title: Reducing the likelihood of long tennis matches.
abstract: Long matches can cause problems for tournaments. For example, the starting times of subsequent matches can be substantially delayed causing inconvenience to players, spectators, officials and television scheduling. They can even be seen as unfair in the tournament setting when the winner of a very long match, who may have negative aftereffects from such a match, plays the winner of an average or shorter length match in the next round. Long matches can also lead to injuries to the participating players. One factor that can lead to long matches is the use of the advantage set as the fifth set, as in the Australian Open, the French Open and Wimbledon. Another factor is long rallies and a greater than average number of points per game. This tends to occur more frequently on the slower surfaces such as at the French Open. The mathematical method of generating functions is used to show that the likelihood of long matches can be substantially reduced by using the tiebreak game in the fifth set, or more effectively by using a new type of game, the 50-40 game, throughout the match. Key PointsThe cumulant generating function has nice properties for calculating the parameters of distributions in a tennis matchA final tiebreaker set reduces the length of matches as currently being used in the US OpenA new 50-40 game reduces the length of matches whilst maintaining comparable probabilities for the better player to win the match.
authors.affiliation: Swinburne University , Melbourne, VIC, Australia.
authors.forename: Tristan
authors.initials: T
authors.lastname: Barnett
authors.affiliation: Swinburne University , Melbourne, VIC, Australia.
authors.forename: Brown
authors.initials: B
authors.lastname: Alan
authors.affiliation: University of Canberra , Canberra, ACT, Australia.
authors.forename: Graham
authors.initials: G
authors.lastname: Pollard
keywords: Tennis; generating functions; long tennis matches; scoring systems; sport