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'Rebound' is a term used in sports to describe the ball (or puck or other object of play) becoming available for possession by either opponent after an attempt to put the ball or puck into the goal has been unsuccessful. Rebounds are generally considered to be a major part of the game, as they often lead either to a possession change or to a second (and often better) opportunity to score by the side whose initial attempt failed.
In sports that have an assigned goalkeeper or goaltender, after that player makes a save, they may (and if they are able, usually should) then retain immediate possession of the ball or puck themselves, thus preventing a rebound from occurring.
Rebounds in basketball
In basketball, rebounds are divided into two categories: offensive rebounds, in which the ball is recovered by the offensive side and does not change possession, and defensive rebounds, in which the defending team gain possession of the loose ball. Generally, most rebounds are defensive because the team on defense tends to be in better position (in other words, closer to the basket) to recover missed shots. Often these are grouped under the heading Rebounds per game which denotes the average number of rebounds a player or team averages for a series or season.