Damage (Fallout 76)

Damage is the amount of Hit Points an attack will remove from its target. Reducing a target's Hit Points to zero will kill it.

Outgoing damage can be modified by weapon mods, perks, legendary effect bonuses, mutations, consumables, and for melee strikes and ranged weapon bash attacks the Strength attribute.

Incoming damage can be modified by Damage Resistance and other reduction, avoidance, and immunity effects.

Damage Formula
In Fallout 76, the damage an attack will deal to a target is calculated as follows:


 * $$Damage = OutgoingDamage \times DamageResistMod \times (1 - DamageReduction_1) \times (1 - DamageReduction_2) \times \dots$$


 * OutgoingDamage is the attack damage after factoring in damage modifiers.
 * DamageResistMod is the percentage of damage (from 1% to 99%) that remains after applying the Resistance corresponding to the damage type.
 * DamageReduction is the percent of damage reduced by an effect.

Each of these factors is outlined below in detail.

Outgoing Damage
Damage before resistances and any other reductions is calculated as follows:


 * $$OutgoingDamage = Base \times (1 + AdditiveMod) \times

{MultiMod}_1 \times {MultiMod}_2 \times \dots$$


 * Base is the base damage according to a weapon's curve table plus any effects or weapon mods that directly add or subtract damage.
 * AdditiveMod or "additive modifier" is the sum of most of the damage modifiers from Perks, weapon mods, and so on.
 * MultiMod or "multiplicative modifier" is a damage modifier that multiplies with the total damage. After One Wasteland, many multiplicative damage bonuses became additive.

For instance, a character using a semi-automatic rifle with a base 40 damage, Rifleman 3 (+20% additive modifier), Bloody Mess 3 (+15% additive modifier), and one stack of Tenderizer 3 (+10% multiplicative modifier) will deal 59 Physical Damage before enemy defenses:


 * $$OutgoingDamage = 40 * (1 + 0.2 + 0.15) * (1 + 0.1) = 59.4$$

Ranged Damage
Ranged weapons are subject to weapon range, which determines the maximum distance at which the weapon will deal its maximum damage.

This "range multiplier" is a multiplicative modifier that starts at 1.0 if the target is within weapon range, scaling down as the target moves further away to a minimum of 0.5 at 200% of the weapon's range.

Going back to the semi-automatic rifle above, if it deals 59.4 Physical Damage at its max range of 150, then it will deal 29.7 Physical Damage to a target that is 300 units away.

Melee and Bash Damage
For one- and two-handed melee weapons and ranged weapon bash attacks, 5% is added to the additive modifier for each point of Strength the character has.

For unarmed melee weapons and fists, 10% is added to the additive modifier for each point of Strength the character has.

A character using a two-handed hammer with a base 50 damage, 5 Strength (+25% additive damage), and Gladiator 3 (+20% additive damage) will deal 72 Physical Damage:
 * $$OutgoingDamage = 50 \times (1 + 0.05 \times 5 + 0.20) = 72.5$$

Visual bug: the Strength bonus is not reflected for any non-Physical Damage on melee weapons on the PipBoy. The correct damage will still be dealt and is visible in floating damage numbers.
 * Bugs

Multiple Damage Types
Many weapons are able to deal multiple Damage Types per attack, such as the Shishkebab which deals both Physical and Fire Damage. To get the total damage before defensive measures are factored in, one has to calculate the damage for each damage type separately and then add the values together.

A character using a fiery sword with a base 20 Physical and 40 Fire Damage, 10 Strength (+50% additive damage), Gladiator 3 (+20% additive damage), Expert Gladiator 3 (+20% additive damage), and Bloody Mess 3 (+15% additive damage) will deal a total of 123 Damage (41 Physical and 82 Fire):


 * $$PhysicalDamage = 20 \times (1 + 10 * 0.05 + 0.2 + 0.2 + 0.15) = 41$$
 * $$FireDamage = 40 \times (1 + 10 * 0.05 + 0.2 + 0.2 + 0.15) = 82$$
 * $$TotalDamage = PhysicalDamage + FireDamage = 123$$

Weapon Mods
Physical Damage weapon mods typically increase or decrease the additive modifier. For example, a handmade rifle's hardened receiver will add 25% damage (+0.25 additive modifier) whereas its automatic receiver will subtract 10% damage (-0.1 additive modifier).

Energy, Fire, and Cryo Damage weapon mods, however, are multiplicative modifiers. The laser gun's prime capacitor will add 25% damage multiplicatively (x 1.25) and it's automatic barrels will subtract 15% damage multiplicatively (x 0.85):
 * $$OutgoingDamage = Base \times (1 + AdditiveMod) \times (1 + 0.25) \times (1 - 0.15)$$

There are some exceptions to the above, where a heating coil will add base Fire Damage to a super sledge, or a plasma blade will multiplicatively reduce the Physical Damage by 50% and add a sizeable amount of base Energy Damage to a war glaive.

