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 BodyPartMult
*OutgoingDamage is the attack damage after factoring in damage bonuses and multipliers.
*DamageResistMult is a damage multiplier that reduces attack damage by a percentage (from 1% to 99%) depending on how high the OutgoingDamage and corresponding enemy Resistance value for the damage type.
*BodyPartMult is a damage multiplier that gets factored in at the end, improving damage if the attack hit a weak point (e.g. a raider's head) and reducing damage if the attack hit a hard point (e.g. a Mirelurk's shell).
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 + DamageBonus) \times
{DamageMult}_1 \times {DamageMult}_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.
* 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 or decreases your total damage by a percentage. Damage multipliers stack multiplicatively with each other. Damage reduction multipliers include the nuke bosses' damage reduction, Ogua and Blue Devil damage reduction, perks like Fireproof and Dodgy, Empath, and Assassin's Legendary armor effect. After One Wasteland, many multiplicative damage bonuses became additive, though some remain, such as Executioner's Legendary weapon effect, Tenderizer, Taking One for the Team, and Follow Through.
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:
:OutgoingDamage = 40 * (1 + 0.2 + 0.15) * (1 + 0.1) = 59.4
===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 Iron Fist 3 (+20% damage bonus) will deal 85 Physical Damage:
:OutgoingDamage = 50 \times (1 + 0.5 + 0.20) = 85
; Bugs
 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.
===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.
===Explosive damage===
Explosive damage dealt by explosive launchers and weapons that cause explosions via the Legendary effect or Gauss effect subject to two explosion radii: inner and outer. Inner radius determines the maximum distance between the center of the explosion and the target at which the explosion will deal maximum damage. If the target is outside of the inner radius but within the outer radius, then the explosion damage is reduced significantly the further away the target is, up to a minimum amount of damage at a distance equal to the outer radius. If the target is outside of the outer radius, they do not get hit by the explosion.
This "radius multiplier" is a damage multiplier that starts at 1.0 if the target is within the inner radius, scaling down as the target moves further away to the outer radius.
===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.
===Sneak attacks===
Sneak attacks are another damage source that adds to the damage bonus, starting at +100% without any modifications from Perks or Chems. 
Sneak Attacks will trigger only when the player is in HIDDEN or CAUTION status, and never in DANGER, and will apply the damage on the enemy's HP bar and in floating damage numbers even if the Sneak Attack text doesn't appear in the heads-up display.
The damage bonus from sneak attacks is not multiplied on a critical hit. "Fallout 76 - How Sneak Bonus Actually Works | Follow Through, Covert Operative & Mister Sandman." by 
Vlad Armstrong
===VATS Critical attacks===
VATS Critical attacks are a sum of the Outgoing damage and the critical damage bonus. The critical damage bonus is equal to base damage of the weapon multiplied by the critical hit multiplier, which is 1.0 and is increased by additive critical damage bonuses. Bonus critical damage does not interact with the bonus from Sneak attacks; 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 CritDamageBonus}_{\rm 1} + {\it CritDamageBonus}_{\rm 2} + {\it CritDamageBonus}_{\rm 3} + ...)
* Ranged criticals: increases the chance to land the attack.
* Melee criticals: multiplies the DamageCritical by 1.5
; Notes
* The base critical hit multiplier for all weapons is 2.0 as per the game files. However, to make it easier to understand how to calculate weapon damage, the formulae were refactored on this page, making the effective base critical hit bonus multiplier a 1.0 instead.
* The bonus critical damage added to the paper damage is not subject to any damage multipliers. This means a large portion of VATS critical strikes will not benefit from effects like Tenderizer or Follow Through. That said, with high enough critical damage bonus, VATS criticals will be mostly unaffected by boss (and player) damage reduction effects, including the Scorchbeast Queen's 70% damage reduction, bypassing a mechanic used to balance boss HP. Until the Fight for Freedom season patch addressed Legendary creature health pools, enemies could not have more than 2^15 HP = 32,768 HP (signed 16-bit int maximum), which implies the damage reductions existed as a workaround for an engine limitation. Boss fights being vulnerable to VATS critical builds may have been an inadvertent side effect.
;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.
==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:
:DamageResistMult = \text{Max}\left(0.0
1, \text{Min}\left(0.99, \left[ \frac{\it Damage \times 0.15}{\it Resist}\right]^{0.365} \right)\right)
The min() and max() clauses ensure armor always reduces 1% of damage but never more than 99% of damage. These thresholds are achieved when the damage greatly exceeds the Resistance value and when the Resistance greatly exceeds the damage value, respectively.
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{Max}\left(0.01, \text{Min}\left(0.99, \left[ \frac{\it 100 \times 0.15}{\it 200}\right]^{0.365} \right)\right) = 38.85
A mixed damage type energy weapon that deals 50 Physical Damage and 75 Cold Damage against a target with 100 (Physical) Damage Resist and 200 Cold Resist will deal 45-46 total Damage:
:PhysicalDamage = 50 \times \text{Max}\left(0.01, \text{Min}\left(0.99, \left[ \frac{\it 
50 \times 0.15}{\it 100}\right]^{0.365} \right)\right) = 19.43
:ColdDamage = 75 \times \text{Max}\left(0.01, \text{Min}\left(0.99, \left[ \frac{\it 75 \times 0.15}{\it 200}\right]^{0.365} \right)\right) = 26.23
:TotalDamage = PhysicalDamage + ColdDamage = 45.66 
; Bugs
* The debuff effect applied by the endangerol syringe barrel can stack if multiple people shoot the same target.When the endangerol syringer was updated in Patch 44, it's magic effect was changed from 000628E5 <EndangerolDamageDamageResistEffect> to 003C6540 <EndangerolDamageDamageResistEffect_Contact>, losing the No Recast flag in the process. "Fallout 76 The Endangerol Syringer Evolved! - Turtle's Lab" by Angry Turtle
===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 200 Damage Resist will deal 45.72 Physical Damage:
:FinalPhysicalDamage = 100 \times \text{Max}\left(0.01, \text{Min}\left(0.99, \left[ \frac{\it 100 \times 0.15}{\it 200 \times (1 - 0.36)}\right]^{0.365} \right)\right) = 45.72
Armor penetration generally produces lesser results than simply increasing the raw damage output. In the above example, adding 36% armor penetration produced only 17% more effective damage (45.72 vs. 38.85). However, increasing raw damage by 36%, on the other hand, would produce 52% more effective damage (59.11 vs. 38.85). 
Ideally, both should be combined, as a 36% increase in damage and a 36% armor penetration value produces 69.57 effective damage (79% more).
; Bugs
* Armor penetration from weapon mods and the Anti-Armor legendary effect stack due to sharing an actor value for dynamic descriptions introduced in Patch 43.ArmorPenetration "Armor Penetration" [AVIF:00097341] is used by both weapon mods and the Anti-Armor legendary effect. "Fallout 76 - The Science Behind Armor Penetration for Ranged Weapons." by Vlad Armstrong
==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
Category:Combat
Category:Fallout 76 gameplay