Two Servebots and Zero Tiebreaks

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Isner had energy to burn since he never needed to count to seven.

Italian translation at settesei.it

There have been plenty of upsets at this year’s US Open, but they all pale in comparison with the surprise that John Isner and Milos Raonic delivered Sunday night in their fourth round match. Isner won, 3-6 6-3 6-4 3-6 6-2, failing to hold twice and breaking Raonic’s serve four times. Rarely has a tiebreak seemed so assured, and the two big men didn’t even get close.

In five previous meetings, Isner and Raonic have been more likely to deliver two tiebreaks than only one, and most of their matches were best-of-three, not the grand slam best-of-five format. In 13 previous sets, they had played 9 tiebreaks. In the last year, 45% of Isner’s sets have reached 6-6, while nearly a quarter of the Canadian’s have. One or the other of these guys is responsible for the longest match in history, the longest ever major semi-final, and the longest match in Olympics history. They are really, really good at holding serve, and really not-so-good at breaking.

Great expectations

The likelihood that Isner and Raonic would play a tiebreak depends on some basic assumptions. If Raonic served like he has for the last 52 weeks, that’s a service-point won percentage (SPW) of 72.8%, which is equivalent to holding 93% of the time. If we use Isner’s actual SPW from the match of 74.3%, that translates to a hold rate of 94.4%. If we choose Isner’s SPW from his previous meetings with Raonic of a whopping 76.5%, that gives us an implied hold rate of 96%. Those all sound high but, as we’ll see, the difference between them ends up affecting the probability quite a bit.

I’m going to run the numbers using three sets of assumptions:

  1. The head-to-head. In five matches (four of them on hard courts, the fifth at Wimbledon this year), Isner won 76.5% of service points, while Raonic won 71.4%. That’s equivalent to hold rates of 96.0% and 91.7%, respectively.
  2. The last 52 weeks (adjusted). Across all surfaces, going back to last year’s US Open, Isner has won 73.6% of service points, against Raonic’s 72.8%. Those numbers, however, are against average opponents. Both players, and especially Isner, have below-par return games. If we adjust each SPWs for the other player’s rate of return points won (RPW), we get 75.5% for Isner and 78.5% for Raonic. In game-level terms, those are hold rates of 95.3% and 97.1%.
  3. The match itself. On Sunday night, Isner won 74.3% of service points and Raonic won 68.8%. Using these numbers doesn’t give us a true prediction, since we couldn’t have known them ahead of time. But maybe, if we used every scrap of information available to us and put them all together in a really smart way, we could have gotten close to the true number. Those rates translate to hold percentages of 94.4% for Isner and 88.5% for Raonic.

Not enough tiebreaks

Apparently, the betting odds for at least one tiebreak in the match set the probability around 95%. That turns out to be in line with my predictions, though the specific assumptions affect the result quite a bit.

I’ve calculated a few likelihoods using each set of assumptions. The first, “p(No brk),” is the probability that the two men would simply hold serve for 12 games. It’s not the only way to reach a tiebreak, but it accounts for most of the possibilities. Next, “p(TB)” is the result of a Monte Carlo simulation to show the odds that any given set would result in a tiebreak. “eTB” is the expected number of tiebreaks if we knew that Isner and Raonic would play five sets. Finally, “p(1+ TB)” is the chance that the match would have at least one tiebreak in five sets.

Model   JI Hld  MR Hld  p(No brk)   p(TB)   eTB  p(1+ TB)  
H2H      96.0%   91.7%      46.5%   51.3%   2.6     97.3%  
Last52   95.3%   97.1%      62.8%   65.3%   3.3     99.5%  
Match    94.4%   88.5%      34.0%   41.2%   2.1     93.0%

Given how the big men played on Sunday, it isn’t unthinkable that they never got to 6-6. In large part because Isner’s return game brought Raonic’s SPW under 70%, each set had “only” a 41.2% chance of going to a tiebreak, and there was a 7% chance that a five-setter would have none. The other two sets of assumptions, though, point to the sort of tiebreak certainty reflected in the betting market … and just about anyone who has ever seen these two guys play tennis.

Perhaps the strangest aspect of all of this is that, in six previous matches at this year’s Open, Isner and Raonic combined for seven tiebreaks–at least one in five of their six matches–before their anticlimactic encounter. Knowing Isner, this is a blip, not a trend, and he’s sure to give us a breaker or two in his quarter-final against Juan Martin del Potro. His tournament record will likely show one or two tiebreaks in every match … except for the one against his fellow servebot. This must be why we stick with tennis: Every match has the potential to surprise us, even if we never really wanted to watch it.

