In today’s third-round match in Rome, Roger Federer posted a truly unusual stat line. He beat Borna Coric in three sets, 2-6 6-4 7-6(7), winning 95 points to Coric’s 107. That’s a total-points-won rate (TPW) 47.0%, not unheard of for a match winner, but near the lower limit of what’s possible. By Dominance Ratio (DR)–the ratio of return points won to serve points lost–Fed comes out at 0.78, where 1.0 represents an evenly-split match. He has won only 24 times in his career with a DR below 1.0, and today was the first time since 2015. These types of decisions are often referred to as “lottery matches,” because there is more luck than usual involved in the result.
Not only did Federer win the match with a TPW below 50% and a DR below 1.0, all three of his individual sets were below those numbers. He won 23 of 55 points in the first set, 31 of 64 in the second, and 41 of 83 in the third. The low total in the first set is to be expected–he lost that set badly. But often, low numbers for an entire match stem from a bad performance in a single set, like the swoon in a 7-6 1-6 7-6 contest. Coric outplayed him–narrowly, at least–in all three sets.
You might suspect that this is extremely rare, and you’d be right. Only 4.5% of ATP tour-level matches end in favor of the player who won fewer points, and 7.2% go the direction of a player with a DR below 1.0. Those numbers usually overlap, but not always. Roughly 4.0% of matches are won by a player with a TPW below 50% and a DR below 1.0. Individual sets are even more likely to be awarded to the player who won more points. Just 2.4% of sets are won by the man who lost more points. The frequency of DR < 1.0 is 7.4%, about the same as at the match level.
It turns out that there is a precedent–exactly one!–for Fed’s feat, of winning a match with TPW < 50% and DR < 1.0 in each of three sets. That’s one previous occurence in my dataset of point-by-point sequences for over 17,000 ATP tour-level matches since 2010. Inevitably, John Isner was involved. At Memphis in 2017, Isner lost his quarter-final match to Donald Young, 7-6 3-6 7-6. Young won only 46.9% of total points, and his DR was 0.66, both marks among the lowest you’ll ever see for a winner. Like Federer, Young came close in the sets he won, tallying 49.3% of all points in both the first and third set. By saving eight of nine break points and withstanding the Isner serve in the tiebreaks, Young managed to overcome a statistically superior opponent.
Federer’s victory today wasn’t particularly reliant on break point performance, though fans will be encouraged that he converted two of his four opportunities. Much has been written about Roger’s ineffectiveness in this sort of match–against his 24 wins with a sub-1.0 DR, he has 49 losses with a DR above 1.0–and break point futility is often to blame. While big servers tend to play a lot of close matches, Federer has managed to record plenty of wins without relying on the lucky ones.
With a guaranteed place in the prominent parts of the record book, Fed is making a move on the obscure pages in the back. Having repeatedly shown us that he can win matches by outplaying the guy on the other side of the net, he finally came up with a victory when the stats pointed in the other direction.