Marketa Vondrousova’s Next-Level Lottery Match

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Vondrousova sits in awe of her own statistical feat.

Italian translation at

By most measures, Marketa Vondrousova wasn’t supposed to win her third-round encounter with Kiki Bertens at the US Open on Saturday. She won a mere 47.1% of points, 12 fewer than Bertens, and she lost her own service game two more times than she broke her opponent’s. That’s not all:

The trick is in the scoreline: 7-6(4) 2-6 7-6(1). Her two sets weren’t as dominant as Bertens’s one, but the Czech was a bit better in the high-leverage moments, especially in the third-set tiebreak. And that’s all: Measured by almost all the peripheral stats available, Bertens played better on Saturday.

Vondrousova’s victory was what has come to be termed a “lottery match.” I use the phrase to refer to all matches in which neither player wins more than 53% of total points, the threshold at which it is almost guaranteed that the winner will be the competitor who wins more points. Between 50% and 53%, clutch and luck play a bigger part. While Vondrousova’s 47.1% is rarely good enough to come out on top–only two WTA matches so far this year have gone the way of a player who won less–it’s possible. According to my win probability model, when a player wins 63% of service points and 44% on return, she’ll end up triumphant 82% of the time.

A unique feat

Lottery matches are fairly common, and matches won by the player who claimed fewer points aren’t that unusual either. Since 2013, there have been about 100 of them each year on the WTA tour, accounting for nearly one in every twenty contests. The rarity of what Vondrousova managed in New York is summed up by Ravi Ubha’s tweet. Usually, the winner in such matches has something going for her, like good fortune on break point chances, or even a beneficial dearth of double faults.

I narrowed Ubha’s list down to five items: total points won (TPW), return points won (RPW), breaks of serve, aces, and double faults. The first two track each other quite closely, but sometimes if one player must serve a lot more than the other, she can win return points at a higher rate than her opponent despite a lower overall TPW. The last three are more independent. Ace and double fault totals aren’t particularly crucial to match outcomes–there are innumerable cases in which players lead in one or both categories yet go home empty-handed–but as they add to the uniqueness of Vondrousova’s feat, I’ve included them here. I would have liked to consider winners and unforced errors as well, but those stats are only published by the grand slams.

Of the 532 loser-won-more-points matches I identified between 2013 and 2018 (not including the US Open), 192 met the first three criteria: The winner had a lower TPW, a lower RPW, and fewer breaks of serve than her opponent. Of those 192, the set that met all five numbers only 39–about 0.3% of the WTA matches in that span with available match stats. Six of those matches happened this year, though two were at WTA $125K events, which some people probably wouldn’t include. (One of them was the Anning $125K final between Irina Khromacheva and the truly unfortunate Saisai Zheng.)

Before Saturday’s match, Coco Vandeweghe was the most-frequent victim of these next-level lottery matches–surprising, because she so often out-aces her opponents–having been victimized three times. Five other players have ended up on the wrong side twice: Johanna Konta, Kristyna Pliskova, Varvara Lepchenko, Alison Van Uytvanck, and … Kiki Bertens. Bertens will move into a tie with Vandeweghe when this year’s US Open matches are entered into the record books.

Bertens has enjoyed a season to remember thus far, winning titles in Charleston and Cincinnati, reaching the championship match in Madrid, and defeating ten of her last eleven top-ten opponents. Her loss to Vondrousova won’t go down as one of the season highlights but, as in so many of her other matches this year, Bertens can be confident she was the better player that day.