Overkill

Overkill is a Guardian Rank reward in Borderlands 3 which adds excess damage of a kill to the next shot. It is unlocked by spending 25 Guardian tokens in the Enforcer tree.

Overview
Whenever the player kills an enemy, all damage dealt exceeding the enemy's remaining hit points will be added as excess damage to the next shot (the Overkill shot). It doesn't matter how the enemy was killed (guns/melee/action skill/grenade/etc.), but the excess damage will only be added to the next gun shot, so the damage of melee strikes/grenades/etc. can't be increased by Overkill. If this gun shot misses, all excess damage is lost.

Excess damage is preserved until the next gun shot is fired, no matter if the player switches weapons, reloads, does melee attacks, throws grenades, moves to another map or waits a long time.

Overkill "stacks" in the sense that if an enemy is killed with an Overkill shot, they may leave even more excess damage. The next (even more powerful) Overkill shot then may leave behind even more excess damage and so on – but this can't be exploited infinitely as there is a damage cap based on the gun damage of the weapon that fires the Overkill shot.

Doing a critical hit on the Overkill shot will multiply the shot's entire damage, so it multiplies both regular damage and excess damage. Thus, the player should attempt to do a critical hit to make the most of Overkill damage.

Damage cap
The damage an Overkill shot can deal is capped at 5x normal damage (the damage the shot would deal without any excess damage added). OverkillMaxDMG = NormalDMG × 5 However, multi-projectile weapons suffer a penalty: OverkillMaxDMG = NormalDMG × (1 + 4/N) where N is the number of projectiles. Thus, the damage cap will be NormalDMG × 3 for a 2-pellet Atlas Q-System and NormalDMG × 1.4 for a 10-pellet shotgun. The more projectiles a weapon has, the worse its Overkill damage potential.
 * This does not apply to weapons with "hidden" multiple projectiles that don't mention the "×N" number of projectiles in their Gun Damage specification, for example Lyuda, Bekah and Antimatter Rifle. They all have OverkillMaxDMG = NormalDMG × 5.

Excess damage
ExcessDMG = DamageDealt - HitPointsLeft where DamageDealt is the number that pops up on the kill. Elemental modifiers don't matter in this formula because they are already included in DamageDealt. The exact number of hit points an enemy has left is usually unknown, but the general rule is that the fewer hit points the enemy had left, the higher the Excess Damage for the following Overkill shot.
 * Multi-projectile weapons: If an enemy is killed with a multi-projectile weapon such as a shotgun, no more projectiles will hit the enemy than required for the kill; e.g. if an enemy with 160 health left is hit by a 100×5 shotgun, only two pellets will connect for 100×2 = 200 damage, so these weapons typically have lower Excess Damage potential. Generally, the higher the damage of a single projectile, the better for Excess Damage.
 * This also doesn't apply to "hidden" multi-projectile weapons: if e.g. the two projectiles of an Antimatter Rifle hit the enemy at the same time, DamageDealt will be the total damage of both projectiles combined no matter how few hit points the enemy has left.


 * Multi-kill: If a shot kills several enemies at once (e.g. with a rocket launcher), the game will use only one of those enemies for Excess Damage calculation, not all combined.
 * Status effects: If an enemy dies of status effects such as burning, only the last number popping up will be used for Excess Damage calculation, which will usually be pretty low.

Overkill damage
The overall damage of the Overkill shot is calculated thus: OverkillDMG = NormalDMG + (ExcessDMG × (100% + GuardRank) × Element) (Redundant brackets added to avoid misinterpretation) Multi-projectile weapons will spread Excess Damage evenly among N projectiles: OverkillProjectileDMG = NormalProjectileDMG + (ExcessDMG/N × (100% + GuardRank) × Element)
 * NormalDMG: the damage the shot would deal without any Excess Damage.
 * GuardRank: the gun damage Guardian Rank is applied again to Excess Damage.
 * Element: elemental modifier (e.g. 175% fire against flesh in Mayhem Modes and True Vault Hunter Mode).
 * This also doesn't apply to "hidden" multi-projectile weapons like Bekah, Lyuda and Antimatter Rifle – every projectile receives full Excess Damage, greatly improving their Overkill potential.
 * Jakobs ricochet: If a Jakobs bullet ricochets to another enemy, that enemy will also receive full Overkill damage. If a Jakobs weapon has several ricocheting projectiles (e.g. Headsplosion, Pa's Rifle), each of them does full Overkill damage.

The Overkill shot doesn't only increase impact damage, but also status effect damage. For example, if OverkillDMG is NormalDMG×3, then status effects are multiplied by ×3 too. OverkillStatusDMG = NormalStatusDMG × OverkillDMG / NormalDMG

Good

 * Unforgiven: this pistol does over ×10 damage on critical hits, which also applies to Overkill damage – so on critical hits, it can turn little Excess Damage into huge overall damage. However, maximum damage is limited by its relatively low gun damage.
 * Lyuda: The bullet spawns two additional projectiles after a short distance, each of which does full Overkill damage, greatly increasing Overkill potential.
 * Bekah: The bullet spawns three additional projectiles after a short distance, each of which does full Overkill damage, greatly increasing Overkill potential. On top of that, on critical hits the projectiles may ricochet to another enemy, dealing full Overkill damage again.
 * Antimatter Rifle: Fires two high-accuracy projectiles at once, each dealing full Overkill damage. These can hit multiple enemies if the shot is lined up, dealing full Overkill damage to every enemy hit. It is also elemental and does great status effect damage for even higher Overkill potential.
 * Proton Rifle / Melter: These Maliwan weapons can be charged up to multiply all damage by ×2, including Overkill damage and status effects.
 * ASMD: If the orb is hit by a bolt, does a big shock explosion with ×2.5 damage to every enemy hit. On an Overkill shot, it can deal massive damage to whole groups of shielded enemies. However, the explosion can't do critical hits.
 * Amplify shields: A +20% amplify shield multiplies NormalDMG by ×1.2, a Re-Router (+120%) by ×2.2. ExcessDMG is not affected, but since Overkill's damage cap is based on NormalDMG, maximum Overkill damage is increased by those amounts.

Bad

 * Shotguns: being multi-projectile weapons, very bad for both gathering Excess Damage and for the Overkill shot for the reasons listed above.
 * Maggie / Masher: very bad for the same reasons. Instead of ×5 OverkillMaxDMG of a single-projectile pistol, the Masher will have only ×1.8 max damage and the Maggie only ×1.67.