Marketa Vondrousova’s Next-Level Lottery Match

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Vondrousova sits in awe of her own statistical feat.

Italian translation at settesei.it

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.

Did Rafael Nadal Almost Lose a Set to David Ferrer?

Italian translation at settesei.it

In David Ferrer’s final grand slam, the draw gods handed him a doozy of a first-round assignment in Rafael Nadal. Ferrer has struggled all year, and no one seriously expected him to improve on his 6-24 career record against the King of Clay. In the end, he didn’t: Ferrer was forced to retire midway through the second set with a calf injury. But before his final Flushing exit, he gave Rafa a bit of a scare.

Nadal won the first set, 6-3. The second set was a bit messier: Ferrer broke to love in the opening game, Rafa broke him back in the next, and a bit later, Ferrer broke again to take a 3-2 lead. He maintained that one break advantage until he physically couldn’t continue. Leading 4-3 and serving the next game, he was been two holds away from leveling the match.

Does that mean Nadal “almost” lost the set? People on the internet argue about these things, and while I don’t understand why, I do love a good probability question. If it overlaps with semantics (yay sematics!), that’s a bonus.

Let’s forget the word choice for now and reframe the question: Ignoring the injury, what were Ferrer’s chances of winning the set? If we assume that both players were equal, it’s a simple thing to plug into my win probability model and–ta da!–we find that from 4*-3, Ferrer had a roughly 85% chance of winning the set.

But wait: I can already hear the Rafa fans screaming at me, these two players aren’t exactly equal. In the 102 points the Spanish duo played on Monday night, Ferrer won 38% on return and Nadal won 47%. For an entire five-set match, those rates work out to a 93% chance of Rafa winning. Maybe that’s not quite high enough, but it’s in the ballpark. Using those figures, Ferrer’s chance of hanging on to win the second set drop significantly, to 57.5%. When you’re winning barely half of your service points, your odds of securing a pair of holds are worse than a coin flip. Had Ferrer won the set, it’s more likely that he would’ve needed to either break Rafa again or come through in a tiebreak.

That’s a pretty big difference between our two initial estimates. 85% sounds good enough to qualify for “almost” (though one study quantifies the meaning of “almost” at above 90%), but 57.5% does not.

That doesn’t quite settle it, though. The win probability model takes all notions of streakiness out of the equation.  According to the formula, there’s no patches of good or bad play, no dips in motivation, so extra energy to finish off a set, etc. I’m not convinced any of those exist in any systematic manner, but it’s tough to settle the question either way. Therefore, if we have the ability to use data from real-life matches, we should.

And here, we can. Let’s start with Nadal. Going back to late 2011, I was able to identify 69 sets in which Rafa was returning down a break at 4-3. (There are probably more; my point-by-point dataset isn’t exhaustive, but the missing matches are mostly random, so the 69 should be representative of the last several years.) Of those 69, he came back to win 21, almost exactly 30%.

Ferrer has been more solid than Nadal’s opponents. (It helps that Ferrer only had to face Rafa once, while Nadal’s opponents had face him every time.) I found 122 sets in which Ferrer served at 4-3, leading by a break. He went on to win the set 109 of those times, or about 89%.

The 89% figure is definitely too high for our purposes: Not only was Ferrer a better player, on average, between 2012 and today, than he is now, but he also had the benefit of facing weaker opponents than Nadal in almost all of those 122 sets. 89%–not far from the theoretical 85% we started with–is a grossly optimistic upper limit.

Even if we take the average of Nadal’s and Ferrer’s real-life results–roughly 90% conversions for Ferru and 70% for Rafa’s opponents–80% is still overshooting the mark. As we’ve established, Ferrer’s numbers refer to a stronger version of the Spaniard, while Rafa is still near the level of his last half-decade. Even 80%, then, is overstating the chances that Nadal would’ve lost a set.

That leaves us with a range between 57%, which assumes Nadal would keep winning nearly half of Ferrer’s service points, and 80%, which is based on the experience of both players over the last several years. Ultimately, any final figure comes down to what we think about Ferrer’s level right now–not as good as it was even a couple of years ago, but at the same time, good enough to come within two games of taking a set from the top-ranked player in the world.

