View source for Damage Formula (NGS)

=Player Damage=

The following sections discuss player damage, i.e., damage done by the player.

==Damage Formula==

Player damage can be described with the following formula:

<p class="lead text-center">Player Damage = ( WeaponATK * Variance + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2</p>

* '''WeaponATK''': The attack value of the weapon equipped as shown on item details.
* '''Variance''': The range in which WeaponATK is scaled. This is shown on page 2 of item details. See [[#Weapon Variance|Weapon Variance]].
* '''PlayerATK''': The attack value shown in stats window with no equipments. See [[Player Stats (NGS)|Player Stats]].
* '''EnemyDEF''': The internal defense value of the enemy. Scales with enemy level. This value is floored when used. See [[Enemy Stats (NGS)|Enemy Stats]].
* '''Damage Multipliers''': Final damage multipliers applied from various sources. See [[#Player Damage Multipliers|Player Damage Multipliers]].

The resulting damage from the calculation is rounded to the nearest integer.

===Weapon Variance===

The variance range of a weapon is shown on page 2 of item details. A value is selected at random from this range to be used as the variance multiplier in the damage formula.
For example, if a weapon has 70% - 100% variance range. A value between 0.7 and 1.0 is randomly selected and used to scale the weapon's attack value in damage calculation. The probability to get each value in the range seems to be the same, i.e., variance is uniformly distributed.

Increasing the variance floor via external sources like Abilities adds a multiplier to the variance floor in calculation. For example, if a weapon has 70% - 100% variance range, having 1% increased variance floor gives us a range of 70 * 1.01 = 70.7% - 100%. Variance floor increase stacks multiplicatively.

With knowledge on variance, we can derive the minimum/maximum player damage from the initial damage formula:

<p class="lead text-center">Minimum Player Damage = ( WeaponATK * Minimum Variance + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2</p>

<p class="lead text-center">Maximum Player Damage = ( WeaponATK + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2</p>

===Player Damage Multipliers===

There are many damage multipliers modifying the resulting damage done. These multipliers stack multiplicatively. Some common sources of damage multipliers are:

* '''PA/Tech Notation''': The damage modifier of the attack used. This is usually shown in-game as a percentage value for Photon Arts and Techniques, but actual testing is required to determine the distribution of damage notation for each hit of those attacks. Other attacks in-game can also be tested in a similar fashion. For example, Barta has 250 power shown in its in-game description, but testing revealed that it does 150% damage uncharged, and 250% damage when charged (used as 1.5 and 2.5 multiplier in calculation respectively).
* '''Part Boost''': Damage multiplier depending on the part of the target enemy where the attack lands. Common values known are:
** '''Elemental Weakness''': 1.2 (Elemental attacks only)
** '''Weak Point''': 1.5
** '''Weak Bullet''': 1.2
** '''Reinforced Weak Bullet''': 1.25
* '''Class Skills'''
* '''Weapon Potentials'''
* '''Preset Abilities'''
* '''Special Abilities'''
* '''Unit stats'''
* '''Region Mag buffs'''
* '''Drome buffs'''
* '''Food buffs'''
** Weak Point Damage Up effect from food buffs applies to natural weak points and when matching element weakness. If Weak Bullet is used and the final Part Boost after Weak Bullet is 1.2 or more, then Weak Point Damage Up applies.
* '''Weapon Boost''': 1.1 damage multiplier is applied to attacks from weapons which can be used by the current main class. This applies to the attacks themselves and thus are unaffected by multi-weapon mechanics. (For example, when using a Rifle/Sword multi-weapon on Hu/Ra, Weapon Boost multiplier will apply to all Sword attacks, while Rifle receives nothing.)
* '''Enemy buffs''': See [[#Enemy Buffs|Enemy Buffs]].
* '''Level Difference Modifier''': Damage reduction from level difference below enemy. See [[#Level Difference Modifiers|Level Difference Modifiers]].
* '''Optimal Range Multiplier''': Damage multipliers depending on the distance between the player and where the attack lands. Only affects certain weapons. See [[#Optimal Range|Optimal Range]].

