Damage (XC3)

Damage is the means of reducing an opponent's to zero in Xenoblade Chronicles 3 and Future Redeemed. s, s, Chain Arts, and Unity Combos deal varying amounts of damage, combined with the user's stats, equipped weapon, and many other factors.

When a party member deals damage, the amount of damage dealt appears as white text on the screen. This is surrounded by a 'burst' visual effect if some damage-increasing condition was met in the attack. The numbers for damage received by party members appear red; damage appears purple; and that caused by damage-over-time effects appears orange.

Playable characters in an Interlink visibly take damage, but cannot have their HP reduced.

In brief
The key parts of the damage formula are as follows:

Attack * (PowerMultiplier/Hits) * (1 + sum of Additives) * (product of Multiplicatives) * (1 - DamageReduction) * (1 - Defense) * (Block)

If the final result is lower than 1, it is set to 1; if it is higher than 9,999,999, it is set to 9,999,999. Non-integer results are rounded down.

In this formula:
 * Attack is the stat of the attacker. For playable characters, this depends on character,, and , as well as equipment and buffs/nerfs.
 * PowerMultiplier is the Power Multiplier of the attack used.
 * Hits is the number of times the Art hits (mostly — see below). All else being equal, this means that an Art with (say) 300% Power Multiplier and 2 hits does the same total damage as an Art with the same multiplier and 1 hit.
 * Additives are a class of additional effects that increase damage. Almost all "boosts damage dealt" effects, such as that of Edge Thrust and Inspirit, fall under this (exceptions are noted below). The key property of these is that they are added together before being multiplied onto the formula, meaning that if there are many additives, the relative contribution of each one is reduced. "Reduces damage dealt" effects also generally fall under these, although they subtract from the total rather than adding to it.
 * Multiplicatives are any damage modifications of the attacker which are not additive. These include s, Power Charge, and the damage ratio, among others (see below).
 * Strictly speaking, some of these are mutually additive (see below for details); however, they are not additive with the 'Additive' effects themselves, making them for all intents and purposes multiplicative.
 * DamageReduction is any effect on the target described by "Reduces damage taken" or "Take X% less damage".
 * If multiple such effects are active, they are added together; because of the negative sign, if there are many damage reduction sources, the relative contribution of each one is increased.
 * Defense is the defence of the target. Whether it is or  depends on the attack being used. Effects that manipulate defence are applied here, but not those that manipulate damage taken.
 * Attacks which ignore defense will only actually ignore defense if  is less than 1; that is, they will take into account defense if and only if doing so increases their damage.
 * Block is 0.5 if the attack is blocked, and 1.0 if it is not. That is, blocking an attack halves its damage.

Technical details
The full damage formula is as follows:

uncapped_damage =  (Attack + rand(0.0, WeaponAttack * WeaponStability)) * PowerMultiplier * MultiHitCorrection * (1 + sum of MultiplierGroup1) * (1 + sum of MultiplierGroup2) * (1 + sum of MultiplierGroup3) * (1 - sum of DamageReductionGroup) * DefenseMultiplier * (1 + sum of EmblemDamageGroup) * (1 + sum of AutoAttackEmblemGroup) * (1 - EmblemDefenseUp) * CritMultiplier * BlockedMultiplier * ComboMultiplier * ShackleRingMultiplier * FusionDamageMultiplier * ChainAttackMultiplier * AOEMultiplier * BackPreemptiveMultiplier * WeaknessMultiplier * LevelMultiplier * DifficultyMultiplier * RandomMultiplier

damage = min(9999999, max(1, floor(uncapped_damage)))

Attack
Attack is the character's stat. It is equal to:

(BaseAttack * ClassAttack + WeaponAttack) * (1 + sum of AttackAdditives) + (sum of FlatAttackBonuses)

where:
 * BaseAttack is dependent upon the character and their ;
 * ClassAttack is a multiplier dependent upon the character's current ;
 * WeaponAttack is an additive modifier dependent upon level and the used in the attack (typically of similar order of magnitude to BaseAttack);
 * AttackAdditives are any effect that "Increases/decreases Attack by XYZ%", such as the effect of Saturni Rings;
 * FlatAttackBonuses are any effect that "Increases/decreases Attack by XYZ" units of absolute value, such as Steelcleaver.

