Damage Resistance

Damage Resistance (DR) is a derived statistic in the SPECIAL character system.

Any damage taken is reduced by this percentage (that is to say, a piece of armor with 10 DR will reduce damage taken by 10%). Damage Resistance can be increased by wearing armor, or by taking certain perks.

Fallout, Fallout 2, Fallout Tactics
In the original Fallout games, DR (Damage Resistance) is one of three stats by which a character can reduce or avoid damage. The other stats are AC (Armor Class) and DT (Damage Threshold). DR occupies the "final step" for combat and simulates the effect of how armor can help diffuse the energy of a bullet and reduce its lethality (like real-life Kevlar armor).

More specifically, after AC is checked for a successful hit and after DT is checked to reduce the damage, if there is any incoming damage, DR applies:
 * $$Final = \text{max}\Bigg(1, Adjusted \times \frac{100-\text{min}(DR,\ 90)}{100}\Bigg)$$

While DT can completely negate damage done, DR cannot. As the equation suggests, DR is capped at 90%, and any damage that goes past DT has a minimum of 1.

Initial level: 0
 * The Damage Resistance Modifier of ammo can pre-emptively reduce the DR of a target.
 * The Toughness perk increases normal DR by 10% per rank.
 * The Dermal Impact Armor implants increase normal and explosive DR by 5%.
 * The Dermal Impact Assault Enhancement implants increase normal and explosive DR by 10%.
 * The Phoenix Armor Implants increase laser, fire, and plasma DR by 5%.
 * The Phoenix Assault Enhancement implants increase laser, fire, and plasma DR by 10%.

Fallout 3
The maximum Damage Resistance is 85%, regardless whether this value is obtained by armor, perks, drugs or a combination of these. This makes the effects of Nerd Rage! and Med-X somewhat less useful, as even without chems, the Lone Wanderer can permanently gain up to 94% Damage Resistance through equipment and perks (with The Pitt additional content). The T-51b power armor and the Enclave Hellfire power armor plus their respective helmets have a max DR of 60. Combined with the five permanent perks (34%) gives the maximum DR without drugs or having less than 20 percent of your hitpoints. Without the additional content you would still be able to obtain a maximum DR of 91% with power armor. Note that these numbers assume a fully repaired suit of armor, which, when the T-51b armor is actually being worn, is only possible if the player boosts Crazy Wolfgang's repair skill to 100 by reverse pickpocketing workman's coveralls from Point Lookout onto him because there is only one copy of this armor and it can only be repaired by non-player characters. Enclave Hellfire armor can be found, but it is rare (only obtainable with Broken Steel loaded). For players who prefer non-power armor, you can still obtain a permanent DR of 82% (79% without The Pitt add-on) with ranger battle armor, ghoul mask, the ranger battle helmet and the perks listed below.

All add-on Combinations

 * Permanent DR of 73% (temporary of 83%), +5 melee weapons and 148 Action Points with the permanent perks below and Superior Defender, Action Boy/Action Girl, tribal power armor, Ledoux's hockey mask, Almost Perfect and waiting to collect all S.P.E.C.I.A.L. Vault Boy bobbleheads until level 30 has been achieved. This produces perfect SPECIAL stats with the exception of Agility which will be 9 due to the power armor effect. The tribal armor can be repaired with common T-45d power armor while the hockey mask is immune to item damage and can be repaired (if found damaged) with regular hockey masks.

The Pitt Combinations

 * Permanent DR of 73%, +1 Strength, +1 Luck, -1 Agility, +5 melee weapons and +65 AP with the permanent perks below and Action Boy/Action Girl, tribal power armor and Ledoux's hockey mask. The tribal armor can be repaired with common T-45d power armor while the hockey mask is immune to item damage and can be repaired (if found damaged) with regular hockey masks.
 * Replace the hockey mask above with Poplar's hood which has 2 lower DR than the hockey mask but can be worn with the ghoul mask producing 5 DR rather than 4. This combination repairs the Agility damage (+2 small guns, +2 sneak, +2 Action Points), adds +10 sneak, permanent 74% DR, +40 Action Points and feral ghouls will not become hostile. It is a possibility for those who have not yet found the hockey mask, or missed acquiring it altogether. This option, however, excludes obtaining the Barkskin perk which offers 5 DR itself.