It would take a lot more work to come up with a more precise estimate, and even then, we’d still be stuck not only trying to establish Ferrer’s current ability level, but also his ability level in that set. Just as the word “almost” refers to a range of probabilities, I’m happy to call it a day with my own range. Taking all of these calculations together, we might settle on a narrower field of, say, 65-70%, or about two in three. There’s a good chance a healthy Ferrer would have taken that set from his long-time tormentor, but it was far from a sure thing … or even, given the usual meaning of the word, an “almost” sure thing.

Podcast Episode 30: US Open Week One

Episode 30 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, is all about week one of the US Open. We talk about the results so far and focus on the slew of high-profile third-round matches coming up, like Serena-Venus and Federer-Kyrgios. We also discuss how slams should deal with the heat, whether tennis should allow more on-court coaching, and the ways the USTA has improved the fan experience.

Thanks for listening!

(Note: this week’s episode is about 65 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

Simona Halep’s Grand Slam First Round Woes

Italian translation at settesei.it

In the first-ever match at the US Open’s new Louis Armstrong Stadium yesterday, No. 1 seed and reigning French Open champion Simona Halep lasted barely an hour, losing to the big-hitting Kaia Kanepi. Halep has held the top ranking for more than six months running, and only ten women have owned the top spot for more total weeks than she has. But Halep fans aren’t exactly the the target market for second-week tickets at the majors.

As Christopher Clarey pointed out on Twitter, yesterday’s loss was Halep’s 12th first-round exit in 34 tries. That isn’t quite as bad as it sounds: Seven of the losses came in her first 12 entries, before she entered the top 50, and since Wimbledon 2013, she’s a more respectable 17-5, with one of those losses to Maria Sharapova in New York last year. Still, it’s not the type of winning percentage you’d expect to see from someone of her caliber.

Just how bad is it? To give us some context, I compared her record in her first 34 majors to other grand slam winners, as well as everybody else whose career lasted long enough to enter at least 30 slam main draws. The deeper we dig, the worse it looks.

Simona vs slam winners

I found 32 major champions who played at least 30 slam first rounds*. Most of them played more than that, but to make sure we compare like to like, I’m focusing on each player’s first 34 majors. The list is topped by some of the usual suspects: Chris Evert, Monica Seles, and Serena Williams all went undefeated in their first 34 round-of-128 matches.

* I’ve excluded majors with fewer than 128 entrants, and my database might be missing first-round results from a few more events early in the Open era. Technically, I’m looking only at round-of-128 results.

The average grand slam champion went 29-5 in her first 34 major first rounds. Only four, including Halep, lost at least 12 of those matches: Angelique Kerber also went 22-12, while Flavia Pennetta and Samantha Stosur lost 13. Only two others lost more than seven first rounders: Marion Bartoli went 24-10 in her first 34 first-round efforts, and Iva Majoli ended up at 23-11.

Simona vs the pack

I found 199 players in Open era history who have contested at least 30 round-of-128 matches at majors. That’s a fairly elite crew–as we’ve seen, more than 15 percent of them are slam champions. It’s challenge enough to maintain a high enough ranking to enter nearly a decade’s worth of majors.

Thus, our remaining 167-player sample of non-champions is still better than average: Considering each of their first 34 majors, they won 57.4% of their opening round matches. That translates into a record of 20-14, only a couple of wins worse than how Halep has fared so far. 58 of the 167 women, about 35%, won at least 22 of their first 34. 45 of them, or 27%, outdid Simona and won at least 23.

Two explanations spring to mind for the discrepancy between Halep’s status at the top of the game and her mediocre career performance at the majors. First, players are taking longer to develop into stars. Simona’s 5-7 record in her first 12 first rounds isn’t indicative of her current level. Standouts of prior generations, like Serena and Seles, skipped that level of development entirely, springing onto the scene as instant contenders. Even Jelena Ostapenko, the almost-still-teenage winner of the 2017 French Open, was a modest 7-5 in her first dozen major first rounds. Sloane Stephens, who won 11 of her first 12 (including one against Halep), currently sits at a more modest 19-8.