The main intricacy here lies in WeaponAttack. The weapon used in Class Arts and Fusion Arts is the weapon of the current class, but the weapon used in non-fused Master Arts and s is that of the Art's original weapon. This means that the effective Attack stat for non-fused Master Arts will be different from that displayed in the menu, which assumes the class's current weapon will be used. (An easy way to remember this is that the weapon which the character wields on-screen for the Art is the one which determines WeaponAttack.)

Stability modifier
The Attack stat is added to a random value between 0 and. The random number generator is called for each hit of a multi-hit attack separately. WeaponAttack is described above. WeaponStability is a -dependent value between 0 and 0.16; a higher WeaponStability means the damage has greater variance, due to the range of the random function being greater.

Because the expected value of the random value is directly proportional to WeaponStability, having a higher WeaponStability means more (expected) damage. However, because WeaponStability is in general small, the total stability modifier tends to be subleading to the Attack stat, and therefore has only a slight effect on damage.

Power Multiplier and multi-hit correction
The Power Multiplier is (as stated above) an Art-dependent value (expressed in-game as a percentage) which determines how strong the Art is. For auto-attacks themselves, this value is 1 during Interlinks, 0.9 for Unlimited Sword, and 0.6 otherwise.

The multi-hit correction ensures that (random variance and rounding error aside) two attacks with the same Power Multiplier but different numbers of hits will deal the same damage. For some attacks, it is simply the reciprocal of the number of hits (in an attack with two hits, each hit will deal half damage). Other multi-hit attacks have the damage distributed differently across their hits, so some hits within the attack deal more damage than others; however, in all cases, it is normalised such that the sum of MultiHitCorrection across all hits of a single attack adds to 1.

The multi-hit correction is bugged in the case of Master Arts used in Fusion Arts: when the Art has fusion bullets but not standard bullets, the multi-hit correction is ignored (set to 1) and each hit individually does the full art's intended damage. In practice, this only affects Quickdraw because it is the only applicable art with more than one hit; as such, it is nicknamed the 'Quickdraw bug'.

Multiplier group 1 (Additives)
Multiplier group 1, also known as DamageBonus1, represents a large class of bonuses to damage which are added together before multiplying onto the rest of the damage, such as Inspirit. The term "additives" used without further clarification refers to this group. Unless a damage bonus is stated to lie elsewhere in the damage formula, it can be expected to be part of this group.

Multiplier group 2 (Power Charge group)
Multiplier group 2, also known as DamageBonus2 or the Power Charge group, contains the following damage bonuses:
 * Power Charge
 * 's bonus with charged Arts
 * Accelerating Attacks' bonus to Arts after Quick Move
 * Element Genesis's bonus with s

While this group is technically added together before multiplying onto the rest of the damage, in practice only Power Charge and one other bonus from this group can be in effect at once. Therefore, the effects can generally be thought of as independent multipliers except in specific situations.

Multiplier group 3 (Cancel group)
Multiplier group 3, also known as DamageBonus3 or the Cancel group, contains the following damage bonuses:
 * Bonuses to ling: the Empowered Combo gem or effects such as that of
 * Supercharged's bonus with charged Arts
 * Piercing Laser's bonus with depleted Arts

Similarly to multiplier group 2, these effects can generally be considered independent multipliers, despite being added together before multiplying onto the rest of the damage.

Damage reduction
Damage reduction is an attribute of an attack's target, and is independent from defense and blocking. All sources of damage reduction are added together and then subtracted from 1 before being multiplied onto the damage formula, and thus can be considered to be part of a Damage Reduction Group.

