There have been a few write-ups on the Isner/Mahut marathon tennis match already. Most notably this one by Carl Bialik of the Wall Street Journal. None have addressed the core issue – was this a conspiracy just so John Isner could appear on Letterman?
Unfortunately, tennis stats are not sophisticated enough to do a proper investigation. Given the extremely limited data provided by Wimbledon, about the most interesting thing to do with the marathon fifth set is to replay it point-by-point using the return percentages of each player in the fifth set.
In the fifth set, Mahut was able to successfully win 23% of points while returning serve, compared to 19% for Isner. I replayed the fifth set one million times given these low return rates in order to see just how unlikely it was to get to 138 games. The results suggest the length of the fifth set wasn’t completely crazy (but kind of crazy) given the poor return rates for each player. Some random findings…
– 3.94% of the fifth sets were at least 138 games in length. This figure is a bit low and suggests the points that were won by the receiver may not have been randomly distributed in the real match. Were I one to believe that the World Trade Center was destroyed by explosives planted by the U.S. Government, I might take this and run with it. But the figure isn’t low enough to be convincing.
– It could have been a lot worse. The longest fifth set in the million-match series finished at 281-279. This actually happened twice.
– One of the 281-279 sets had 53 break points before the final point was successfully converted. That would have been suspicious.
– However, that wasn’t the worst conversion percentage observed on break points. Two matches had 57 break points before a success.
– Due to the woeful return games of each player, you might think a single break would guarantee victory. But that’s not quite true. In 2.3% of matches, there was more than one break, and in 156 of the matches, serve was broken at least five times.
– The most breaks in the fifth set occurred in match #719672, where seven of 14 chances were converted in a 16-14 Mahut victory. Somehow, serve was broken in four of the first eight games in that one.
– My favorite match is #695460. Mahut broke first, but incredibly not until it was 145-145. Then Isner saved the match with a break of his own. The match continued to 158-158 when Mahut broke again. But fake Isner miraculously broke back. The match concluded with a Mahut victory, 182-180.
– A total of 49 matches finished at 6-0. Mahut won 48 of them.
– Even with a significant advantage in return percentage, Mahut won just 74.5% of the matches.
– In the real match there were seven break points in the fifth. That seemed low to me, but of the 1,793 simulated matches that finished at 70-68, 249 (13.9%) contained seven break points or fewer.
– In two of those matches, there was just a single break point.
– The longest fifth set with only one break point occurred in match #361739. Isner converted to win 100-98.
In conclusion, if both players were truly unable to return serve in the way that their fifth-set stats suggest, then what happened isn’t completely out of line. It will remain a mystery as to why nothing anywhere close to this has occurred in the history of the game. Perhaps this was the right combination of great servers and horrible returners, but it’s hard to believe that hasn’t happened many times before.