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:
 * $$Damage = OutgoingDamage \times DamageResistMult \times (1 - DamageReduction_1) \times \dots$$

Each of these factors is outlined below in detail.
 * OutgoingDamage is the attack damage after factoring in damage modifiers.
 * DamageResistMult is a multiplier that reduces your attack damage by a percentage (from 1% to 99%) depending on how high the OutgoingDamage and corresponding enemy Resistance value for the damage type.
 * DamageReduction is a multiplier that reduces your attack damage by a percentage outside of Resistance, e.g. the Scorchbeast Queen's 70% reduction, or a Mutant Slayer armor's 75% reduction. DamageReductions stack through multiplication.

Outgoing Damage
Damage before resistances and any other reductions is calculated as follows:
 * $$OutgoingDamage = Base \times (1 + DamageBonus) \times

{DamageMult}_1 \times {DamageMult}_2 \times \dots$$ For example, a character using a semi-automatic rifle with a base 40 damage, Rifleman 3 (+20% damage bonus), Bloody Mess 3 (+15% damage bonus), and one stack of Tenderizer 3 (+10% damage received, or a 1.1x damage multiplier) will deal 59 Physical Damage before enemy defenses:
 * Base is the base damage according to a weapon's curve table plus any effects or weapon mods that directly add or subtract damage.
 * DamageBonus is the sum of most damage bonuses from Perks, weapon mods, consumables, and so on. This is an "additive bonus."
 * DamageMult is a damage multiplier that increases your total damage. After One Wasteland, many multiplicative damage bonuses became additive, though some remain, such as weapon receiver and barrel mods for non-physical damage types, Executioner's Legendary effect, Tenderizer, and Follow Through.
 * $$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 damage multiplier 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 units, 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 damage bonus for each point of Strength the character has.

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

A character using an unarmed gauntlet with a base 50 damage, 5 Strength (5 x 10% = +50% damage bonus), and Gladiator 3 (+20% damage bonus) will deal 85 Physical Damage:
 * $$OutgoingDamage = 50 \times (1 + 0.5 + 0.20) = 85$$

Visual bug: the damage bonus from Strength is not reflected on the PipBoy for any non-Physical Damage on melee weapons. 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 (10 x 5% = +50% damage bonus), Gladiator 3 (+20% damage bonus), Expert Gladiator 3 (+20% damage bonus), and Bloody Mess 3 (+15% damage bonus) will deal a total of 123 Damage (41 Physical and 82 Fire):
 * $$PhysicalDamage = 20 \times (1 + 0.5 + 0.2 + 0.2 + 0.15) = 41$$
 * $$FireDamage = 40 \times (1 + 0.5 + 0.2 + 0.2 + 0.15) = 82$$
 * $$TotalDamage = PhysicalDamage + FireDamage = 123$$

Weapon Mods
Physical Damage weapon mods typically increase or decrease the damage bonus. 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).
 * $$OutgoingDamage = Base \times (1 + 0.25 - 0.1)$$

Energy, Fire, Cryo, and Poison Damage weapon mods, however, are damage multipliers. 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 (1 - 0.15) = x 0.85):
 * $$OutgoingDamage = Base \times (1 + DamageBonus) \times 1.25 \times 0.85$$

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.

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


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