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.

Damage Variance

The above section can be summarized as the following table:

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

To determine the minimum 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 same minimum damage equivalent to "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 damage has a large modifier, resulting in generally higher minimum damage.
  • Crafts that are below Silver tier, common, uncommon, Red and Blue weapons, non-main primary types (Vibrace Weapon's tech power) → calculated minimum damage has a small modifier, resulting in generally less minimum damage.

In the case of non-rare, the value of minimum 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 damage of both weapons would still be the same.

See Minimum Damage for more details on minimum 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 disabled
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 is considered striking based.

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, etc, 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	Not treated the same as a weapon
SP Auto Action (R-ATK)	R-ATK	R-DEF	R-ATK	Ranged	None	Not treated the same as a weapon
SP Auto Action (T-ATK)	T-ATK	T-DEF	None	Elemental Attribute	Tech	Treated as an uncharged technique with weapon scaling
Photon Blast (S-ATK)	S-ATK	S-DEF	None	Striking	None	Not treated the same as a weapon
Photon Blast (R-ATK)	R-ATK	R-DEF	None	Ranged	None	Not treated the same as a weapon
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 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 extra 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 the section regarding 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 Damage	Damage Variance

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

• Non-rare weapons are defined as through , normal crafted weapons, and the Blue and Red Series of weapons.

Weapons that were not mentioned are defined as Rare Weapons. Although Striking/Ranged Weapons and Techniques share a similar damage formula to that of non-rare weapons, there's a growing number of differences that split them apart. However, not all weapons however have been thoroughly tested and may yield different exceptions to the formula.

• After the update on Oct 08, 2014, it was found that:
  • The weapons that shared the same formula as non-rare weapons were: Till Traitor, Falclaw, the Vibrace Weapon Series, Neidaryl. Dalz Varley, and Helen Tramer.
  • The weapons that shared the same forumla as rare weapons were: Rikauteri, Biskedrop, Madullard Varis, and the Orbit Weapon Series.
  • The weapon that shared the same forumla as either Rare or Silver-crafted weapons was: Soul of Wopal. (Due to the Attack Power being so low, they were unable to verify what category the weapon followed)
  • Skills and other offensive abilities that are not bound by main-class usage include: Techniques, Snatch Step, Tool-related skills (Gravity Bomb, traps, etc), Ignition Skills (Such as Freeze Ignition), Mag Auto Actions, and Photon Blasts.

• The Invade OT and Val weapon series have their own damage modifiers.

• The Grind Level is defined as the current Grind Level of the weapon. For instance, a weapon of at +10 is written as 160% of its original attack power. Thus 160% becomes 1.60 in decimal format.

• Weapon Modifier reference:
  • DEX modifiers: ★4-6 +10 is 30.0, ★7-9 +10 is 37.5, and ★10 Ex8 +10 is 235.0

• It was often confusing to use the term "Minimum Attack Power" in the formula, so this variable was changed to "Effective Attack Power".

As mentioned earlier in Damage Variance, minimum damage can be calculated as the following:

Weapon Modifier =
	For non-rare weapons or Iro/Steel Crafts:
		50 × (Grind Level - 1)
	For Silver Crafts (Twin Daggers, Double Sabers, Gunslashes):
		50 + 100 × (Grind Level - 1)
	For Silver Crafts (Other Weapons):
		100 + 150 × (Grind Level - 1)
	For Invade OT, Val Weapons:
		150 + 200 × (Grind Level - 1)
	For 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 = 
	If Rare Weapon: 
		90% Cap
	If non-rare:
		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 the Pet PAs DEX modifier 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 + Attack Stat Ups, etc	Weapon & Armor Abilities	Photon Flare, etc		Minimum Damage	Damage Variance

Shifta, Drinks, Team Tree Buffs, etc can only be applied to the "Base Stats + Mag + Attack Stat Ups, etc" section on the figure above. This includes the Player's Base Stats, Mag Stats and Skills, and Stat Up skills (Such as S-ATK Up or R-ATK Up). "Stat Up" does not include skills that give you a dynamic stat bonus such as Photon Flare.

A fraction of the stats caused by Buffs are preserved, even if you cannot view them in-game. Under very high multiplier conditions, damage cannot be reproduced without taking this fractional part into account.

Additionally, not only does Shifta increase a pet's attack power, but it also affects the affixed special abilities and set bonus (if available) of your units, as well as a pet's extra stats.

Thus the formula calculation for Shifta is { (Base Stats + Mag + Attack Stat Ups) × Team Tree × Shiftaride + Unit Affixes + Pet Extra Stats } × Shifta.

The Effect of Shifta on Pets

The effects of Shifta on Pets works differently than it does on normal players, thus it's insufficient to just multiply a Pet's Attack Power by Shifta's multiplier.

• Thus the formula for Shifta becomes: Shifta x [No Weapon Attack Power + Pet Extra Stats + Support Roll Attack Boost].
  No Weapon Attack Power is having no weapon equipped, only Unit Affixes, Unit Set Effect, Mag Stats and Attack Power Skills.
  The above formula assumes that the Shifta applied is your own, as Shiftas from another player can introduce unknown variables to the calculation.
  • A Pet's base stats (not the Pet's Extra Stats) are not affected by Shifta.
  • The Attack Boost granted by Cookies are not affected by Shifta.
  • A Takt's Attack Power is not affected by Shifta.
  • It is not known whether Timed Abilities Stat Bonuses are affected by Shifta.
• Using Switch Skills will cause the Attack Power type to change on Units, as noted by the above section Damage Type Reference. For instance, if one were to have Switch Shoot active, not only will the Attack Power change from T-ATK to R-ATK, but the if the Unit equipped has any R-ATK affixes or a set bonus with R-ATK, it will use those values instead of the T-ATK values.
• A Player's Attack Power Boost from Shifta has no effect on the Pet itself. Must be applied on to the Pet.
• A Pet's Elemental Attributes are not affected by 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 percentage is 5%, and cannot go any lower than that or higher than 6%. Maybe even 5%. Each skill is closer to the actual measurement when added up.

The higher the critical rate, the higher the average damage will be than the mid-range (the average of the highest and lowest damage). 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 Strike into account:

Mid-range = (Critical without Maximum Value + Maximum Value) ÷ 2 
Expected Value = Mid-range + Critical Rate × (Critical with Maximum Value - Mid-range)

The expected value calculated by this method and the average value in the actual measurement showed about 1% damage variance in the amount of damage in crafts with large damage variance. Whether it's due to the calculation from this formula or the sample size, one cannot be used to measure over a thousand samples. However, it is much more useful than trying to obtain the expected value from the Maximum and Minimum average.