===Critical Damage===

Critical damage is shown with a larger font in-game (not to be confused with weak point damage which is shown in blue, see [[#Weak Point Damage (Blue Damage)|Weak Point Damage (Blue Damage)]]). Critical damage is 120% of maximum player damage, as shown with the following formula:

<p class="lead text-center">Critical Damage = Maximum Player Damage * 1.2</p>

or in expanded form:

<p class="lead text-center">Critical Damage = ( WeaponATK + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2 * 1.2</p>

Where 1.2 is the critical multiplier.

The default critical rate is approximated to be 5%. This can be increased (likely additively) via other sources like Potentials and Abilities.

===Optimal Range===

Optimal Range (適正距離) is a term used to describe the mechanics of certain weapon types having increased damage depending on the distance from the player to where the attack lands. Each range gives a specific damage multiplier to most attacks. The range giving the highest damage multiplier (AKA the Optimal Range) is indicated by the target marker turning orange in-game.

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white"
! Weapon
! Close Range
! Mid Range
! Far Range
|-
| Wired Lance
| 1.0
| 1.2
| 1.0
|-
| Rifle
| 1.1
| 1.2
| 1.0
|-
| Twin Machinegun
| 1.2
| 1.1
| 1.0
|}
</div>

Note: Actual distance for each range differs for each weapon type.

=Enemy Damage=

The following sections discuss enemy damage, i.e., damage done to the player.

==Damage Formula==

Enemy damage formula is quite similar to player damage:

<p class="lead text-center">Minimum Enemy Damage = ( FLOOR(EnemyMinATK * EnemyATK Modifer) - PlayerDEF ) * Damage Multipliers * 0.2</p>

<p class="lead text-center">Maximum Enemy Damage = ( FLOOR(EnemyMaxATK * EnemyATK Modifer) - PlayerDEF ) * Damage Multipliers * 0.2</p>

* '''EnemyMin/MaxATK''': The internal attack values of the enemy. Unlike players, enemies have their internal values for minimum and maximum attack set separately. The actual values scale to enemy levels but the variance range stays mostly consistent (approximately 49/51 or 0.960784, but rounded so the ratio is not always exact). See [[Enemy Stats (NGS)|Enemy Stats]].
* '''EnemyATK Modifier''': Each enemy has a set modifier used to multiply the base attack value. The resulting attack value is then floored. Modifier values found so far range around 0.99 - 1.03.
* '''PlayerDEF''': The defense value shown in stats window. See [[Player Stats (NGS)|Player Stats]].
* '''Damage Multipliers''': Final damage multipliers applied from various sources. See [[#Enemy Damage Multipliers|Enemy Damage Multipliers]].

The resulting damage from the calculation is rounded to the nearest integer.

===Enemy Damage Multipliers===

There are many damage multipliers modifying enemy damage. These multipliers stack multiplicatively. Some common sources of damage multipliers are:

* '''Attack Notation''': The damage modifier of the attack used. Most common values seem to be multiples of 50 (e.g., 100%, 150%, 200%, 250%), but there are also exceptions (e.g., Vyne Hog's Spike attack is 80%).
* '''Player Damage Reduction''': Damage reduction (or negative reduction which increases damage instead) the player has. Common sources known are:
** '''Class Skills'''
** '''Weapon Potentials'''
** '''Preset Abilities'''
** '''Special Abilities'''
** '''Unit stats'''
** '''Food buffs'''
* '''Enemy buffs''': See [[#Enemy Buffs|Enemy Buffs]].
* '''Level Difference Modifier''': Damage increase from level difference above player. See [[#Level Difference Modifiers|Level Difference Modifiers]].

=Enemy Healing=

The following sections discuss enemy healing.