The other reason is more prosaic: the parity at the top of the women’s game. Even as Simona racks up weeks as number one, she just isn’t as good as many previous top-ranked players. Her greatness stems from managing to stay at a reasonably high level more consistently than any of her peers. That means lots of of second-tier titles, impressive (overall) won-loss records, and on the flip side, some unfortunate losses on big stages. On a tour without a dominant presence, that’s good enough to make her, by a healthy margin, the best in the game. But “best” is more fragile than it used to be, even in the first round of the grand slams.

Gerald Melzer’s 28-Point Hold, and Other Interminable Deuce Games

Italian translation at settesei.it

Last week during the second round of US Open qualifying, Gerald Melzer battled through a 28-point service game–that’s eleven deuces–en route to defeating Kenny De Schepper. (Perhaps mentally exhausted, he lost the next day to Felix Auger-Aliassime.) Watching the scoreboard from a nearby court, I assumed it had malfunctioned and the match was long over.

Such marathon games are rare, but they aren’t unheard of. Yesterday, another qualifier, Lloyd Harris, needed ten deuces to hang on to one game against Gilles Simon in their first round match. Neither Melzer’s nor Harris’s tally are close to the record, which is likely still a 28-deuce game in a 1996 contest between Alberto Berasategui and Marcelo Filippini. That’s 62 points–one point more than the legendary 28-minute full match between Bernard Tomic and Jarkko Nieminen. The entire match. An even longer game, spanning 37 deuces and 80 points, took place at the non-tour-sanctioned Surrey Championships in 1975.

The odds on paper

On the ATP tour, the server wins about 63% of points. In the last year, Melzer has won roughly 64%, about the same as De Schepper’s opponents, so we’ll use the slightly higher number. With a server winning 64% of points, the odds of reaching deuce are 24.4%. After that, the chances of getting to another deuce are a bit less than half, or 46.1%. The odds of an at-least-two-deuce game are 24.4% times 46.1%, the odds of an at-least-three-deuce game are 24.4% times 46.1% times 46.1%, and so on. Melzer’s eleven-deuce game is 24.4% times (46.1% ^ 10), a little bit better than one in ten thousand. The match required 30 games, so the chances of a 28-point game (or longer) at some point–assuming the underlying numbers are the same for De Schepper’s service games–are roughly 30 times better, one in three hundred.

The Simon-Harris 26-pointer is even more likely. On the challenger tour, Harris has won nearly 65% of his service points, while Simon wins better than 40% of return points against tougher competition. Combining those numbers to account for competition is beyond the scope of this post, but let’s say Harris was expected to win 61% of his service points. (He ended up winning only half, though that overall rate is heavily influenced by the marathon game.) The odds of any individual Harris service game lasting 26 points, assuming a 61% serve win rate, is about one in three thousand.

One last example: The Berasategui-Filippini record-setter was primed for some long games, as neither player won very many serve points, and the Casablanca clay has never been speedy. But even with favorable circumstances, 28 deuces is nearly impossible. Using a service points won rate of 58% for Filippini (he won 59.6% that year, while Berasategui’s opponents won 57.7%, and I’ve rounded down a tiny bit for the surface), the odds of an individual game lasting at least 62 points are nearly one in one billion.

Delayed toilet breaks

Let’s see how well the odds predict the real-life frequency of marathon games. In my database of about 435,000 tour-level games back to 2012, 42 games reached the 28-point mark, a rate of approximately one per ten thousand–the same as the theoretical number we saw for Melzer-De Schepper. Many of the games terminated after 28 points, and none went longer than 36 points. The most recent 36-pointer was in this year’s Australian Open third round, when Kyle Edmund broke Nikoloz Basilashvili’s serve (and his spirit) to take a 2-0 lead in the fourth set.

28-pointers–and long games in general–are a bit more common on the challenger tour. I found 81 in about 600,000 games–about one per 7,500 games–including three 38-pointers. Edmund figured in one of those prolonged games, barely failing to break Grega Zemlja’s serve at the 2016 Dallas Challenger. Melzer appears in the list as well, having fought through 28 points to hold against Robin Haase in the 2015 Trnava Challenger, though he ended up losing the match.

Theory and practice also match when we look at WTA data. Using a tour-average rate of service points won of 58%, we would expect to see a 28-pointer once every 4,600 games or so. In 367,000 recorded games, I found 89 instances, or one per 4,100. The record here outstrips anything in the last few years of ATP or Challenger data: Mathilde Johansson broke Elena Vesnina on the 40th point, after 17 deuces. She consolidated the break to win the second set, but dropped the decider.

