The Simpson-Yule Effect in Tennis

Roxanna Anspach Devlin, a former vice president with Paine Webber (now UBS), currently works as a realtor with Keller Williams Realty in Nashville, Tennessee. Roxanna Devlin spends her free time engaged in rowing, tennis, and other athletic activities.

In probability and statistics, Simpson’s paradox describes an occurrence in which multiple sets of data demonstrate a shared relationship or pattern that gets reversed or otherwise changes when two or more sets are combined. The paradox, also known as the Simpson-Yule effect, is sometimes seen in professional sports like tennis.

A professional tennis match generally consists of three or five sets of six games each. In order to win a game, players must score a minimum of four points. If opponents tie at three points apiece, however, the game is knotted at deuce and continues until one player scores a two-point advantage. Similarly, players who tie at six games each enter into a seven-point tie break. A tie break must also be won with a two-point advantage.

Due to the deuce and tie break scoring structure, however, an individual who wins fewer overall points can still take a set. For example, Player A could win each of his or her service games four points to zero while losing return games five points to three. Player A could go on to lose a tie break seven points to five. He or she would have 47 points for the set, compared to 31 points for Player B. Despite the 16-point disadvantage, Player B would win the set, illustrating Simpson’s paradox. Roger Federer, a winner of 17 major championships, has lost 24 of the 28 Simpson’s-paradox matches he has played over the course of his career.

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