==Healing Formula==

Some enemies are capable of recovering HP of itself and other enemies nearby. The recovery value can be described by the following formula:

<p class="lead text-center">Enemy Healing = FLOOR( FLOOR(EnemyMinATK * EnemyATK Modifer) * Healing Notation )</p>


* '''EnemyMinATK''': The internal minimum attack value of the enemy. Scales with enemy level. See [[Enemy Stats (NGS)|Enemy Stats]].
* '''EnemyATK Modifier''': Each enemy has a set modifier used to multiply the base attack value. The resulting attack value is then floored. Modifier values found so far range around 0.99 - 1.03.
* '''Healing Notation''': The healing modifier of the healing used. This is specifically set for each enemy/healing. See [[#Healing Notation|Healing Notation]].

'''The resulting healing value from the calculation is rounded down.'''

==Healing Notation==

So far each enemy only has one healing move so notations are simply listed per enemy.

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white"
! Enemy
! Healing Notation
|-
| [[Metis]]
| 6.5
|-
| [[Gilnach]]
| 3
|}
</div>


=Appendix=

==Enemy Buffs==

There are several sources of buffs modifying an enemy's damage done and received. Most modifiers stack additively.  
(Note for clarity: +50% means additive, while 1.5 means multiplicative)

===Title Buffs===

Enemies with title included in their names receive the following damage modifiers:

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white"
! Title
! Damage done
! Damage received
|-
| Silver<br>白銀の
| -
| -
|-
| Golden<br>金色の
| -
| -
|-
| Battle-Hardened<br>老練の
| +30%
| -
|-
| Despair<br>絶望の
| +150%
| -50%
|-
| Elite<br>精鋭の
| +150%
| -
|}
</div>

===Weather Buffs===

Weather buff is indicated in-game by a small icon next to enemy name when targeted. This buff gives certain enemies +20% damage done during specific weather conditions. <!-- TODO: list them here or list them with enemies? best is to list in both places -->

===Daynight Shift===

Alters enemies change their appearances significantly during night time. This is called "Daynight Shift" which also gives them +30% damage done in their night forms.

===Shifta/Deband===

Some enemies/objects can cast Shifta/Deband, affecting themselves and/or other nearby enemies. The buff has been found to stack additively up to a set number of times. The following table lists all enemies capable of casting Shifta/Deband known so far and their buff properties.

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white"
! Enemy
<!--! TODO: Range-->
! Duration (max)
! Damage done
! Damage received
! Stacks
|-
| [[Gulf Roar]]
| 30s (30s)
| +5%
| -5%
| 5 times
|-
| [[Fangulf Roar]]
| 30s (30s)
| +5%
| -5%
| 5 times
|-
| [[El Discythe]]
| 30s (30s)
| +25%
| -5%
| 2 times
|-
| [[Ciacurio]]
| 30s (30s)
| +25%
| -10%
| 2 times
|-
| [[Metis]]
| 30s (30s)
| +50%
| -
| -
|-
| [[Transorve]]
| Permanent
| +50%
| -10%
| -
|}
</div>

===Enhanced Enemies===

Enhanced Enemies have an Enhancer core attached to them and glow red. The Enhancer core has HP equal to 30% of the max HP of the enemy it is attached to, and when destroyed, reduces that enemy's HP by 40%. Enhanced Enemies receive the following damage modifiers:

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white"
! Core state
! Damage done
! Damage received (multiplicative)
|-
| Intact
| +50%
| Core: 1.2<br />Body: 0.1
|-
| Destroyed
| -
| Natural weak point/weak element: 1.5<br />(stacks with weakness multiplier)
|}
</div>

For "core-destroyed" state, weak damage up does not work with Weak Bullet applied to parts with neutral damage modifiers (hence "natural weak point").  
As noted, Enhanced Enemies' damage received modifiers seem to be applied as multiplicative part boosts unlike damage reduction from other enemy buffs.

