Category: Serve statistics

Break Point Serve Tendencies on the ATP Tour

Italian translation at settesei.it

Every player has their “go-to” serve, their favorite option for high-pressure moments. At the same time, their opponents notice patterns, so no server can be too predictable. Let’s dive into the numbers to see who’s serving where, how it’s working out for them, and what it tells us about service strategies on the ATP tour.

Specifically, let’s look at ad-court first serves, and where servers choose to go on break points. For today’s purposes, we’ll focus on a group of 43 men, the players with at least 20 charted matches from 2010-present in the Match Charting Project dataset. For each of the players, we have at least 85 ad-court break points and another 800-plus ad-court non-break points. (I’ve excluded points in tiebreaks, because many of those are high-pressure as well, but it’s less clear cut than in other games.) For most players we’ve logged a lot more, including nearly 1,000 ad-court break points each for Novak Djokovic and Rafael Nadal.

First question: What’s everybody’s favorite break point serve? On average, these 43 men hit about 20% more “wide” first serves than “T” first serves on break points. (Body serves are a factor as well, but they make up only about 10% of total first serves, and comparing two options is way more straightforward than three.) That 20% difference isn’t quite as big as it sounds, since on non-break points in the ad court, players go wide about 10% more often. So while the wide serve is the typical favorite, it’s only a bit more common than on other ad-court points.

Tour-wide averages don’t tell us the whole story, so let’s look at individual players. Here are the ten men who favor each direction the most when choosing an ad-court first serve on break point:

Player                       BP Wide/T  
Philipp Kohlschreiber             2.58  
Pablo Cuevas                      2.46  
Denis Shapovalov                  1.94  
Rafael Nadal                      1.87  
Jack Sock                         1.84  
David Goffin                      1.78  
Nick Kyrgios                      1.69  
Alexandr Dolgopolov               1.66  
Dominic Thiem                     1.64  
Pablo Carreno Busta               1.58  
…                                       
Gilles Simon                      0.94  
Alex De Minaur                    0.94  
Gael Monfils                      0.90  
Feliciano Lopez                   0.83  
Tomas Berdych                     0.83  
Karen Khachanov                   0.82  
David Ferrer                      0.81  
Fabio Fognini                     0.77  
Diego Schwartzman                 0.69  
Borna Coric                       0.67

You’re probably as unsurprised as I was to find Rafael Nadal near the top of the list. The combination of Rafa and Denis Shapovalov suggests that lefties all follow the same pattern, but Feliciano Lopez swats away that hypothesis, as one of the players who most favors the T serve on break points. The other two lefties in our 43-player set, Adrian Mannarino and Fernando Verdasco, both hit more wide serves than average, so perhaps Feli is the odd man out here. We don’t have a lot of data on other contemporary lefties, so it’s tough to be sure.

Second question: How do break point tendencies compare to ad-court tendencies in general? We’ve already seen that players opt for wide first serves about 10% more than T deliveries in non-break point ad-court situations. That difference doubles on break points. These modest shifts lend themselves to an easy explanation: Most players serve a little better wide to the ad court, and under pressure, they’re a bit more likely to go with their most reliable option.

For some guys, though, there’s no “little” about it. We’ve already seen that Philipp Kohlschreiber goes wide every chance he gets on break points, more often than anyone else in our group. Yet on non-break points in the ad court, he splits his deliveries almost fifty-fifty. That’s a huge difference between break point and non-break point tendencies. He’s not alone. Borna Coric is similar (albeit less extreme) in the opposite direction, splitting his ad-court first serves about fifty-fifty in lower-pressure situations, then heavily favoring T serves when facing break point.

The next table shows the players who shift tactics most dramatically on break points. The first two columns show the ratio of wide serves to T serves on break points and on other ad-court points. The rightmost column shows the ratio between those two. At the top of the list are the men like Kohlschreiber, who go wide under pressure. At the bottom are the men like Coric. I’ve included the top ten in both directions, as well as the three members of the big four who aren’t in either category. Djokovic, for example, doesn’t let the situation alter his tactics, at least in this regard.

