Damage Formula
Attack Types: Normal Attack | Charge Attack
Other Damage: Plain Damage | Destruction Damage | Bonus Damage | Critical Damage | Supplemental Damage | DMG Taken Amplified
Damage Formula: Basic Concepts | Detailed Formula | Damage Cap
The damage formula is the process through which a character's stats, weapon skills, status effects, etc. are turned into the final damage that is observed in game. While there are slight differences to the formula depending on the type of damage being dealt, the shared general structure of the formula is:
[math]\displaystyle{ \underset{\mathrm{Soft\ Cap}}{f} \left( \frac{Raw\ DMG}{Enemy\ DEF} \right) \times DMG\ Amp.\ +\ Supp.\ DMG }[/math]
This page covers the important parts of the damage formula at a basic level. A detailed breakdown of every step, including the actual math, is available on the detailed damage formula page.
Estimated Damage Panel
The Estimated Damage in the Party screen can provide some insight into the damage formula. While it can be useful for making rough comparisons between grid weapons, there are several limitations:
- The estimate given is a Normal Attack damage instance against a foe with 10 defense (DEF).
- As a result, weapon skills that do not directly improve N.A. Damage may lower the Estimated Damage despite providing other beneficial effects, such as Normal Attack Bonus Damage and Skill or Charge Attack-related effects.
- Once a certain amount of raw damage is present, weapons that provide DMG Cap/Amp to Normal Attacks will be favored by the Estimated Damage.
- Passive effects are not consistently taken into account.
- For example, the DMG Cap from
Supplement damage (Damage cap: 30,000) and normal attacks deal 2-hit damage to random foes.
If main weapon is an Axe:
100% / 20% boost to critical hit rate100% chance of dealing 20% more damage. and 10% boost to damage cap.
At level 40:
No longer requires Spear or Axe. affects Estimated Damage, but other effects granted by the support skill do not.
- For example, the DMG Cap from
- Critical Hit DMG and other effects that are only applied on critical hits are only calculated if the grid has 100% critical hit chance.
- In-combat effects such as character skills or enemy debuffs are not reflected. This also includes raid unique effects such as the 60% boost to Omega weapon skills present in Impossible Omega III Raids.
The Formula
Raw Damage
[math]\displaystyle{ \text{Raw Damage} = \text{Base ATK}\ ×\ \text{DMG Modifier}\ ×\ ∏\text{ATK Boosts} }[/math]
Base ATK
- The orange number found next to the
- Each class/character will have an initial value that can be increased by flat amounts. Notable sources include:
- Base ATK from equipped Weapons
- Base ATK from equipped Summons
- EMP nodes
- Awakening
- Over Mastery
DMG Modifiers
- Every damage instance has an associated damage modifier.
- Normal Attacks always have a modifier of 100%.
- Skills and Charge Attacks vary per source. e.g.
Inflict
Strength: 25%Base Accuracy: 200%Duration: 6 turnsLocal status effect,
Strength: 25%Base Accuracy: 200%Duration: 6 turnsLocal status effect,
Strength: 100%Base Accuracy: 200%Duration: 6 turnsLocal status effect,
Strength: 100%Base Accuracy: 200%Duration: 6 turnsLocal status effect, and
Base Accuracy: 100%Duration: 2 turnsLocal status effect. - 500%
All Water allies gain
Strength: 5000Duration: 0.5 turnsApplied during the attack phase.
On the next turn, it'll have 0 turns remaining.. - 1250%
ATK Boosts
- ATK boosts are additive within their own category but are multiplicative with other categories.
- Has the biggest influence on raw damage.
- Consists of many different categories.
Common categories of ATK Boosts include:
| Category Name | Common Examples | Notes |
|---|---|---|
| Normal |
|
|
| Omega |
|
|
| Odious |
|
|
| EX |
|
|
| Elemental |
|
|
| Perpetuity |
|
Due to the multiplicative nature of ATK boosts, sometimes it is more beneficial to have smaller ATK boosts from multiple categories rather than a large ATK boost from a single category. For example:
Grid 1:
Raw Damage Boost = (Omega ATK) × (EX ATK)
= 1.2 × 1.18
= 1.416
= 41.6%
Grid 2:
Raw Damage Boost = (Omega ATK)
= 1.2 + 1.2
= 1.4
= 40%
Enemy Defense
[math]\displaystyle{ \text{Enemy DEF} = \text{Base DEF} \times \text{DEF modifiers} }[/math]
An enemy's defense (DEF) value is a core component of the damage formula, reducing the amount of damage dealt. As discussed previously, the estimated damage panel assumes an enemy DEF of 10, the same value as the Old or Used Lignoid found in Trial Battles. However in practice, many raids will have higher DEF values, typically around 15 or 20 depending on their difficulty.
An enemy's base DEF can be further modified during combat by statuses such as 
and 
. These modifiers stack additively, meaning that an enemy with 25% DEF Up combined with 50% DEF Down will result in a net 25% DEF Down.
The DEF modifier normally has a lower limit of -50%. However, 
and other related debuffs can lower this limit further to -60%.
Soft Damage Cap
For more in-depth information, see Damage Cap.
Every source of damage has its own soft damage cap, commonly referred to as the soft cap. The soft cap acts as a way to keep damage numbers under control. While the specifics of the soft cap formula vary per damage source, functionally they are very similar. Once damage exceeds a certain threshold (the soft cap), the excess damage is reduced significantly.
