A killing blow refers to when a player causes damage to a target that results in the target's death.
Certain abilities and effects are only activated if a player gets the killing blow on a monster, regardless of how much damage the player actually caused or how much influence the player has had in the fight.
Some monsters and players have spells or abilities they can use that may recoil or backfire, causing damage to the person who cast the spell or ability. If the monster or player kills itself with this ability, they would have in effect scored the killing blow on themselves. Thus it is possible for a player to not get the killing blow on a monster or player when it seems like they should have, even if he or she was the only one attacking them.
Most abilities that require a player to land the killing blow to activate also require that the target would also have given the player experience or honor under normal circumstances. This does not mean that targets such as PvP guards in enemy towns (which yield neither experience nor honor) do not count as killing blows as far as the ability is concerned, it simply means that the level of the person being attacked must not be as far below the attacker's level as to show up as gray in the standard WoW interface - which usually means the enemy in question can be no lower than 8 levels under that of the player. This level range requirement is not constant, however, and varies based on the attacker's level.
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