Simpson’s Paradox can happen at the both the game level and point level in tennis. The former would be where the score is, for example, 0-6, 7-5, 7-5; the match’s loser wins more total games than the winner of the match. Such matches are exceedingly rare in tennis. The latter, those when the winner of the match wins less than 50 percent of the total points played, occur with some regularity and can be analyzed on a per-player basis.

In a recent academic article in the International Journal of Performance Analysis in Sports, Jeff Sackmann, Ben Wright, and I investigated the incidence of point-level Simpson’s Paradox in tennis. 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. (In tennis, “tanking” occurs when players opt to exert less effort than they are capable of. In some cases, a player may tank an entire match.) The more common scenario is strategic tanking in-match for one or more short time spans. The latter is something Isner himself acknowledged when interviewed by Andrew Lawrence for a Sports Illlustrated piece in 2013:

The strength of Isner's game is his serve, which has topped out at 149 mph. “I need to have as much energy as possible in my service games,” says Isner, who relies on motion stretching and light weight training to keep his right arm strong. On defense, though, he picks his spots. Kind of. “If I'm up a break in a set, I can just ride out my serve,” he says. “That doesn't necessarily mean that I'm tanking the return games, but it gives me the opportunity to conserve energy for the service game, knowing that I have that break in hand.”

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.