Player                 BP W/T  Other W/T  Wide BP/Other  
Philipp Kohlschreiber    2.58       1.04           2.49  
Nick Kyrgios             1.69       0.74           2.28  
Juan Martin del Potro    1.52       0.81           1.87  
Jack Sock                1.84       1.05           1.75  
Pablo Cuevas             2.46       1.50           1.64  
Kevin Anderson           1.18       0.74           1.59  
David Goffin             1.78       1.13           1.58  
John Isner               1.43       0.91           1.58  
Grigor Dimitrov          1.41       0.94           1.49  
Dominic Thiem            1.64       1.11           1.48  
…                                                        
Andy Murray              1.19       0.86           1.39  
Rafael Nadal             1.87       1.51           1.24  
Novak Djokovic           1.20       1.16           1.03  
…                                                        
Stan Wawrinka            0.99       1.15           0.87  
Roberto Bautista Agut    1.38       1.60           0.86  
Fabio Fognini            0.77       0.91           0.85  
Roger Federer            1.08       1.35           0.80  
Benoit Paire             1.36       1.73           0.78  
Adrian Mannarino         1.45       1.86           0.78  
Diego Schwartzman        0.69       0.89           0.78  
Feliciano Lopez          0.83       1.09           0.76  
Borna Coric              0.67       0.97           0.69  
Karen Khachanov          0.82       1.25           0.66

Some of the tour’s best servers feature near the top of the list. While many of them favor the ad-court T serve in general, they go wide more often under pressure. This tactic offers an explanation of why some players outperform (at least sometimes) on break points and in tiebreaks. Nick Kyrgios, for instance, is deadly serving in all directions, but in the ad court, he’s even better out wide. Overall, he wins 78.8% of his wide first serves in the ad court, against 75.8% of his T first serves. By “saving” the wide serves for big moments, he is able to defend more break points than his overall ad-court record would suggest. The same theory applies to tiebreaks, where a player could deploy their favored serve more often.

Third question: Could these tactics be improved? I usually start with the assumption that players know what they’re doing. If Kyrgios goes down the middle most of the time and then out wide more often on break points, it probably isn’t a random choice. There’s an easy rule of thumb to check whether servers are making optimal choices, which my co-podcaster Carl Bialik described a few years ago:

If your T serve is better than your wide serve, hit the T serve more. But don’t hit it 100 percent of the time because if you do, your opponent knows you’ll hit it and can stand in the middle of the court waiting for it instead of guarding against the wide serve. So how often should you hit it? Exactly as often as it takes to make it just as successful, but no more, than when you hit a wide serve. If your success rates on different choices are different, you’re not serving optimally.

For instance, facing break point in the ad court, Kyrgios wins 79.7% of his wide first serves and 76.1% of his T first serves. By Carl’s game-theory-derived logic, Kyrgios should be going wide even more often. His win rate on wide serves will go down a bit, as returners find him more predictable, but the average result of all of his break point serves will go up, as he trades a few T serves for more successful wide deliveries.

On average, our 43 players have a 4% gap between their break point win percentages on wide and T serves. Some of that is probably just noise. We’ve logged only 94 break points served by Alexandr Dolgopolov, so his 15% gap isn’t that reliable. Still, some gaps appear even for those players with considerably more data.

The following table shows the ten players with the most break points faced in the dataset. The third column–“BP Wide/T”–shows how much they favor the wide serve on break points. The next two columns show their winning percentages on break point first serves in the two primary directions. Finally, the last column shows the difference between those winning percentages, also in percentage terms. The closer the gap to 0%, the closer to an optimal strategy.

Player             BPs  BP Wide/T  Wide W%   T W%    Gap  
Novak Djokovic     973       1.20    73.1%  72.9%   0.3%  
Rafael Nadal       971       1.87    67.3%  76.7%  12.2%  
Roger Federer      865       1.08    77.1%  77.1%   0.0%  
Andy Murray        730       1.19    71.1%  72.2%   1.6%  
Alexander Zverev   493       1.04    72.4%  76.6%   5.5%  
Stan Wawrinka      379       0.99    72.7%  71.9%   1.2%  
Kei Nishikori      366       1.18    59.5%  69.6%  14.5%  
David Ferrer       347       0.81    59.7%  63.7%   6.2%  
Diego Schwartzman  338       0.69    72.2%  67.8%   6.5%  
Dominic Thiem      294       1.64    71.8%  73.9%   2.8%

Djokovic, Roger Federer, Andy Murray, and Stan Wawrinka are close to the tactical optimum. Nadal is … not. He loves the wide serve on break points, yet he is considerably more successful when he lands his first serve down the T.