Based on the last several years of data, Berasategui’s and Filippini’s record appears to be safe. Given the efforts to speed up the game, in which tennis executives would prefer no-ad to Berasategui’s brand of 28-ad, that’s probably for the best.

The Victims of Tiebreak Pressure

The conventional wisdom is that tiebreaks are all about two things: serves and mental strength. Despite my previous efforts, pundits continue to promote the idea that big servers have an edge in the first-to-seven shootout. Less contestably, experts remind us that a lot is at stake in a tiebreak, and the player who can withstand the pressure will prevail.

Back in 2012, I wrote a few articles about tiebreaks, using a year’s worth of data from men’s matches at grand slams to discover that servers hold less of an advantage during shootouts. On average, more points go the direction of the returner. I also found that very few players exceeded expectations in tiebreaks–that is, a player’s performance in non-tiebreak situations did a very good job of predicting his chances of winning tiebreaks. Last, I determined that big servers were not any more likely than their weaker-serving peers to be among the small group of players who boasted stronger-than-expected results in shootouts.

I’ve dug into a much larger dataset to revisit the first of these conclusions. My collection of sequential point-by-point data allows us to look at over 15,000 tiebreaks from the ATP tour alone, compared to fewer than 400 that I used in my earlier study. The broader and deeper sample will allow us go beyond general statements about serve or return advantages and look at how particular players fare in the jeu décisif.

Serving under pressure

First, the basics. In these 15,000 tour-level breakers, servers won 3.4% fewer points than they did in non-tiebreak situations. This is an apples-to-apples comparison: For each player in each match, I used his rate of service points won (SPW) on non-tiebreak points and his SPW on tiebreak points. To get the aggregate figure, I calculated the average of all player-matches, weighted by the number of tiebreaks in the match.*

* Initially, I weighted by the number of tiebreak points, thinking that, say, a 16-point tiebreak should be weighted more than an 8-point breaker. That gave me results that pointed to a huge improvement in SPW in tiebreaks … because of selection bias. When a tiebreak goes beyond 12 points, it often means that both players are serving well. Thus, when two servers are hot, they must play more points, increasing their weight in this calculation. It’s always possible that an extra-long tiebreak results from a lot of return points won, but in the serve-leaning men’s game, it is the much less likely scenario.

The 3.4% decrease in serve points won means that, for instance, a server who wins 65% on his own deal in the twelve games before the tiebreak will fall to 62.8% in the breaker. Fortunately for him, his opponent probably suffers the same drop. Benefits only accrue to those players who either maintain or increase their SPW after the twelfth game of the set.

It makes sense that servers suffer a bit under the pressure. In the men’s game, at least, the returner has little to lose. Since tiebreaks are thought to be serve-dominated, every return point won seems like a lucky break. Perhaps if players knew the real numbers, the mental game would shift back in their favor. They wouldn’t have to focus on becoming superhuman, unbreakable servers; they would need only to maintain the level that got them into the tiebreak in the first place.

The less-breakables

When we split things up by player, the dataset conveniently spits out 50 players with at least 100 tiebreaks. (Well, 49, but Nicolas Mahut was next on the list, so we’ll include him also.) The guys who play the most tiebreaks are either good, lucky, or both, because they’ve managed to stick around and play so many tour matches, so the average player on this list is a little better than the average player in general.

Here are the top and bottom ten in our group of the 50 most prolific tiebreak players. The first stat, “SPW Ratio,” is the ratio between tiebreak SPW and non-tiebreak SPW, so a higher number means that the player wins more serve points in tiebreaks than otherwise. Because that stat awkwardly centers on 0.966 (the 3.4% decrease), I’ve shown another stat, called here “Ratio+,” with all numbers normalized so the average is 1.0. Again, a higher number means more serve points won in tiebreaks. The 1.09 held by John Isner at the top of the list means that the big man wins 9% more breakers than expected, where “expected” is defined as the tour-average 3.4% drop.

