The Simpson’s Paradox in Tennis

Dr. Paul Ebben, a graduate of the Wisconsin School of Professional Psychology, has practiced forensic neuropsychology at Insight Psychological Consultants in Frankfort, Kentucky, since 2002. Dr. Paul Ebben likes to stay physically active by playing tennis whenever possible.

The sport of tennis features a unique scoring system that does not take into account cumulative points. This system sometimes results in a player winning a match despite failing to win as many points as his or her opponent. This event is a representation of Simpson’s Paradox, a statistical anomaly that sees two seemingly connected variables result in a reversed outcome when combined. Perhaps the most famous instances of Simpson’s Paradox in tennis came in 2010 when John Isner and Nicolas Mahut played the longest match of all time. Mahut won 24 more points than his opponent over the course of more than 11 hours, but went on to lose the match by a score of 70 games to 68 in the final set.

Interestingly, few players have been a victim of Simpson’s Paradox as often as Roger Federer, widely regarded as one of the best athletes ever to play the sport. When compared to over 70 players who have contested at least 20 Simpson’s Paradox matches over their career, Federer’s 4-24 mark is by far the worst. The statistic indicates that on four occasions the winner of a record 17 major titles defeated his opponent despite winning fewer points, while 24 times Federer found himself on the losing end of that equation. Jim Courier’s 11-15 mark was the only other non-winning record among the sampled players who had won multiple major titles.

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