But again, we need to work from the assumption that the players know what they’re doing–especially when that player is as accomplished and otherwise strategically sound as Rafa. My focus throughout this post has been on first serves. In general, players make first serves at about the same rate regardless of which direction they choose. In the ad court, down-the-middle attempts are a bit more likely to land in than wide deliveries. But for Rafa, it’s a different story. His wide serve isn’t particularly deadly, but it is the picture of reliability. His ad-court first serve wide hits the mark 77.8% of the time, compared to a mere 59.5% down the middle. The T serve is effective when it lands in, but that in itself is not sufficient reason to make more attempts.

The same reasoning can’t save Kei Nishikori. He has an even bigger gap than Rafa’s, winning about 70% of his break point first serves down the T but only 60% when he goes wide. This is almost definitely not luck: Assuming 180 serves in each direction and the average success rate of about 65%, the chances of either number being at least five percentage points above or below the mean is about 18%. The probability that both are so extreme is roughly 3.5%, so the odds that they are extreme in opposite directions is less than 2%, or one in fifty.

Like Nadal, he is one of the few players who makes a lot more first serves in one direction than the other. But unlike Nadal, his first-serve-in discrepancy makes the gap even more pronounced! In the 366 break points we’ve logged, he landed 48.8% of his break point wide first serve attempts and 62.8% of his tries down the T. He lands more first serves down the middle and those serves are more likely to result in points won. Nishikori needs to hit a lot more of his break point serves down the T. His T-specific winning percentage will probably decrease as opponents discover the more pronounced tendency, but his overall results would likely improve.

At the most basic level, players should be aware of their opponents’ serving tendencies, whether by rumor, advance scouting, or data like the Match Charting Project. Beyond that, we’ve seen that there’s even more potential in the data, showing that some men are leaving break points on the table. Most elite tennis players have a good intuitive grasp of game theory, but even elite-level intuition gets it wrong sometimes.

The Impact of Rafael Nadal’s New Serve

Italian translation at settesei.it

A couple of years ago, the story of the Australian Open was a certain veteran Swiss player’s new backhand. Roger Federer won the tournament, raced back up the rankings, and eventually reclaimed the No. 1 spot. This season has kicked off with another superstar, Rafael Nadal, attempting to shore up his own relative weakness by streamlining his serve.

The early results are extremely positive. Through the semi-final, Nadal’s first serves in Melbourne have averaged 115 mph, compared to 110 mph at the US Open last fall. He hasn’t been broken in five straight matches, dating back to the second round, and has faced only 13 break points in his last 15 sets. True, he hasn’t faced a truly tough test, as the draw has handed him only two seeds, neither in the top ten. But his lopsided results thus far could equally be ascribed to his own dominance. After all, he demolished Stefanos Tsitsipas only a few days after the Greek prospect ousted Federer.

Serve speed numbers are encouraging and lopsided wins are great for the body, but our focus should always be on points, and how many of them he’s winning. By that measure, Rafa’s retooled serve has excelled, helping the Spaniard post some of the best-ever serving numbers of his grand slam career.

In six matches, Nadal has won 80.9% of his first-serve points. (Fellow finalist Novak Djokovic has won 77.5% of his. Both numbers are outstanding, as the hard-court tour average is below 75%, a figure that includes the contributions of much more dominant servers.) At hard and grass court grand slams, Rafa has done better only twice: 83.6% at the 2010 US Open and 81.3% and Wimbledon in 2008. Here are his top-ten first-serve performances through the semi-finals at hard court majors:

Tournament            1st W%  2nd W%            
2010 US Open           83.6%   66.9%            
2008 Wimbledon         81.3%   64.3%            
2019 Australian Open   80.9%   58.0%            
2013 US Open           79.5%   64.7%            
2017 Wimbledon         79.4%   58.6%            
2011 Wimbledon         79.4%   59.4%            
2010 Wimbledon         79.3%   61.6%            
2006 Wimbledon         77.9%   62.1%            
2012 Wimbledon         77.3%   61.5%            
2012 Australian Open   76.8%   56.7%

You might notice a pattern at the top of this list: Those are slams that he went on to win. The 2010 US Open was his first hard court major title, sealed with a four-set win over Djokovic, his most dominant non-clay victory over his long-time rival. 2008 Wimbledon was his first title there, in the memorable final against Federer. The 2013 US Open was another relatively tidy triumph over Djokovic. All the Wimbledons that clutter the bottom half of this list are inflated a bit by the surface, and it is revealing that Rafa’s next-best performance at the Australian Open sits so far down the list, with his 76.5% first-serve mark in 2012. That fortnight didn’t end in his favor, but it took nearly six hours for Djokovic to beat him.