Critical attacks
Critical attacks in VATS are added onto the Outgoing damage. The sum is equal to base damage of the weapon multiplied by the critical hit modifier (usually 2.0; but can be increased with buffs and perks). Critical damage does not interact with sneak multiplier, it is added separately.


 * $${\it OutgoingDamage} = {\it Damage}_{\rm Paper} + {\it Damage}_{\rm Critical}$$
 * $${\it Damage}_{\rm Critical} = {\it Damage}_{\rm Paper} + ({\it Damage}_{\rm Base} \times {\it CriticalMultiplier})$$
 * $${\it CriticalMutiplier} = {\it CriticalMultiplier}_{\rm Base} + ({\it AdditiveMod}_{\rm 1} + {\it AdditiveMod}_{\rm 2} + {\it AdditiveMod}_{\rm 3})$$


 * Ranged criticals: increases the chance to land the attack.
 * Melee criticals: multiplies the DamageCritical by 1.5


 * Bugs
 * Holding down the critical button while performing successive criticals while using an automatic weapon will consume the charge, but will not apply the bonus damage.
 * Critical hits dealt by explosive launchers, such as the Fat Man will not factor in the damage of the explosion. These weapons will instead calculate using the on-hit impact damage of the projectile, which is usually 1.

Damage Resistance
Most damage types have a corresponding Resistance that reduces the magnitude of that source of damage. The percentage of damage an attack deals after encountering its corresponding resistance is the following:


 * $$DamageResistMod = \text{Min}\left(0.99, \left[ \frac{\it Damage \times 0.15}{\it Resist}\right]^{0.365} \right)$$

A semi-automatic rifle that deals 100 Physical Damage against a target with 200 (Physical) Damage Resist will deal 38 Physical Damage:


 * $$FinalDamage = 100 \times \text{Min}\left(0.99, \left[ \frac{\it 100 \times 0.15}{\it 200}\right]^{0.365} \right) = 38.85$$

Elemental Resistances
Non-physical damage types (e.g. Energy, Fire, Cryo, Poison, Rad Exposure, and Rad Ingestion) only factor in the base damage of the attack when determining the effect of Resistance. This modifies the percentage of damage dealt after resists to the following:


 * $$DamageResistMod = \text{Min}\left(0.99, \left[ \frac{\it BaseDamage \times 0.15}{\it Resist}\right]^{0.365} \right)$$

For example, assume that we have a mixed damage plasma gun that deals 20 Physical / 20 Energy base damage, but 100 Physical / 100 Energy after damage bonuses. Against a target with 200 (Physical) Damage Resist / 200 Energy Resist, this weapon will deal 60 total Damage (instead of the expected 38.85 x 2 = 77.7):


 * $$FinalPhysicalDamage = 100 \times \text{Min}\left(0.99, \left[ \frac{\it 100 \times 0.15}{\it 200}\right]^{0.365} \right) = 38.85$$
 * $$FinalEnergyDamage = 100 \times \text{Min}\left(0.99, \left[ \frac{\it 20 \times 0.15}{\it 200}\right]^{0.365} \right) = 21.59$$
 * $$FinalDamageTotal = FinalPhysicalDamage + FinalEnergyDamage = 60.44$$

Armor Penetration
Resistances, or armor, can be reduced with armor penetration effects from weapon mods, perks, and legendary effects. In the formulae above, armor penetration is reflected by reducing the Resist value by the penetration amount.

For example, a 100 Physical Damage pistol shot with Tank Killer 3 (+36% armor penetration) against 150 Damage Resist will deal 50 Physical Damage:


 * $$FinalPhysicalDamage = 100 \times \text{Min}\left(0.99, \left[ \frac{\it 100 \times 0.15}{\it 150 \times (1 - 0.36)}\right]^{0.365} \right) = 50.79$$

Damage Reduction
Damage reductions from perks like Dodgy or innate to an enemy like the Scorchbeast queen's 70% reduction apply to all damage regardless of the Damage Type. They can also stack, multiplying together to greatly reduce incoming damage.

For example, when taking 200 Cryo Damage from an explosive cryo grenade, Fireproof 3, Dodgy 3, dense torso armor mod, and zero Cold Resist will all stack to reduce its damage to 38 Cryo Damage:


 * $$FinalDamage = 200 \times (1 - 0.45) \times (1 - 0.3) \times (1 - 0.5) = 38.5$$