The new challenge system for close line calls in tennis has been used on the ATP and WTA tour for grand slam events since the 2007 Australian Open, and was designed to increase fairness for players by obtaining accurate line calls and enhance spectator interest by using video technology. In the current system, players have unlimited opportunity to challenge, but once three incorrect challenges are made in a set, they cannot challenge again until the next set. If the set goes to a tiebreaker game, players are given additional opportunities to challenge (usually one extra). If the match is tied at six games all in an advantage set, the counter is reset with both players again having a limit of up to three incorrect challenges in the next 12 games, and this resetting process is repeated after every 12 games. Having limited incorrect challenges raises questions as to when players should use their challenges to maximize the chance of winning. If a player was to use their challenges at every reasonable opportunity in a set, then they run the risk of running out of challenges on points that could significantly make a difference to the outcome of the set. If a player was too cautious in using their challenges early in a set, then he/she could lose the set with challenges left over and perhaps become annoyed with himself/herself for not challenging earlier when the opportunities were there. Devising a model that accurately determines when players should be making challenge decisions is a complex process involving the rate at which challenges occur, the expected number of points remaining in the set, the number of challenges remaining in the set, the probability of the challenge decision being successful and the probability error that will occur if a wrong decision is made (known as the "importance" of the point). Further, the probability of the challenge decision being successful differs for each point that is played and is a subjective decision to be made by the player. Given all this objective and subjective information, it should come as no surprise that players have different views and strategies as to which points they will challenge on. This is reflected by an article Replay System Becomes Part of Players` Strategies in The New York Times by Greg Bishop during the 2009 US Open. http://www.nytimes.com/2009/09/1 1/sports/tennis/11challenges.html Our task is to provide insight and strategies as to which points to challenge on to maximize a player`s chances of winning. Methods based on the work of Barnett et al, Morris, and Pollard et al will be used to address this problem. This research could be used by players and coaches to possibly improve players´ performance.
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