This is all encouraging and, at the very least, it will make for an interesting aspect of tomorrow’s final, between the newly dangerous serving of Nadal and the ever-brilliant return game of Djokovic. But with only six matches on record, it’s tough to push the analysis much further. Rafa was dominant against Tsitsipas, but barely better than he was against the Greek when they met in Canada last summer. In Australia, he won 80.3% of service points, including 85% of his firsts; in their previous meeting, he won 78.9% of service points and 93.8% of his firsts. A more positive comparison is between his fourth-round win over Tomas Berdych (75.3% service points won, 80.4% firsts) and his previous hard court meetings with the Czech (66.6%, 72.7%). On the other hand, they hadn’t played since 2015 and Berdych is returning from injury, so we can’t put too much weight on the comparison.

Nadal’s more pessimistic fans will be keeping an eye on his second serve in Sunday’s final, as that delivery has not demonstrated the same jump in effectiveness. In the six Melbourne matches, Rafa has won 58.0% of second-serve points, just barely above his career average of 57.3% at hard court majors. That relative weakness was exploited by Alex De Minaur, the best returner of his Aussie Open opponents, who held Nadal to a measly 36.4% of second serve points won. Djokovic is even better, neutralizing bigger second-serve weapons than Rafa’s, so it remains a concern.

If Nadal wins the title, his new serve will rightfully take much of the credit. Not only has it improved his effectiveness on that side of the ball, it has helped keep his matches short and his body ready for the challenges of hard court tennis. Years ago, I bucked the conventional wisdom and argued that Rafa could reach 17 slams. Since then, Federer has shifted the goalposts, but a bigger-serving Nadal makes 20 or 21 look more realistic than ever before.

The Oddity of Naomi Osaka’s Soft Second Serves

Italian translation at settesei.it

Naomi Osaka has quickly risen to the top of the women’s game on the back of some big hitting, especially a first serve that is one of the fastest in the game. Through Thursday’s semi-final, Osaka’s average first-serve speed in Melbourne was 105 mph, faster than all but two of the other women who reached the third round. Even those two–Aryna Sabalenka and Camila Giorgi–barely edged her out, each with average speeds of 106.

Shift the view to second serves, and Osaka’s place on the list is reversed. While Sabalenka’s typical second offering last week was 90 mph and Giorgi’s was 94, Osaka’s has been a mere 78 mph, the fourth-slowest of the final 32. That mark puts her just ahead of the likes of Angelique Kerber and Sloane Stephens, both whose average first serves are nearly 10 mph slower.

Osaka’s 27 mph gap is the biggest of anyone in this group. The next closest is Caroline Wozniacki’s 23 mph gap, between her 102 mph first serve and 79 mph second serve–both of which are less extreme than the Japanese player’s. Expressed as a ratio, Osaka’s average second serve is only 74% the speed of her typical first. That’s also the widest gap of any third-rounder in Melbourne; Wozniacki is again second-most extreme at 77%.

The following table shows first and second serve speeds, along with the gap and ratio between those two numbers, for a slightly smaller group: women for whom the Australian Open published at least four matches worth of serve-speed data:

Player          Avg 1st  Avg 2nd   Gap  Ratio  
Osaka             105.5     78.5  27.0   0.74  
Keys              105.2     85.4  19.7   0.81  
SWilliams         103.8     88.6  15.2   0.85  
Barty             102.0     88.2  13.7   0.87  
KaPliskova        101.9     80.5  21.4   0.79  
Collins           101.2     82.2  19.1   0.81  
Kvitova            99.6     91.6   8.0   0.92  
Muguruza           98.1     82.5  15.6   0.84  
Pavlyuchenkova     97.9     84.5  13.4   0.86  
Sharapova          97.9     89.6   8.2   0.92  
Svitolina          97.6     78.2  19.4   0.80  
Stephens           96.1     75.1  21.0   0.78  
Halep              95.3     80.9  14.4   0.85  
Kerber             94.0     78.4  15.7   0.83

Oddly enough, having such a slow second serve doesn’t seem to be causing any problems. In today’s semi-final against Karolina Pliskova, Osaka won 81% of first serve points and only 41% of second serve points, but her typical performance behind her second serve is better than that. And in this match, both women feasted on the other’s weaker serves: Pliskova won only 32% of her own second serves. (Though to be fair, Pliskova had the second-largest gap of the players listed above. She tends to rely more on spin than speed when her first serve misses.)