Permanently increasing Damage Resistance

 * The Cyborg perk gives +10% damage resistance.
 * The Toughness perk gives +10% damage resistance.
 * The Barkskin perk gives +5% damage resistance.
 * The Survival Expert perk gives up to +6% damage resistance.
 * The Superior Defender perk gives +10% damage resistance when standing still.
 * The Pitt Fighter perk gives +3% damage resistance.

Temporarily increasing Damage Resistance

 * The Nerd Rage! perk gives +50% Damage resistance, but only if your Health is below 20%.
 * The Med-X drug gives +25% Damage resistance, and it is possible to double up the effect by wearing the prototype medic power armor and also manually administering the drug.

Fallout: New Vegas
In Fallout: New Vegas, DR is mostly replaced by DT (Damage Threshold). Med-X and the new items Slasher, battle brew, and Rebreather still provide bonuses to DR, which functions identically to the DR from Fallout 3. If all 3 items are taken together, they provide the maximum 85% damage resistance allowed by the game engine.

Damage Resistance is applied before damage threshold, contrary to the original Fallout games. So, for a character with 30 DR and 20 DT (i.e. a NCR Veteran Ranger), an attack that deals 80 damage is first reduced by 30% (leaving 56 damage), then the damage threshold is subtracted from that number, leaving a final damage of 36. As a result of this, a high damage resistance has a very large effect on a character's ability to withstand damage. For full damage formula see Fallout: New Vegas combat.

The only pieces of equipment in the game that raise DR instead of DT are: In addition, DR can be conferred via the console by entering player.forceAV DamageResist xx where xx is between 0 and 85. Values beyond 85 are ignored by the game; 85 is the maximum DR, a likely holdover in the game engine from Fallout 3.
 * Rebreather from the quest Volare!
 * Vault 11 jumpsuits
 * the normally non-playable trenchcoat found on the investigator during the quest Beyond the Beef.
 * Scientist outfits
 * Regulator duster

A rare few non-player character characters have perks which grant them DR in addition to the DT from their armor. These include:
 * All companions if using Ferocious Loyalty.
 * Sunny Smiles (10% DR)
 * Ranger Stella (10% DR)
 * Legion vexillarius (10% DR)
 * Praetorian guards (10% DR)
 * Lucius (10% DR)
 * Certain Legionary assassins (10% DR)
 * Ulysses (10% DR)
 * Blister (10% DR)
 * Beast (10% DR)
 * Bonesaw (10% DR)
 * Blade (10% DR)
 * Colonel Royez (10% DR)
 * Gaius Magnus (10% DR)
 * Mean Sonofabitch (20% DR)
 * Motor-Runner (20% DR)
 * Nightkin (30% DR)
 * Dog (but not God) (30% DR)
 * Certain NCR Rangers (30% DR)
 * NCR Veteran Rangers (30% DR)

Fallout 4
Damage resistance returns in Fallout 4. However, the stat is no longer a 1-1 relationship with actual % damage reduced, as its value can be seen to be as high as 1000 on power armor.

Instead, the amount of damage reduction you get out of your damage resistance is actually based on how much potential weapon damage is coming in; net damage reduction is based on a ratio between the potential weapon damage and the damage resistance, with diminishing returns for high damage resistance. Some examples:
 * Against 0 damage resistance, 100% of damage is done.
 * If damage resistance is half of potential weapon damage, then ~35% of the weapon damage is negated.
 * If damage resistance is equal to potential weapon damage, then ~50% of weapon damage is negated.
 * If damage resistance is twice that of potential weapon damage, then ~61% of weapon damage is negated.
 * If damage resistance is 20x that of potential weapon damage (easily possible with power armor), then ~83% of weapon damage is negated.