As a simplified example, consider the following:
Raw Damage = 1,000,000
Soft Cap = 500,000
Damage Reduction = 99%
Final Damage = (Raw Damage - Soft Cap) + [(Raw Damage - Soft Cap) * (1 - Damage Reduction)]
= (1,000,000 - 500,000) + [(1,000,000 - 500,000) * (1 - 0.99)]
= 500,000 + (500,000 * 0.01)
= 500,000 + 5,000
= 505,000
In this example, the first 500,000 damage is dealt normally, while the 500,000 damage exceeding the soft cap is reduced by 99%, resulting in 505,000 damage.
Due to this behavior, sufficiently large amounts of raw damage can effectively "overwhelm" the soft cap, allowing for significant amounts of damage to be dealt beyond it.
Damage Amplification and Supplemental Damage are applied after the soft cap and are therefore not affected by it.
Damage Amplification
[math]\displaystyle{ \text{Total DMG Amp.} = 1 + \text{Seraphic Amp.} + \sum (\text{Non-Seraphic Amp.}) }[/math]
Damage Amplification (DMG Amp.) is a damage modifier that is applied after the soft damage cap. With the exception of Seraphic Amp. where only the highest value takes effect, all sources of DMG Amp. are additive. The resulting DMG Amp. modifier is then multiplied with the post-soft cap damage.
Seraphic Amplification
These sources of DMG Amp. are mutually exclusive, with only the highest value taking effect:
| Source | Amp. Value | Notes |
|---|---|---|
| Seraphic Weapons | 23% | |
| Ultima Weapons | 25% | |
| Destroyer Weapons | 30% | |
Character Support Skills e.g.
|
Varies per source | Does not include Support Skills that amplify specific damage types. e.g.
|
Non-Seraphic Amplification
DMG Amp. modifiers in this category are additive with each other. Common examples include:
| Source | Amp. Value | Notes |
|---|---|---|
| Certain Arcarum Summons | 10% | |
Transcended Dark Opus Weapons
|
Varies per source | Pendulums only affect certain damage types. |
Certain Odious Weapons
|
Boostable 1.8% | |
 |
0.5% - 5% |
Supplemental Damage
For more in-depth information, see Supplemental Damage.
Supplemental Damage (Supp. DMG) is another source of damage that is applied after the soft damage cap. However, unlike DMG Amp., Supp. DMG is added to the capped damage rather than multiplied with it.
Since Supp. DMG is added each damage instance, it is particularly effective on damage sources that deal many instances of damage. To illustrate, the following is how 100,000 Supp. DMG would be applied in various scenarios:
Triple Attack:
Supp. DMG = 100,000
# of Hits per TA = 3
Total Supp. DMG = Supp. DMG x # of Hits
= 100,000 x 3
= 300,000
Triple Attack with one source of 
:
Supp. DMG = 100,000
# of Hits per TA = 3
# of Bonus DMG Sources = 1
Total Supp. DMG = Supp. DMG x [Hits per TA x (1 + Bonus DMG Sources)]
= 100,000 x [3 x (1 + 1)]
= 100,000 x 6
= 600,000
Triple Attack with 3-hit 
and one source of
:
Supp. DMG = 100,000
# of Hits per TA = 9
# of Bonus DMG Sources = 1
Total Supp. DMG = Supp. DMG x [Hits per TA x (1 + Bonus DMG Sources)]
= 100,000 x [9 x (1 + 1)]
= 100,000 x 18
= 1,800,000
All charge attacks are only one damage instance, despite what the animation may show. Therefore, Supp. DMG would only be added once. However, if the charge attack auto-activates a skill (e.g. 
Gain 
Strength: 10% (Max: 30%)Duration: Indefinite.
Activate 
When 1 
is consumed: Also inflict 
Strength: 20%Base Accuracy: 100%Duration: 180 seconds.
At level 55:
Damage increased to 300%-400%.
At level 95:
Damage further increased to 500%.
Also inflict 
Strength: 5% (Max: 30%)Base Accuracy: 100%Duration: 180 seconds and 
Strength: 5% (Max: 30%)Base Accuracy: 100%Duration: 180 seconds.
Also gain 1 
Duration: Indefinite..) or deals additional skill damage hits (e.g. 
5-hit, 100% Bonus Fire damage to foe (Damage cap: 121,500).
All Fire allies gain 
Strength: 10% (Max: 30%)Multiplier: Unique StackableDuration: Indefinite, 
Strength: 20% (Max: 60%)Duration: Indefinite, and 
Strength: 5% (Max: 15%)Duration: Indefinite.), then Supp. DMG would be applied separately to those damage instances.
Almost all sources of Supp. DMG are a percentage of a foe's max HP up to a fixed cap. However, due to the HP values of commonly fought foes, the fixed cap is easily reached and as such, supplemental damage is usually calculated with the value of the fixed cap.
Additional Resources
- https://gbf-wiki.com/index.php?システム仕様関連 - (JP) gbf-wiki article
- https://www.youtube.com/watch?v=ujE6ZVTMdqI - (JP) soufflex YouTube video
- https://resoleil.hatenablog.com/entry/2020/08/06/201436 - (JP) resoleil blog article