Across her six matches, Osaka has won 73.3% of her first serve points and 49.7% of her second serve points–a bit better than the average quarter-finalist in the former category, a very small amount worse than her peers in the latter. The ratio of those two numbers–68%–is almost identical to those of Danielle Collins, Petra Kvitova, Anastasia Pavlyuchenkova, and Serena Williams, all of whom have smaller gaps between their first and second serve speeds. Of the eight quarter-finalists, Kvitova has the smallest speed gap of all, yet the end result is the same as Osaka’s, she’s just a few percentage points better on both offerings.

Here are the first- and second-serve points won in Melbourne for the eight quarter-finalists, along with the ratio of those two figures and each player’s serve-speed ratio from the previous table:

QFist           1SPW%  2SPW%  W% Ratio  Speed Ratio  
Kvitova         77.9%  52.8%      0.68         0.92  
Williams        74.7%  50.0%      0.67         0.85  
Osaka           73.3%  49.7%      0.68         0.74  
Collins         72.5%  50.0%      0.69         0.81  
Barty           70.8%  55.7%      0.79         0.87  
Pliskova        70.5%  50.0%      0.71         0.79  
Pavlyuchenkova  67.0%  44.9%      0.67         0.86  
Svitolina       66.5%  48.1%      0.72         0.80

Clearly, there’s more than one way to crack the final eight. With Kvitova, we have a server who racks up cheap points with angles instead of speed, rendering the miles-per-hour comparison a bit irrelevant. Serena’s results are close to Osaka’s, though she gets there with bit more bite on her second serves. And then there’s Svitolina, who doesn’t serve very hard or that effectively but can beat you in other ways.

Knowing all this, should Osaka hit harder second serves? In extreme cases, like today’s 81%/41% performance against Pliskova, the answer is yes–had she simply hit nothing but first serves and succeeded at the same rate, she would’ve piled up a lot of double faults but won more total points. But the margins are usually slimmer, and as we’ve seen, her second-serve performance isn’t bad, it just might offer room for improvement. Every player is different, but faster is usually better.

A thorough analysis of that question may be possible with the available data, but it will have to wait for another day. In the meantime, Saturday’s final will offer us a glimpse of contrasting styles: Osaka’s powerful first offering and soft second ball, against Kvitova’s angles and placement on both serves. Both my forecast and the betting market see the title match as a close one–perhaps Osaka’s second serve will be the shot that makes the difference.

A Closer Look at Tiebreak Tactics

Italian translation at settesei.it

In theory, tiebreaks are a showcase for big serving, the skill that generates enough holds of serve to push a set to 6-6. But no matter how two players get there, the tiebreak itself doesn’t always work out that way.

Two examples suffice from Wednesday’s Australian Open action. Roger Federer’s second-round match against Daniel Evans opened with twelve straight service holds, threatened by only one break point. Yet in the tiebreak, which Federer won 7-5, the returner claimed 9 of 12 points. Across the grounds in front of a much smaller crowd, Thomas Fabbiano and Reilly Opelka forced a fifth-set super-tiebreak. Through 52 games and 319 points, Opelka hit 67 aces and the pair averaged 2.9 shots per “rally.” In the match-deciding tiebreak, Opelka hit no aces, Fabbiano got all but one of his serves back in play, and they averaged 5.5 shots per point.

When I started researching tiebreaks several years ago, I found that the balance of power shifts away from the server: returners win more points in tiebreaks than at other points during the set. It’s not a huge effect, accounting for about a 6% drop in server winning percentage, possibly due to the fact that players almost always give 100% on each point, unlike weak returners facing 40-0 in the middle of the set. Sure, Federer-Evans and Fabbiano-Opelka are outliers: even if servers suffer a bit in the typical tiebreak, the whole sport doesn’t usually turn upside down. Still, the effect is worth a deeper dive.

Isner isn’t the only conservative

Let’s start with some overall trends. Filtering for men’s matches from 2010-19, I found 831 tiebreaks with shot-by-shot data from the Match Charting Project. For each set that ended in a tiebreak, I tallied several stats for both tiebreak points and non-tiebreak points, calculated the single-set ratio for each stat, and then aggregated all 831 breakers to get some tour-wide numbers. Here’s what happens to stats in tiebreaks:

  • Service points won: -6.5%
  • Aces: -6.1%
  • First serve in: +1.3%
  • Returns in play: +8.5%
  • Rally length: +18.9%

(Technical note: When aggregating the ratios from all 831 tiebreaks, I weighted by the number of points in each tiebreak, but only up to a maximum of 11. Longer tiebreaks tend to be the ones if which servers are the strongest, like the 17-15 marathon in the first set of Fabbiano-Opelka. If those were weighted for their true length, we’d bias the results towards the best serving performances.)

