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:

Player Damage = ( WeaponATK * Variance + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2

• 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.
• PlayerATK: The attack value shown in stats window with no equipments. See Player Stats.
• EnemyDEF: The internal defense value of the enemy. Scales with enemy level. This value is floored when used. See Enemy Stats.
• Damage Multipliers: Final damage multipliers applied from various sources. See 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:

Minimum Player Damage = ( WeaponATK * Minimum Variance + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2

Maximum Player Damage = ( WeaponATK + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2

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 (Note: this only affects elemental attacks, e.g., Techniques.)
  • Weak Point: 1.5
  • Enhancer Core: 1.2
  • Enhanced Enemy after Enhancer core breaks: 1.5 on weak element
  • Weak Bullet: 1.2
  • Reinforced Weak Bullet: 1.25
• Class Skills
• Weapon Potentials
• Preset Abilities
• Special Abilities
• Unit stats
• Food buffs
• Region Mag buffs
• Enemy buffs: See Enemy Buffs.
• Level Difference Modifier: Damage reduction from level difference below enemy. See 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.

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)). Critical damage is 120% of maximum player damage, as shown with the following formula:

Critical Damage = Maximum Player Damage * 1.2

or in expanded form:

Critical Damage = ( WeaponATK + PlayerATK - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2 * 1.2

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.

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

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:

Enemy Damage = ( FLOOR(EnemyATK * EnemyATK Modifer) * Variance - PlayerDEF ) * Damage Multipliers * 0.2

• EnemyATK: The internal attack value of the enemy. Scales with enemy level. See 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.
• Variance: The range in which attack is scaled. Enemy damage has a set variance range of 96% - 100%.
• PlayerDEF: The defense value shown in stats window. See Player Stats.
• Damage Multipliers: Final damage multipliers applied from various sources. See 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. All values found so far seem to be multiples of 50 (e.g., 100%, 150%, 200%, 250%).
• 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
• Enhancer: An enhanced enemy has 1.5 damage multiplier until Enhancer is destroyed. (Unconfirmed on how it stacks with other enemy buffs).
• Enemy buffs: See Enemy Buffs.
• Level Difference Modifier: Damage increase from level difference above player. See Level Difference Modifiers.

Appendix

Enemy Buffs

There are several sources of buffs modifying an enemy's damage done and received. These modifiers stack additively.

Title Buffs

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

Title	Damage done	Damage received
Silver 白銀の	-	-
Golden 金色の	-	-
Battle-Hardened 老練の	+30%	-
Despair 絶望の	+150%	-50%

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.

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 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.

Enemy	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

Enhanced Enemies

Enhanced Enemies have an Enhanced core attached to them and glow red. They receive the following damage modifiers:

Core state	Damage done	Damage received
Intact	+50%	Core: +20% Body: -90% (multiplicative)
Destroyed	-	Weak element: +50% (multiplicative)

As noted, Enhanced Enemies' damage received modifiers seem to be applied as multiplicative part boosts unlike damage reduction from other enemy buffs.

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:

Damage Reduction = (Level Difference - 1) * 10%

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.

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:

Damage Increase = (Level Difference) * 20%

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

This section contains data derived from datamining the game files. All values may be changed in the future.

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

Player Damage = ( MIN(WeaponATK * Variance + PlayerATK, AtkLimit(EnemyLevel)) - FLOOR(EnemyDEF) ) * Damage Multipliers * 0.2

Enemy Damage = ( MIN(FLOOR(EnemyATK * EnemyATK Modifer) * Variance, AtkLimit(PlayerLevel)) - PlayerDEF ) * Damage Multipliers * 0.2

So far the attack limit value used is the same for both players and enemies at the same level. 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.

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

Weak Point Damage (Blue Damage)

When an attack lands on a weak point, the damage number is shown in blue in-game. The following are known sources of blue damage numbers:

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

See Also

• NGS検証データ置場: Google Sheets collecting various information on damage-related mechanics. Published by Twitter user @flowerint1034.
• NGS Verification Data Storage: Translation of the above sheet with some additional information. Published by Twitter user @TheuberClips.
• NGS 敵攻撃力調査: Google Sheets collecting information related to enemy damage. Published by Twitter user @dilute_rin.