Player               TBs  SPW Ratio  Ratio+  
Andy Murray          141       1.05    1.09  
John Isner           368       1.05    1.09  
Nick Kyrgios         109       1.05    1.08  
David Ferrer         132       1.01    1.05  
Alexandr Dolgopolov  116       1.01    1.05  
Lukas Rosol          100       1.01    1.05  
Jo-Wilfried Tsonga   188       1.01    1.04  
Roger Federer        175       1.01    1.04  
Nicolas Mahut         94       1.01    1.04  
Benoit Paire         139       1.00    1.04  
…                                            
Denis Istomin        120       0.94    0.98  
Viktor Troicki       104       0.94    0.97  
Tomas Berdych        181       0.93    0.96  
Nicolas Almagro      118       0.93    0.96  
Fernando Verdasco    156       0.93    0.96  
Robin Haase          123       0.93    0.96  
Adrian Mannarino     101       0.91    0.95  
Jiri Vesely          105       0.90    0.93  
Ryan Harrison        100       0.89    0.92  
Pablo Cuevas         100       0.87    0.90

Most of the big names who aren’t shown above (Rafael Nadal, Novak Djokovic, Juan Martin del Potro, Milos Raonic) are a bit better than average, with a Ratio+ stat around 1.02. I’m not surprised to see Isner or Roger Federer near the top, as those two have traditionally won more tiebreaks than expected. Less predictable is the chart-topping Andy Murray, who apparently manages to raise his serve game in breakers as well as anyone else.

Warning: Negative result ahead

Murray, Isner, and Federer have consistently served well in tiebreaks over the last seven years, the time span of this dataset. But even they have had seasons where they just barely edged out the tour average: Murray was 9% better than his peers in 2013 and 10% better in 2016, serving better in tiebreaks than non-tiebreaks by a 5% and 6% margin, resepectively, but in between, he was merely average. Isner, who was at least 10% better than tour average in each season from 2012 to 2015, served slightly worse in tiebreaks than in non-tiebreaks in 2016, and is just barely better than average in his first fifty shootouts of 2018.

These are small margins, and most players do not sustain positive or negative trends from year to year. To take another example, from 2014 to 2017, Raonic recorded single-season Ratio+ numbers of 1.11, 0.92, 1.00, and 0.98. I wouldn’t recommend putting any money on Milos’s full-season 2018 figure, let alone his tiebreak serve success in 2019.

Despite the evocative appearance of Isner, Federer, and Murray at the top of the list and some players considered to be mentally weaker near the bottom, there is no evidence that this is a skill, something that players will predictably repeat, rather than luck. As I did in my match point study earlier this week, I divided each player’s tiebreaks randomly into two groups. If tiebreak serve prowess were a skill, a player’s SPW Ratio in one random group would be reasonably predictive of his corresponding number in the other group. It is not to be: No matter where we set the minimum number of tiebreaks for inclusion, there is no correlation between the two groups.

If you’ve gone through many of my posts, you’ve read something like this before. Handling the pressure and serving well in tiebreaks seems like something that certain players will do well and others will not. This overall finding isn’t sufficient proof to say that no players have tendencies in either direction–most tour pros simply don’t contest enough tiebreaks over their entire careers to know that for sure. But with possible exceptions like Isner, Murray, Federer, and the unfortunate Pablo Cuevas, players converge around the tour average, which means their service game becomes a little less effective in breakers. If someone posts a particularly high or low SPW Ratio for a season, it probably means luck figured heavily in their results. If you’re going to bet on something using these numbers, the smart money suggests that most players will revert to the mean.

What Cincinnati Taught Us About the Serve Clock

Italian translation at settesei.it

So far, the serve clock has not made matches faster. In my article for The Economist earlier this week, I showed that in the handful of tournaments played with the new technology thus far, players took longer to play each point than they did at the same events last year.

That article included data from San Jose, Washington, Toronto, and Montreal. Last week, the combined Masters/Premier event in Cincinnati gave us another several dozen matches, with a slightly different mix of players, to further test how the serve clock is affecting the speed of play. Given another week of experience with the visible timers, the pace of play remains slower than it was one year ago.

In the Cincinnati men’s event, players used 41.2 seconds per point this year, compared to 39.8 seconds per point last year. In the women’s draw, it was 40.8 seconds per point this year, up from 40.2 seconds per point last year. Both increases are roughly the average change that we saw in the tournaments of the two previous weeks. Here is a breakdown of the time per point at each event, where “S/P” means seconds per point. Also shown are tour and overall averages, weighted by the number of matches at each event:

M/W      Tournament  2017 S/P  2018 S/P  Change  
Men      Cincinnati      39.8      41.2    +1.4  
Men      Canada          40.2      41.4    +1.2  
Men      Washington      40.3      42.2    +1.9 
 
Women    Cincinnati      40.2      40.8    +0.6  
Women    Canada          40.7      41.8    +1.1  
Women    Washington      40.2      41.6    +1.4  
Women    San Jose        40.3      40.7    +0.4  
                                                 
Men      Average         40.1      41.6    +1.5  
Women    Average         40.4      41.2    +0.8  
Overall  Average         40.2      41.4    +1.2

* alert readers might notice small discrepancies between these figures and those cited in the Economist, which are due to rounding errors.