Despite being commonly called 'damage reduction', not everything applicable actually reduces damage; some effects have negative modifiers and therefore increase damage taken. Such effects tend to be rare and are noted below.

The sources of damage reduction are as follows:
 * (Note that this does not actually affect the defense stats!)
 * Reduce All (negative modifier — increases damage taken)
 * I'll Protect You
 * I'll Help
 * Grace of the Land
 * Safe and Sound
 * Abundant Oceans
 * Incredible Guard
 * Awakilling
 * Exoshell
 * Defense Time
 * Defender Mastery
 * Shadow Parade (negative modifier — increases damage taken)
 * Determination
 * Total Destruction
 * Steady Assault
 * The Protectors
 * Sturdy Anklets/Vigorous Anklets
 * Plate Belt/Shield Belt
 * Victor Gauntlet/Challenger Gauntlet (negative modifier — increases damage taken)
 * Humongous Nopon Doll (negative modifier — increases damage taken)
 * Interlink level effects: damage taken reduced by -40% at Interlink level 0, +30% at level 2, +60% at level 3
 * Certain Future Redeemed enemies take less damage if there are other enemies in the fight (30% per extra enemy, up to 90%).
 * Humongous Nopon Doll (negative modifier — increases damage taken)
 * Interlink level effects: damage taken reduced by -40% at Interlink level 0, +30% at level 2, +60% at level 3
 * Certain Future Redeemed enemies take less damage if there are other enemies in the fight (30% per extra enemy, up to 90%).

Because these stack additively, it is entirely possible to have enough sources of damage reduction such that their sum exceeds 1.0. In this case, due to the lower bound on damage, each hit will deal only 1 damage.

Defense
The effects of a character's defense on the damage they receive vary depending upon the type of attack. If an attack is physical, the relevant stat is Physical Def.; if it is Ether, the relevant stat is Ether Def..

For the most part, the DefenseMultiplier in the above formula is given by, where DefenseStat is the physical or ether defense, and DefenseReduction adds together all sources that "reduce the target's defense by X%" (e.g. Pinion Primed) or "deal damage as though enemy's defense is X% lower" (e.g. Ultimate Qigong).

The story is more complicated when a hit "bypasses defense" (e.g. Brave Assault)/"deals defense-bypassing damage" (e.g. Total Destruction). In this case, DefenseMultiplier is set to 1 if and only if it is below 1. That is, if the target's effective defense is negative (i.e. the sum of DefenseReduction is greater than their DefenseStat), the target takes the same (greater) damage regardless of whether or not the incoming attack bypasses defense.

Emblem modifiers
During the Archsage's Gauntlet, the effects of Emblems are added together before being multiplied onto the rest of the damage formula (the Emblem damage group). (Despite their description, they do not modify Attack directly, and as such do not change the damage of abilities that "deal X% of Attack damage".)

These include:
 * Attack Up After Use
 * Debuff Duration Up
 * Combo Duration Up
 * Combo to Attack
 * Curse to Attack
 * Rescue to Attack
 * Focus: Attackers/Defenders/Healers
 * Kevesi/Agnian/Other Zeal
 * Last-Ditch Effort
 * Moneybags
 * Last-Ditch Effort
 * Moneybags

When the attack in question is an, other emblems are taken into account as well. These are added together separately from the above emblems before being multiplied onto the damage formula (the Auto-attack Emblem Group):
 * Area Attack
 * Absorb HP
 * Debuffing Attack
 * Debuffing Attack

The emblem multiplies damage taken by , where EmblemDefenseUp is the amount displayed in the emblem description. It is independent of other damage reduction sources.

Critical hits
If an attack is a, its damage is multiplied by a CritMultiplier of , where CritPower contains any effect that increases critical hit damage: Critical Hit Plus, Critical Strike, etc.