===Equalizing Enemies===

Equalizing Enemies have a distinctive red aura with a small red spike visually attached to them. They give damage modifiers similar to those of Enhanced Enemies to surrounding regular enemies (special enemies such as Enhanced Enemies, Megalotixes, Gigantixes, and other Equalizing Enemies are unaffected), and also have their own set of damage modifiers.
Killing the Equalizing Enemy will cause an explosion, reducing surrounding enemies' HP by 40% (of each enemy's HP), and giving them weak damage up debuff, similar to Enhanced Enemies.

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white"
! Target
! Damage done
! Damage received
|-
| Equalizing Enemy
| +50%
| -25% (additive)
|-
| Surrounding enemies
| +50%
| 0.1 (multiplicative)
|-
| Surrounding enemies (post-kill)
| -
| Natural weak point/weak element: 1.5<br />(stacks with weakness multiplier, multiplicative)
|}
</div>

An enemy can be both Enhanced and Equalizing, causing their damage modifiers to stack (damage boosts: 50+50=100%, damage received: 0.75*0.1=0.075).

===Trinitas Challenge Modifiers===

Trinitas Quest offers different challenges giving modifiers to enemies HP and damage.  
(Information related to enemy HP will be extracted to a different page in the future.)

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white"
! Challenge
! Effect
|-
| Enemy HP +25% ~ +400%
| Increase enemy HP by 1.25 ~ 5.0 (multiplicative)
|-
| Enemy Attack Power +25% ~ +300%
| Increase enemy '''damage''' by +25% ~ +300% (additive)
|}
</div>


==Level Difference Modifiers==

Both player damage and enemy damage are modified when the player's level is lower than the enemy's.

===Player Damage Modifier based on Level Difference===

When the enemy level is higher than the player's Main Class level by 5 levels or more, player damage done to the enemy is reduced. The damage reduction can be calculated with the following formula:

<p class="lead text-center">Damage Reduction = (Level Difference - 1) * 10%</p>

For example, against an enemy at level 15, level 10 players' damage will be reduced by 40%, level 7 players' damage reduced by 70%, while level 11 and above players do not get their damage reduced. This modifier seems to have a maximum value of 90% damage reduction.

Changelog:
* [https://pso2.jp/players/news/28173/ 2021/07/14 Update]: Against Gigantix, damage from underleveled players will be reduced to 1 instead.
* [https://pso2.jp/players/news/28246/ 2021/08/04 Update]: Players can bypass this damage reduction if their Power Level is high enough. Specific values required depend enemy levels.

===Enemy Damage Modifier based on Level Difference===

When the enemy level is higher than the player's Main Class level, enemy damage done to the player is increased. The damage increase can be calculated with the following formula:

<p class="lead text-center">Damage Increase = (Level Difference) * 20%</p>

For example, against an enemy at level 15, level 10 player will receive 100% increased damage, level 12 player will receive 60% increased damage, while level 15 player will receive the normal amount of damage.  This modifier has a maximum value of 100% damage increase.

==Attack Limit==

<div class="warningbox">This section contains data derived from datamining the game files. All values may be changed in the future.</div>

There is a maximum limit set to post-variance attack value used in calculating damage done to an enemy at each level. The damage formula can be rewritten as follows:

<p class="lead text-center">Player Damage = ( <span class="text-primary">MIN(</span>WeaponATK * Variance + PlayerATK<span class="text-primary">, AtkLimit(EnemyLevel))</span> - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2</p>

As of 2021/08/04, the attack limit value is only applied to player damage. All values up to level 200 have been found from datamining the game files. Note that these values may require in-game verification and can be changed in the future.

