Overkill damage
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The term overkill damage refers to a difference between damage dealt in one hit and target's life remaining before death. It doesn't work with damage over time because a hit is required.
Mechanics
Damage
Overkill damage is being calculated from target's full health, but it only makes sence on kill, when overkill damage becomes a positive number. For example, if a target has 20 life and a player deals a hit of 100 damage, target dies and overkill damage equals to 80.
Interactions with culling strike
If culling strike or Bane of Legends is triggered, there is no overkill damage since those effects bring an enemy's life to 0.