When one of the two teams has a man advantage over the other, this usually occures when a player has been sent the penalty box or kicked out of the game. The team who has the man advantage is known to be on the powerplay and the other team is known to be shorthanded, who are penalty killing.
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In hockey, a power play is when one of the teams has committed a foul , such as a trip or an illegal check, and is one man short. The team is one man short because the player with the foul is thrown into the penalty box, almost like a timeout, thus making the team one man short for usually two minutes.