<div class="table-responsive">
{| class="table table-bordered darkmode-text-white mw-collapsible mw-collapsed"
! Level
! Attack Limit
|-
| 1 || 900
|-
| 2 || 918
|-
| 3 || 935
|-
| 4 || 953
|-
| 5 || 972
|-
| 6 || 990
|-
| 7 || 1009
|-
| 8 || 1028
|-
| 9 || 1049
|-
| 10 || 1068
|-
| 11 || 1090
|-
| 12 || 1110
|-
| 13 || 1132
|-
| 14 || 1153
|-
| 15 || 1176
|-
| 16 || 1199
|-
| 17 || 1220
|-
| 18 || 1244
|-
| 19 || 1268
|-
| 20 || 1292
|-
| 21 || 1318
|-
| 22 || 1343
|-
| 23 || 1369
|-
| 24 || 1396
|-
| 25 || 1422
|-
| 26 || 1450
|-
| 27 || 1477
|-
| 28 || 1506
|-
| 29 || 1535
|-
| 30 || 1565
|-
| 31 || 1595
|-
| 32 || 1625
|-
| 33 || 1656
|-
| 34 || 1687
|-
| 35 || 1721
|-
| 36 || 1753
|-
| 37 || 1788
|-
| 38 || 1823
|-
| 39 || 1858
|-
| 40 || 1892
|-
| 41 || 1930
|-
| 42 || 1967
|-
| 43 || 2004
|-
| 44 || 2042
|-
| 45 || 2082
|-
| 46 || 2123
|-
| 47 || 2162
|-
| 48 || 2204
|-
| 49 || 2248
|-
| 50 || 2291
|-
| 51 || 2334
|-
| 52 || 2380
|-
| 53 || 2425
|-
| 54 || 2472
|-
| 55 || 2520
|-
| 56 || 2568
|-
| 57 || 2617
|-
| 58 || 2668
|-
| 59 || 2719
|-
| 60 || 2772
|-
| 61 || 2825
|-
| 62 || 2879
|-
| 63 || 2934
|-
| 64 || 2990
|-
| 65 || 3048
|-
| 66 || 3107
|-
| 67 || 3167
|-
| 68 || 3228
|-
| 69 || 3289
|-
| 70 || 3353
|-
| 71 || 3418
|-
| 72 || 3484
|-
| 73 || 3551
|-
| 74 || 3619
|-
| 75 || 3689
|-
| 76 || 3760
|-
| 77 || 3833
|-
| 78 || 3906
|-
| 79 || 3980
|-
| 80 || 4057
|-
| 81 || 4135
|-
| 82 || 4216
|-
| 83 || 4296
|-
| 84 || 4379
|-
| 85 || 4463
|-
| 86 || 4549
|-
| 87 || 4637
|-
| 88 || 4727
|-
| 89 || 4817
|-
| 90 || 4909
|-
| 91 || 5004
|-
| 92 || 5100
|-
| 93 || 5198
|-
| 94 || 5298
|-
| 95 || 5400
|-
| 96 || 5504
|-
| 97 || 5610
|-
| 98 || 5718
|-
| 99 || 5828
|-
| 100 || 5940
|-
| 101 || 6054
|-
| 102 || 6172
|-
| 103 || 6289
|-
| 104 || 6412
|-
| 105 || 6534
|-
| 106 || 6660
|-
| 107 || 6788
|-
| 108 || 6919
|-
| 109 || 7051
|-
| 110 || 7188
|-
| 111 || 7326
|-
| 112 || 7468
|-
| 113 || 7610
|-
| 114 || 7758
|-
| 115 || 7907
|-
| 116 || 8059
|-
| 117 || 8214
|-
| 118 || 8371
|-
| 119 || 8533
|-
| 120 || 8698
|-
| 121 || 8864
|-
| 122 || 9036
|-
| 123 || 9209
|-
| 124 || 9386
|-
| 125 || 9568
|-
| 126 || 9751
|-
| 127 || 9938
|-
| 128 || 10129
|-
| 129 || 10325
|-
| 130 || 10524
|-
| 131 || 10727
|-
| 132 || 10933
|-
| 133 || 11143
|-
| 134 || 11358
|-
| 135 || 11575
|-
| 136 || 11798
|-
| 137 || 12025
|-
| 138 || 12258
|-
| 139 || 12493
|-
| 140 || 12733
|-
| 141 || 12979
|-
| 142 || 13229
|-
| 143 || 13483
|-
| 144 || 13742
|-
| 145 || 14008
|-
| 146 || 14276
|-
| 147 || 14551
|-
| 148 || 14832
|-
| 149 || 15118
|-
| 150 || 15408
|-
| 151 || 15704
|-
| 152 || 16007
|-
| 153 || 16314
|-
| 154 || 16628
|-
| 155 || 16949
|-
| 156 || 17275
|-
| 157 || 17608
|-
| 158 || 17946
|-
| 159 || 18292
|-
| 160 || 18643
|-
| 161 || 19002
|-
| 162 || 19368
|-
| 163 || 19741
|-
| 164 || 20120
|-
| 165 || 20508
|-
| 166 || 20903
|-
| 167 || 21305
|-
| 168 || 21715
|-
| 169 || 22133
|-
| 170 || 22559
|-
| 171 || 22993
|-
| 172 || 23436
|-
| 173 || 23886
|-
| 174 || 24347
|-
| 175 || 24815
|-
| 176 || 25291
|-
| 177 || 25778
|-
| 178 || 26275
|-
| 179 || 26780
|-
| 180 || 27295
|-
| 181 || 27822
|-
| 182 || 28357
|-
| 183 || 28902
|-
| 184 || 29459
|-
| 185 || 30025
|-
| 186 || 30604
|-
| 187 || 31193
|-
| 188 || 31793
|-
| 189 || 32405
|-
| 190 || 33029
|-
| 191 || 33665
|-
| 192 || 34313
|-
| 193 || 34973
|-
| 194 || 35645
|-
| 195 || 36331
|-
| 196 || 37031
|-
| 197 || 37742
|-
| 198 || 38470
|-
| 199 || 39210
|-
| 200 || 39965
|}
</div>