Judging by the increase in successful first offerings, it looks like servers are a bit more conservative in tiebreaks. The large drop in aces and even bigger increase in returns in play provide additional evidence. Focused returners may be able to erase a small number of aces, but not that many, and they wouldn’t be able to convert so many into successful returns. The nearly 20% increase in rally length can be explained in part by the drop in aces (those one-shot rallies are replaced with more-shot exchanges), but the magnitude of the rally length effect suggests that players are more conservative on both sides of the ball.

More than one way

Not every player handles breakers the same way. Several men, including Federer, serve about as well as usual in these high-pressure situations. Certain others, like Rafael Nadal, appear to be more conservative, but make up for it by feasting on the toned-down offerings of opposing servers. Still others, like the impossible-to-write-about-tiebreaks-without-bringing-up Ivo Karlovic, underperform on both sides of the ball.

Here are the 20 players with the most tiebreaks recorded by the Match Charting Project since 2010. For each one, you can see how their rates of service points and return points won in tiebreaks compare to non-tiebreak situations. For instance, Jo Wilfried Tsonga wins 5.4% more service points in tiebreaks than otherwise, compared to the usual shift of 6.5% in the opposite direction. But Tsonga’s rate of return points won falls 3.4%, while the typical player increases his haul on return by 6.5%.

Player                    SPW    RPW  
Jo Wilfried Tsonga       5.4%  -3.4%  
Roger Federer            0.4%   3.2%  
Stan Wawrinka           -0.1%   4.2%  
John Isner              -0.6%   6.4%  
Novak Djokovic          -0.8%  11.8%  
Andy Murray             -2.2%   8.7%  
Alexander Zverev        -2.7%  18.7%  
Juan Martin del Potro   -3.3%   5.3%  
Nick Kyrgios            -4.1%  10.5%  
Dominic Thiem           -4.6%  12.1%  
----ATP AVERAGE----     -6.5%   6.5%  
Kevin Anderson          -7.1%   8.9%  
Gilles Simon            -8.0%  16.3%  
Tomas Berdych           -8.4%   6.8%  
Milos Raonic            -9.2%   9.1%  
Rafael Nadal            -9.4%  13.6%  
Marin Cilic            -10.2%   5.8%  
Bernard Tomic          -11.3%   4.5%  
Ivo Karlovic           -12.6%  -0.9%  
Grigor Dimitrov        -13.8%   5.1%  
Karen Khachanov        -25.1%  -5.4%

For most players, the goal appears to be to win enough extra return points to counteract the drop in service success. Nadal is the most extreme example, winning almost 10% fewer service points than usual, but doing even more damage to his opponents. Alexander Zverev is the most impressive of the bunch, dropping his serve level only a bit, while converting himself into a Rafa-like returner. As you might expect, his tiebreak record is outstanding, winning far more than expected last season. We’ll see whether his eye-popping numbers persist.

A winning strategy

Ideally, I would wrap up a post like this with a recommendation. You know, analyzing the various approaches, based on these numbers, we can confidently say that players should….

It’s not that easy. It’s hard enough to identify which players are good at tiebreaks, let alone why. As I’ve written many times before, tiebreak results are closely related to overall tennis-playing skill, but not to serving prowess or excellence in the clutch. In any given season, some players amass outstanding tiebreak records, but their success one year rarely translates to the next. At various times in the past, I’ve highlighted Federer, Isner, Nadal, and Andy Murray as players who defy the odds and consistently outperform expectations in tiebreaks, but even they don’t always manage it. Isner, the poster boy for triumph via tiebreak, won slightly fewer breakers than expected in both 2016 and 2018.

Still, let’s look at these four guys in the light of the shot-by-shot data I’ve shared so far. Federer, Isner, and Murray are in the minority of players who hit more aces in tiebreaks than otherwise. However, it it doesn’t necessarily mean they are much more aggressive; of the the three, only Federer makes fewer first serves than usual. Isner manages to reduce the number of returns in play by 10%, compared to non-tiebreak situations, while the other two do not. Nadal breaks the mold entirely, making 6% more first serves than usual and hitting barely half as many aces.

