tech
JB Double Jump	T-ATK	T-DEF	None	Elemental Attribute	None
Elemental Burst	T-ATK	T-DEF	None	Elemental Attribute	None
Hero Talis Marking Shot	T-ATK	T-DEF	T-ATK	Tech	Striking
Hero One More Jump	T-ATK	T-DEF	None	Tech	None
DB Snatch	S-ATK	S-DEF	S-ATK	Striking	Striking
Just Reversal B	S-ATK	S-DEF	S-ATK	Striking	Striking
Angelic Adept	S-ATK	S-DEF	S-ATK	Striking	Striking
Retaliating Fist	S-ATK	S-DEF	S-ATK	Striking	Striking
Hexing Spirit	S-ATK	S-DEF	S-ATK	Striking	Striking
Thundering Blades	S-ATK	S-DEF	S-ATK	Striking	Striking
Mysterious Conjurer	S-ATK	S-DEF	S-ATK	Striking	Striking
Dissipating Wave	S-ATK	S-DEF	S-ATK	Striking	Ranged
Antique Shot	R-ATK	R-DEF	R-ATK	Ranged	Ranged
Soaring Brilliance	R-ATK	R-DEF	R-ATK	Ranged	Ranged
Auxiliary Dart	R-ATK	R-DEF	R-ATK	Ranged	Ranged
Glance of Darkness	T-ATK	T-DEF	None	Elemental Attribute	Tech	Treated as an uncharged Technique
SP Auto Action (S-ATK)	S-ATK	S-DEF	None	Striking	None	Only scales from base stats
SP Auto Action (R-ATK)	R-ATK	R-DEF	R-ATK	Ranged	None	Only scales from base stats
SP Auto Action (T-ATK)	T-ATK	T-DEF	None	Elemental Attribute	Tech	Treated as an uncharged Technique with equipment stats scaling
Photon Blast (S-ATK)	S-ATK	S-DEF	None	Striking	None
Photon Blast (R-ATK)	R-ATK	R-DEF	None	Ranged	None
Photon Blast (T-ATK)	T-ATK	T-DEF	None	Tech	None
Dash Panel Boost Kick	S-ATK	S-DEF	None	Striking	None	Power 250%, 3500%, 5000%

Photon Art & Technique Exceptions

Method of Attack	Attack Power	Defense Power	Weapon Element Damage	Part Boost	Final Attack Type	Notes
Physical Moves from TMG PAs	R-ATK	R-DEF	R-ATK	Striking	Ranged
Crazy Smash Impact Slider Kick Kamikaze Arrow Kick Tritt Shooter Kick	R-ATK	R-DEF	R-ATK	Striking	Striking
Kamikaze Arrow Dash	R-ATK	R-DEF	R-ATK	Ranged	Striking
Hero Talis PAs	T-ATK	T-DEF	T-ATK	Tech	Striking
Phantom Rod PAs	T-ATK	T-DEF	T-ATK	Striking	Striking
Vol Graptor Explosion Banish Arrow Explosion	None	None	None	Attribute-less	Not Applicable
Zanverse Boost Effect	None	None	None	Wind Attribute	None	Is not boosted by Wind Mastery skills

Maximum Damage

Maximum Damage
Player Damage	Weapon Element Damage	Weapon Damage 100%
		Minimum Weapon Damage	Damage Variance

To calculate the Maximum Damage as shown in the figure above:

• Replace Attack Power, Defense Power, and Part Boost in the formula with their respective values.
• Weapon Attack Power refers to the relevant Attack Power of the weapon, excluding Special Abilities (affixes).
• 1.05 is from the latent 5%, colloquially referred to as the "Mystery Multiplier" in the Japanese community.
  • This multiplier did not exist during PSO2's intial Japanese launch, however its existence was confirmed with the release of subclasses.
  • With the exception of a few attacks, all damage is eventually affected by it. The only exception currently confirmed is the direct damage from Zonde.
  • On a side note, when calculating enemy's attack multiplier based on red damage numbers when hit by an enemy's attack. Dividing the damage by 1.05 reveals a rounder value, suggesting that there is a high probability that even the enemies themselves are affected by this multiplier.
• Total Multiplier is the product of all the relevant damage multipliers except Part Boost. This includes the 1.05, PA notation, Skills, Potential Abilities, etc.
• For Pets, use Pet's Attack Power instead of weapon's.
  • Pet's default base ATK → Weapon Attack Power
  • Pet's Bonus Stats → Special Abilities (affected by Shifta).
  • Stats from Candies → Special Abilities (unaffected by Shifta).
  • Interactions between Pet stats and Shifta will be explained in detail later in Applying Buffs.