Changelog:
* [https://pso2.jp/players/news/28250/ 2021/08/04 Update]: Fixed a bug which applies the attack limit to enemy damage.

==Weak Point Damage (Blue Damage)==

When an attack lands on a weak point, the damage number is shown in blue in-game. This has no direct indication on how the damage is calculated. The following are known sources of blue damage numbers:

* Natural weak points on enemies
* Enhancer
* Weak Bullet
* Reinforced Weak Bullet

=See Also=
* [https://docs.google.com/spreadsheets/d/1h3gSISqcFIkZUiV_Z4thvFmycuTajw5-6V1Y36rx64w/ NGS検証データ置場]: Google Sheets collecting various information on damage-related mechanics. Published by Twitter user [https://twitter.com/flowerint1034 @flowerint1034].
* [https://docs.google.com/spreadsheets/d/1_OgubzM5QFe4rua4Xu0GSMAI8Idoq8r2yI8Ioyec6oY/ NGS Verification Data Storage]: Translation of the above sheet with some additional information. Published by Twitter user [https://twitter.com/TheuberClips @TheuberClips].
* [https://docs.google.com/spreadsheets/d/1N0WPMFXLnHK76RzznlI15psfP73i46YTNteehrxOSEQ/ NGS 敵攻撃力調査]: Google Sheets collecting information related to enemy damage. Published by Twitter user [https://twitter.com/dilute_rin @dilute_rin].
* [https://docs.google.com/spreadsheets/d/e/2PACX-1vQj8D29IiNYuH3-Vx474oYbyjWNrbTcUDE6z4g6XuWYTvHAfPpufnGygZxenANvMzYrdVylc3TqeGZ3/pubhtml PSO2 Attack Table]: Google Sheets collecting damage notations, down accumulation, and Photon Blast generation of various player attacks. Published by Discord user Deathcream#1576.
* [https://docs.google.com/spreadsheets/d/1p-e83XVE44Nj3OdLz6zliUftqckeMZXe1ZhpN011tF4/ PSO2NGS Bestiary] Google Sheets collecting stats and scaling of enemies. Published by Discord user Deathcream#1576.


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