In other words, there’s no single path to success. Federer and Isner maintain their superlative serving while taking advantage of their opponents’ nerves or conservative tactics. (I’ve previously suggested that the difference in serve points won comes from players like Isner upping their return game in pressure situations. He does, but not any more than the average player.) Nadal plays to his own strengths, forcing players into rallies from both sides of the ball. There may be some quality that ties these four men together (like focus), but we’re not going to find it here.

Ivo Karlovic and the Odds-On Tiebreak

Italian translation at settesei.it

Ivo Karlovic is on track to accomplish something that no player has ever done before. Over the course of his career, Karlovic, along with John Isner, has set a new standard for one-dimensional tennis playing. The big men win so many service points that they are almost impossible to break, making their own service-return limitations manageable. With a player on court who maximizes the likelihood of service holds, tiebreaks seem inevitable.

This season, Karlovic has taken tiebreak-playing to a new level. Through last night’s semi-final at the Calgary Challenger (final score: 7-6, 7-6), the 6-11 Croatian has played 42 matches, including 115 sets and 61 tiebreaks. In percentage terms, that’s a tiebreak in 53% of all sets. Among player-seasons with at least 30 matches across the ATP, ATP qualifying, and ATP Challenger levels since 1990, no one has ever before topped 50%.

Even approaching the 50% threshold marks someone as very unusual. Less than 20% of tour-level sets reach 6-6, and it’s rare for any single player to top 30%. This year, only Isner and Nick Kyrgios have joined Karlovic in the 30%-plus club. Even Reilly Opelka, the seven-foot American prospect, has tallied only 31 tiebreaks in 109 sets this season, good for a more modest rate of 28.4%.

Karlovic is in truly uncharted territory. Isner came very close in his breakthrough 2007 season on the Challenger tour, playing 51 tiebreaks in 102 sets. The rest of the all-time top ten list starts to get a little repetitive:

Rank  Year  Player        Sets  TBs    TB%  
1     2018  Ivo Karlovic   115   61  53.0%  
2     2007  John Isner     102   51  50.0%  
3     2005  Ivo Karlovic   118   56  47.5%  
4     2016  Ivo Karlovic   146   68  46.6%  
5     2017  Ivo Karlovic    91   42  46.2%  
6     2006  Ivo Karlovic   106   48  45.3%  
7     2015  Ivo Karlovic   168   76  45.2%  
8     2018  John Isner     149   65  43.6%  
9     2001  Ivo Karlovic    78   34  43.6%  
10    2004  Ivo Karlovic   140   61  43.6%

* Karlovic’s and Isner’s 2018 totals are through matches of October 20th. 

For more variety, here are the 15 different players with the highest single-season tiebreak rates:

Rank  Year  Player           Sets  TBs    TB%  
1     2018  Ivo Karlovic      115   61  53.0%  
2     2007  John Isner        102   51  50.0%  
3     2004  Amer Delic         95   37  38.9%  
4     2008  Michael Llodra    117   45  38.5%  
5     2008  Chris Guccione    173   65  37.6%  
6     2002  Alexander Waske   109   40  36.7%  
7     1993  Greg Rusedski      99   35  35.4%  
8     2017  Reilly Opelka     115   40  34.8%  
9     2005  Wayne Arthurs      95   33  34.7%  
10    2004  Dick Norman        97   33  34.0%  
11    2001  Ivan Ljubicic     148   50  33.8%  
12    2004  Max Mirnyi        137   46  33.6%  
13    2014  Samuel Groth      172   57  33.1%  
14    2005  Gregory Carraz     98   32  32.7%  
15    2007  Fritz Wolmarans    80   26  32.5%

Karlovic is truly in a class by himself. He’ll turn 40 next February, but age has had little impact on the effectiveness of his serve. While he reached his career peak ranking of No. 14 back in 2008, it was more recently that his serve was at its best. In 2015, he won more than three-quarters of his service points and held 95.5% of his serve games. Both of those marks were career highs. His recent serve stats have remained among his career bests, winning 73.5% of service points in 2018, though as his ranking has tumbled, these feats have come against weaker competition, in ATP qualifying and Challenger matches.

Age has taken its toll, however, and Ivo’s return game is the victim. From 2008-12, he broke serve in more than one out of ten chances, while in 2016-18, it has fallen below 8%. Neither mark is particularly impressive–Isner and Kyrgios are the only tour regulars to break in less than 17% of games this season–but the difference, from a peak of 12.0% in 2011 to a low of 7.1% this year, helps explain why the Croatian is playing more tiebreaks than ever.