Damage Reduction
The basic damage reduction formula is close to (99.95% accurate):
 * $$DamageCoeff = \text{Min}\Bigg(0.99, \Bigg[ \frac{Damage}{DamageResist}\Bigg]^{0.366} \times 0.5\Bigg)$$


 * Note that this is a coefficient (multiplier) for the net damage done not the actual damage reduction; so lower numbers are better (more damage is negated).
 * If you want the actual % damage reduction simply do $$DamageReduction = 1 - DamageCoeff$$

There are variations on this DamageCoeff calculation based on weapon used:
 * Projectile and close combat weapons use PaperDamage (essentially the number you see in the PIP Boy), RangeMultiplier and PowerAttackMultiplier for the damage part
 * Energy weapons use WeaponBaseDamage and RangeMultiplier for the damage part (essentially, they are more vulnerable their respective damage resistance).


 * $$PaperDamage = WeaponBaseDamage \times Perk1 \times Perk2 \times ... \times RangeMulti$$


 * WeaponBaseDamage is affected by weapon mods and is e.g. doubled with a 2x charged Laser musket
 * RangeMulti is
 * 1.0, when inside WeaponRange
 * 0.5 to 1.0, when between WeaponRange and 2xWeaponRange
 * 0.5, when outside 2xWeaponRange

Projectile Damage

 * $$DamageCoeff = \text{Min}\Bigg(0.99, \Bigg[ \frac{PaperDamage}{DamageResist*RiflemanMulti}\Bigg]^{0.366} \times 0.5\Bigg)$$


 * a Hunting Rifle with 37 BaseDamage and 48.84 PaperDamage (PipBoy Value) does 24.2 damage vs 50 DamageResist at point blank range
 * ( 48.84 / 50 )^0.366 x 0.5 x 48.84

Energy Damage

 * $$DamageCoeff = \text{Min}\Bigg(0.99, \Bigg[ \frac{WeaponBaseDamage\times RangeMulit}{DamageResist}\Bigg]^{0.366} \times 0.5\Bigg)$$


 * a Laser Rifle with 38 BaseDamage and 50.16 PaperDamage does 22.7 damage vs 50 EnergyResist at point blank range
 * ( 38 / 50 )^0.366 x 0.5 x 50.16

CloseCombat Damage

 * $$DamageCoeff = \text{Min}\Bigg(0.99, \Bigg[ \frac{PaperDamage \times PowerAttackMulti}{DamageResist}\Bigg]^{0.366} \times 0.5\Bigg)$$


 * PowerAttackMulti = 1.5

Final Damage

 * $$FinalDamage = PaperDamae \times ArmorMulti \times HeadshotMulti \times SneakAttackMulti$$

Damage Reduction for VATS Critical Attack
CriticalDamage = [ PaperDamage x CloseCombatMulti ] + [ WeaponBaseDamage x CriticalMulti ]
 * CloseCombatMulit = 1.5 for most melee/unarmed weapons
 * CriticalMulti = 1 + BobbleheadBonus(0.25) + MagazineBonus(0.05 to 0.5) + WeaponModBonus(2.0)

Projectile / CloseCombat

 * $$FinalDamage = \text{Min}\Bigg(0.99, \Bigg[ \frac{CriticalDamage}{DamageResist}\Bigg]^{0.366} \times 0.5\Bigg) \times CriticalDamage \times HeadShotMulti \times SneakMulti$$

Energy

 * $$FinalDamage = \text{Min}\Bigg(0.99, \Bigg[ \frac{WeaponBaseDamage}{DamageResist}\Bigg]^{0.366} \times 0.5\Bigg) \times CriticalDamage \times HeadShotMulti \times SneakMulti$$

Difficulty Modifier
Added to every FinalDamage (for a player attacking an enemy)
 * x2.0 Very easy
 * x1.5 Easy
 * x1.0 Normal
 * x0.75 Hard
 * x0.5 Very hard
 * x0.5 Survival

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