Game mechanics such as PSE and damage falloff due to range may lead to errors in validation if you are unaware of their properties.

Damage Source = (Total Attack Power - Defense Power) x Part Boost

Weapon Element Damage = Weapon Attack Power x Element Percentage x Elemental Part Boost
(If Technique: Weapon Element Damage = 0)

Total Multiplier = 1.05 x PA Notation x Skill Multiplier x Potential Multiplier etc.

Maximum Damage = (Damage Source + Weapon Element Damage) ÷ 5 × Total Multiplier

Advanced Calculation (same formula but distributed into parts): Show/Hide

Player Damage = (Total Attack Power from Base Stats, Units, Mag, Special Abilities, etc. ÷ 5) × Part Boost × Total Multiplier

Weapon Attack Damage = (Weapon Attack Power ÷ 5) x Part Boost x Total Multiplier

Weapon Element Damage = (Weapon Attack Power x Element Percentage ÷ 5) x Elemental Part Boost x Total Multiplier
(If Technique: Weapon Element Damage = 0)

Defense Damage Reduction = (Defense Power ÷ 5) × Part Boost × Total Multiplier
		
Maximum Damage = Player Damage + Weapon Attack Damage + Weapon Element Damage - Defense Damage Reduction

Minimum Damage

Maximum Damage
Player Boost	Weapon Element Type	Weapon Damage 100%
		Minimum Weapon Damage	Damage Variance

As mentioned earlier in Damage Variance, weapons are divided into groups based on the formula used in the calculation:

• Non-rare group consists of the following:
  • Weapons with through rarity.
  • Crafted weapons using less than Silver tier recipes.
  • Blue and Red Series of weapons.
  • Any weapon when using a non-primary ATK stat (e.g. Vibrace weapon's T-ATK).
• Silver Craft group consists of any weapon crafted using Silver tier recipe.
• Invade OT & Val group consists of said weapon series.
• Rare group consists of other weapons not mentioned above.

Note that not all weapons have been thoroughly tested and there may be exceptions to the grouping and formula not yet discovered.

• As of Oct 08, 2014, it was found that:
  • The following weapons shared the same formula as Non-rare group: Till Traitor, Falclaw, Vibrace Weapon series, Neidaryl. Dalz Varley, and Helen Tramer.
  • The following weapons shared the same formula as Rare group: Rikauteri, Biskedrop, Madullard Varis, and Orbit Weapon series.
  • The following weapons shared the same formula as either Rare or Silver Craft group:: Soul of Wopal. (Due to the Attack Power being so low, they were unable to verify which group it was supposed to be.)

• Grind Modifier is defined as the growth rate of weapon stats based on the current grind level of the weapon. For instance, a weapon of at +10 has 160% of its original ATK, which is equal to 1.60 in decimal format. In this case, the Grind Modifier used in the formula becomes 1.60.
• As a reference, the following Weapon Modifier values can be calculated using the formula:
  • - +10 (Non-rare, Grind Modifier = 1.60): 30.0
  • - +10 (Non-rare, Grind Modifier = 1.75): 37.5
  • Ex8 craft +10 (Silver Craft, Grind modifier = 1.90): 235.0

Weapon Modifier =
        Non-rare group:
                50 × (Grind Modifier - 1)
        Silver Craft group (Twin Daggers, Double Sabers, Gunslashes):
                50 + 100 × (Grind Modifier - 1)
        Silver Craft group (Other Weapons):
                100 + 150 × (Grind Modifier - 1)
        Invade OT & Val group:
                150 + 200 × (Grind Modifier - 1)
        Pets:
                -50
                (If self-inflicted damage, use 0 instead)