Several readers have commented on the imprecision of this measurement. (I did too, in the original post.) Short of taking a stopwatch to every single match, there’s no way of auditing umpires by collecting the exact length of time between each pair of points. The exact mix of players in any given draw can affect the overall measurements–I experimented with a simple model to control for players, but it presented more problems than it solved. I agree, this is far from the final word on the serve clock, even apart from the fact that the way that umpires use it will probably evolve.

Still, these numbers point in only one direction. A similar survey of unaffected tournaments confirms that 2018 is not slower in general: For instance, of the men’s and women’s draws in Indian Wells, Miami, and Madrid this year, four of the six brackets decreased in average time per point, and one of the others increased by only 0.1 seconds per point.

Also, it’s important to remember that one presumed goal of the clock is to speed up play, not simply keep it steady. If time per point were staying roughly the same as last year, that itself would indicate that the new technology isn’t living up to its billing. That seven out of seven events have all gotten slower allows us to make an even stronger claim.

Fortunately for the tours, there is plenty of room for the use of the clock to evolve. The most glaring example is the umpiring practice of waiting until crowd noise dies down to start the clock. Yes, players can’t be expected to serve in a noisy stadium, but the cheering usually stops after ten seconds or so. Rather than add that ten seconds to the time allotment between points, umpires should start the clock immediately and then, on the rare occasions when the crowd remains disruptive, pause as necessary.

Its unlikely that matches will still be slower when the serve-clock dust has settled. But the goalposts have moved: At this stage of the process, it would be progress if matches with visible timers were simply the same speed as the ones that came before.

Simona Halep’s Match Points

Italian translation at settesei.it

In the second-set tiebreak of Sunday’s Cincinnati final, Simona Halep reached match point against Kiki Bertens. She failed to convert, then Bertens claimed the tiebreak, and the third set–and the championship–went the way of the Dutchwoman. It was a bit of painful deja vu for Halep fans, who watched the top-ranked player reach match point against Su Wei Hsieh at Wimbledon only to miss her chance and crash out in the third round.

Halep has a reputation as a bit of a weak closer–not just match points, but set points and, more generally, service games with the set or match on the line. Her overall ability to finish matches is beyond the scope of a single post, but we can start by biting off the smaller chunk of, specifically, her performance on match points, and how that compares to the rest of the WTA.

Let’s start with the basics. For everyone, reaching match point is (obviously!) a really good sign that she’ll go on to win the match. Across about 16,000 WTA matches since 2011 for which I have sequential point-by-point data, players who hold match point end up winning the match a bit more than 97% of the time. That doesn’t mean that they convert on the first try, or even in the game or set of their first opportunity, but even when conversion is elusive, players manage to generate more chances until they finish the job.

If Simona really is a weak closer, we’ll need to look elsewhere for evidence. In the matches for which I possess the point-by-point sequence*, there are 251 contests in which Halep held a match point, stretching between the end of 2011 and this month’s Rogers Cup in Montreal. Of those, she eventually converted a match point 250 times. That is, with the exception of the Wimbledon match against Hsieh, she didn’t lose any matches in which she was a point away from victory.

* I don’t have the point-by-point sequence for every Halep match, but I have most of them, and the missing ones are random. The same applies to just about every WTA player. Some of the raw data is available here; I’m hoping to update with 2017 and 2018 data in the near future.

Compared to the best players, this level of MP conversion doesn’t even stand out. Among the 50 women with at least 100 matches in which they held match point, five–Serena Williams, Victoria Azarenka, Andrea Petkovic, Ekaterina Makarova, and Elena Vesnina—always converted, if not always on the first try. (Again, I’m missing some matches, but that doesn’t take away from the fact that in a random sample of 259 matches, Serena remains perfect.) Until Sunday’s Cincinnati final, Halep was one of eight more–with Petra Kvitova, Maria Sharapova, and Ana Ivanovic, among others–who failed to convert only once.