Blocking
If an attack is blocked, its damage is multiplied by a BlockMultiplier of.

Here, FusionBlockMultiplier is 1 in almost all cases; however, if the character is using Eye of the Storm as part of a Fusion Art, it is 1.5.

FlatBlockBonuses includes any effect that reduces damage taken on block, such as Mind for Guarding.

Other independent multipliers
The following effects are multiplied directly onto the damage formula, and therefore their relative effects are each independent of any others. (If they are not relevant, they each default to 1.)


 * ComboMultiplier: If an enemy is ed, this is 1.25; otherwise it is 1.
 * If the enemy is ed, they receive an additional hit of damage ('impact damage') equal to the total damage received before in the attack, multiplied by a further multiplier (see the page for details).
 * ShackleRingMultiplier: The Chain Ring, Shackle Ring, and Mighty Link effects cause damage-dealing Arts to do more damage if used in a chain of different Arts (see the linked pages for details).
 * FusionDamageMultiplier: Some Arts receive a 1.5x bonus to damage if used in a Fusion Art. (All Arts receive some sort of bonus, but only some receive increased damage.) (The effects of the Gold Cube, Platinum Cube, and Lunae Rings are part of multiplier group 1 and unrelated to this.)
 * ChainAttackMultiplier: During a, there is an additional damage multiplier which increases throughout the Chain Attack (see the linked page for details).
 * AOEMultiplier: If an AOE attack hits someone that is not its main target, the damage dealt to this additional target is 0.75x the damage dealt to the main target.
 * BackPreemptiveMultiplier: If combat initiates by a playable character using a surprise attack on an enemy's back, this attack receives a 1.5x damage multiplier.
 * WeaknessMultiplier: In Future Redeemed, attacks that target an enemy's weakness receive a 1.5x damage multiplier. This stacks additively with All But Fatal, which increases this effect.
 * LevelMultiplier: If a party member is the target of an attack from an enemy with a substantially above or below that of the party member, the attack's damage will be increased or reduced respectively; the multiplier ranges from 0.64x (enemy is 20+ levels below) to 4.5x (enemy is 20+ levels above).
 * DifficultyMultiplier: On, damage from enemies is multiplied by 0.75x. On , it is multiplied by 1.25x.
 * RandomMultiplier: Every attack is multiplied by a random value between 0.9 and 1.1. The exception is if the attack is a surprise attack on the enemy or if the enemy attacks the party when weapons are sheathed, in which case the random value is between 1.0 and 1.1.

Exceptions to the damage formula
If an ability causes a character to "deal X% of Attack damage" (chiefly damage), it deals X% of the  stat as damage, where the relevant weapon is that associated with the weapon of the character's class. The rest of the damage formula is ignored.

-inflicting attacks deal damage equal to the target's remaining, ignoring effects such as damage reduction and the 9,999,999 damage cap.

Effects which allow a character to "survive a KO with 1 HP", such as Hot Soul, reduce the damage of a deadly hit to the character's current HP minus 1.

characters take no damage. This overrides Doom.

The effects of Ultranull Shield, Physical Absorber, Spiritual Absorber, and Deflector Plate cause damage taken to be 0 when successful, overriding the lower bound on damage. (This does not apply to Deflector Field, despite its similar description.)

Certain enemy attacks deal damage based upon the target's maximum HP rather than using the damage formula.

Outside of battle
Not all damage is sustained from enemy attacks; wandering into dangerous areas or falling from too high will also inflict damage. These sources of damage do not stop when in battle, so it is important to avoid them when possible while fighting. Computer-controlled party members cannot be killed by fall damage or terrain damage unless a fight is ongoing; they will drop to 1 instead.

Terrain damage
Various liquids are hazardous to swim in, dealing damage based on max HP every few seconds. Auto-healing does not activate when in such a substance. The Hazard Neutralization Party Skill nullifies this damage.