Guaranteed Minimum Attack = (Player DEX x PA DEX Modifier - Enemy DEX + Weapon Modifier) x 2

90% Cap = Weapon Attack Power x 90%
10% Cap = Weapon Attack Power x 10%

Effective Attack Power = 
        Rare group:
                90% Cap
        Else:
                90% Cap if Guaranteed Minimum Attack > 90% Cap
                10% Cap if Guaranteed Minimum Attack < 10% Cap
                Guaranteed Minimum Attack otherwise

Minimum Weapon Damage = Effective Attack Power ÷ 5 × Part Boost x Total Multiplier

It has not been verified whether Pet PAs' DEX modifiers can be applied to the Pet's DEX and Pet Candy. For PAs with 100% DEX Modifier, all the measured and calculated values in addition to the Player's DEX are almost identical.

Applying Buffs

Maximum Damage
Player Damage, Mag Stats |			Weapon Element Damage |	Weapon Damage 100%
Base Stats, Mag, Stat Ups, etc. |	Special Abilities |	Photon Flare, etc. |		Minimum Weapon Damage |	Damage Variance

Fraction of stats caused by calculations from buffs are kept in calculation, even if numbers are rounded before being displayed in-game. Thus, when calculating damage, do not round off decimal values, as they can become significant under very high multipliers.

Based on the figure above, Base Stats, Mag, Stat Ups, etc. includes:

• The player's base stats.
• Mag stats.
• Stat Up skills (e.g. S-ATK Up, R-ATK Up, T-ATK Up).
  • Mag-based stats skills such as Braver Mag are also included.
  • Skills which increase stats dynamically such as Photon Flare are not included.

Stat buffs e.g. Shifta, Drinks, Team Tree Buffs can only be applied to the "Base Stats, Mag, Stat Ups, etc." section. As an exception, Shifta can affect Special Abilities on Units, Set Bonuses, and Pet Bonus Stats (Stats acquired from feeding, AKA Plus Values/プラス値). It is not known whether Timed Abilities Stat Bonuses are affected by Shifta.

To put it simply, the formula to calculate Attack Power with Shifta is:

{ (Base Stats + Mag + Stat Ups) × Photon Tree Buff × Shifta Drink + Special Abilities on Units + Set Bonuses + Pet Bonus Stats } × Shifta

The Effect of Shifta on Pets

The effects of Shifta on Pets have certain specific exceptions compared to non-Pet scenarios.

• Attack Power bonus from Support Roll is affected by Shifta.
• The Pet's base stats (not Pet Bonus Stats) are not affected by Shifta.
• Pet Bonus Stats is affected by Shifta.
• The Attack Boost granted by Cookies are not affected by Shifta.
• Takt's Attack Power is not affected by Shifta.
• Using Switch Skills will cause the referenced Attack Power to change, as noted in Damage Type Reference. For instance, if Switch Shoot is active, the referenced Attack Power will change from T-ATK to R-ATK, then R-ATK values from Special Abilities on equipped Units and Set Bonuses will be used instead.
• The player's increased Attack Power from Shifta has no effect on the Pet's damage output. Shifta must be applied on the Pet to take effect.

Thus, expanding from the above section, the formula for Shifta becomes:

{ (Base Stats + Mag + Stat Ups) × Photon Tree Buff × Shifta Drink + Special Abilities on Units + Set Bonuses + Pet Bonus Stats + Support Roll bonus } × Shifta

Criticals and Expected Values

When you deal critical damage, the damage will show up in-game as a blue damage number. The default critical rate is estimated to be 5%.

The higher the critical rate, the higher the average damage will be. To calculate the expected value considering the critical rate, the following is recommended:

Mid-range = (Maximum Value + Minimum Value) ÷ 2
Expected Value = Mid-range + Critical Rate x (Maximum Value - Mid-range)

And taking critical damage bonuses (e.g. Critical Strike) into account:

Mid-range = (Maximum Value + Minimum Value) ÷ 2
Expected Value = Mid-range + Critical Rate × (Maximum Value x Critical Damage bonus - Mid-range)