Simpson’s Paradox is a statistical quirk where seemingly correlated variables are reversed when combined. The application to tennis is nuanced: In tennis, a derivative of Simpson’s Paradox is seen in the small percentage of matches where players win more individual points than their opponent, but lose the overall match. This anomaly is an artifact of tennis’s decidedly unique scoring system. Its “best of N” format (best of three sets, usually, or best of five sets in some men’s professional matches) follows a point-game-set-match hierarchy with neither a running score nor a clock. The results can sometimes be peculiar. The only point the winning player must win is the last one.
In a data set composed of more than 61,000 men’s ATP and Grand Slam matches dating back to 1990, we found that about 4.5 percent exhibited these paradoxical characteristics. We then looked at the outlier players with the best and worst respective records to put our results in context.
At one end of the spectrum was American player John Isner. At 6’10,” Isner unleashes one of the most intimidating serves in tennis history. He is also often remembered as the winner of the longest match in the history of tennis–an 11-hour epic at Wimbledon in 2010 that ended with a 70-68 fifth set win over Frenchman Nicolas Mahut. A quick inspection of the box score, however, shows that Mahut won 24 more points than Isner. A review of Isner’s career record in two dozen similar matches—that is, matches in which the winner won fewer points than the loser—revealed an impressive 19-5 record.
Isner’s success in these odd matches was unsurprising. His playing style consists of a dominating serve and one of the weakest service returns among top 100-ranked players. The result is lopsided point-level score lines, frequent tiebreakers, and a certain degree of energy-conserving tanking when returning serve.
At the other end of the Simpson’s Paradox spectrum was, of course, Roger Federer. In completed matches, he was 4-24 in contests where the winner prevailed on less than 50 percent of the total points. Federer’s winning percentage in these matches (14.29 percent) was the worst among all 72 players in the sample who participated in at least 20 matches of this type during their careers. This result surprised us, as it differed wildly from other players who had similarly won multiple Grand Slam singles titles. Andre Agassi, Rafael Nadal, Pete Sampras, Sergi Bruguera, Marat Safin, Lleyton Hewitt, Yevgeny Kafelnikov, and Gustavo Kuerten were all .500 or better in Simpson’s Paradox matches. Jim Courier was the only player worse than 50-50 in such matches, with a non-alarming 11-15 record.