Situational performance

It’s no accident that the most dominating names in tennis are near the top of that list. Yes, the best players are most likely to win at match point, but just as important, the best players are more likely to earn several opportunities. Deep in a tiebreak, one missed chance can represent the final hope, but most of the time when Halep, Serena, or someone else of their ilk fails to convert an opportunity, they’re still leading by, say, a set and a break, making it easy to generate more chances.

That leads us to another question: How do players perform on match point itself? Does the pressure lead to fewer points won, compared to non-MP serve and return points? Or do other factors, like momentum or crowd support, cause players to do even better when one point away from victory?

It turns out that there’s no single answer; the results are a bit different depending on whether the player holding match point is serving or returning. When a player is serving to finish off a match, she is slightly less likely to win the point, compared to her serve performance up to that point. It’s not a big difference–a bit less than a 3% drop in the rate of serve points won–but it is persistent across several years of WTA results. When players are one point away from victory but are returning, there is no match-point effect. They win return points at the same rate regardless of whether a handshake is imminent.

Match points are almost evenly distributed between serve and return points–on the WTA tour, about 55% are serve points, leaving 45% return points. Thus, given the 3% drop on serve performance and the lack of change on return points, players win approximately 1.5% fewer points when one step away from victory than otherwise. One player who almost exactly parallels the average is Caroline Wozniacki–in 271 match-point matches and 474 match points, she won those MPs at a rate 1.7% lower than non-MPs.

Some of the players who almost always win their match-point matches aren’t any better than average when we look at individual points. For instance, Sharapova wins MPs a rate 1.2% lower than non-MPs, and Azarenka’s success rate drops by 1.4%. Dominika Cibulkova won 198 of the 201 match-point matches in my dataset despite her success rate falling by a whopping seven percent.

Halep, however, doesn’t fit in that category. In her 251 match-point matches, she has held 420 individual match points, which she has won at a rate 4.4% higher than her non-MP rates in the same set of matches. Few players are better, though a handful are overwhelmingly so, such as Kvitova at +9.0%, and Vesnina at +13.9%. The vast majority of women are within a few percentage points of neutral: They win match points, whether serve or return, about as often as they win non-match-points.

Random results

These numbers tell us only one thing: what has happened in the past. It is tempting to use them to make predictions, or perhaps lay down a sizable wager the next time Vesnina is a point away from victory. But when most players are so close to neutral, it’s a warning that much of what we’re looking at may be random.

If players have consistent tendencies in match point situations, we would be able to identify that in the data. For instance, we might see that Kvitova converts match points at a high rate in each individual season. Since the single-season totals make for sometimes small samples, I took a slightly different approach. For players with at least 60 match-point matches, I randomly divided their matches into two separate groups, and determined how their performance at MP compared to their success rate on other points. Again, if this were a real skill, we would expect that players would be roughly the same in each of their two random groups–better than usual on MP in both groups, or worse.

Alas, for this population of 80 players with sufficient match-point samples, there is no correlation at all. If women have consistent, predictable tendencies to outperform or underperform in match-point opportunities, these inclinations are either extremely small, or they don’t persist over several years.

This is a familiar refrain when looking at specific situations in tennis matches. Our hyperactive, pattern-seeking brains find it easy to identify apparent tendencies, but in general, players win points at about the same rate regardless of the context. Over the medium term, like the half-decade represented by my point-by-point dataset, some players will stick out, like Kvitova, Vesnina, and to a lesser extent, Halep. But past results are hardly a guarantee of future match-point performance. The smart prediction for any player’s upcoming results on match point is that she’ll do exactly as well as she does the rest of the time. It’s a rather boring conclusion. Thankfully, the match points situations themselves are usually exciting enough on their own.

Economist: The new serve clock in tennis appears to be backfiring

At the Economist Game Theory blog, I wrote about the early effects of the new serve clock. The outwardly stricter time policy didn’t speed up Rafael Nadal, nor did it cut down match times in general over its first two weeks:

The Toronto champion wasn’t the only player who slowed down once on the clock. At each of the completed tournaments where the serve clock has been used—Toronto, Montreal, San Jose, and Washington, D.C.—the average point took longer in 2018 than it did in 2017, without the clock. The differences varied from 0.3 seconds per point at the women’s event San Jose (an event that was held in nearby Stanford last year) to 2.0 seconds at the men’s competition in Washington.

Read the whole thing.