Karlovic has long been one of the most unique players on tour, thanks to his height, his extreme statistical profile, and his willingness (or maybe his need) to approach the net. As he gets older and his game becomes even more one-dimensional, it’s only fitting that he breaks some of his own records, continuing past the age when most of his peers retire in order to hit even more aces and play even more tiebreaks.

How Fast Was the Laver Cup Court?

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Italian translation at settesei.it

Laver Cup has redefined what a tennis event can be, and so far, the new definition seems to involve fast courts. Last year, we saw nine tiebreaks out of eighteen traditional sets, plus a pair of match tiebreaks that went to 11-9. This year’s edition wasn’t quite so extreme, with five tiebreaks out of sixteen traditional sets, but it still featured more tight sets than the typical tour event, in which tiebreaks occur less than once every five frames.

As usual, teasing out surface speed comes with its share of obstacles. Yes, there were lots of tiebreaks and yes, there were plenty of aces, but the player field featured more than its share of big servers. John Isner, Nick Kyrgios, and Roger Federer each contested two matches each year, and in Chicago, Kevin Anderson represented one-quarter of Team World’s singles contribution. No matter what the surface, we’d expect these guys to give us more serve-dominated matches than the tour-wide average.

Let’s turn to the results of my surface speed metric, which compares tournaments by using ace rate, adjusted for the serve and returning tendencies of the players at each event. The table below shows raw ace rate (“Ace%”) and the speed rating (“Speed”) for ten events from the last 52 weeks: The four 2018 grand slams, the fastest and slowest tour stops (Metz and Estoril, respectively), the two Laver Cups, and the two events that rate closest to the Laver Cups (Antalya and New York).

Year  Event            Surface   Ace%  Speed  
2018  Metz             Hard     10.6%   1.57  
2018  Antalya          Grass     9.9%   1.28  
2017  Laver Cup        Hard     17.0%   1.26  
2018  Australian Open  Hard     11.7%   1.17  
2018  Wimbledon        Grass    12.9%   1.16  
2018  Laver Cup        Hard     13.3%   1.09  
2018  New York         Hard     15.7%   1.09  
2018  US Open          Hard     10.8%   1.02  
2018  Roland Garros    Clay      7.7%   0.74  
2018  Estoril          Clay      5.2%   0.55

The speed rating metric ranges from about 0.5 for the slowest surfaces to 1.5 for the fastest, meaning that the stickiest clay results in about half as many aces as the same players would tally on a neutral surface, while the quickest grass or plexipave would give the same guys about half again as many aces as a neutral court would.

Last year’s Laver Cup, despite a whopping 17% ace rate, was barely among the top ten fastest courts out of the 67 tour stops I was able to rate. The surface in Chicago was on the edge of the top third, behind the speedy clay of Quito and considerably slower than the Australian Open.

These conclusions come with the usual share of caveats. First, surface speed is about more than ace rate. I’ve stuck with my ace-based metric because it’s one of the few stats we have for every tour-level event, and because despite its simplicity, it tracks closely with intuition, other forms of measurement, and player comments. Second, we’re not exactly overloaded with observations from either edition of the Laver Cup. Last year’s event featured nine singles matches, and this year there were eight. It’s even worse than that, because third sets are swapped out for match tiebreaks, leaving us even less data. That said, while we don’t have many matches to work with, we know a lot about the players involved, which isn’t as true of, say, Newport or Shenzhen, where a larger number of matches are contested by players who don’t make many appearances on tour.

The two Laver Cup surfaces rate as speedy, but not out of line with other indoor hard courts on the ATP tour. There will be tiebreaks and plenty of aces wherever Isner and Anderson go, no matter what the conditions.

The Right Amount of Serve-and-Volley

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Italian translation at settesei.it

In modern tennis, players approach the net at their own peril, especially behind their serve. Technological advances in both strings and rackets have made passing shots faster and more accurate, giving an added edge to the returner. It’s hard to imagine the game changing so that serve-and-volleying would once again become a dominant tactic.

Yet pundits and commentators often suggest that players should approach the net more often, sometimes advocating for more frequent serve-and-volleying. In a recent article at FiveThirtyEight, Amy Lundy brought some numbers to the discussion, pointing out that at the US Open this year, women have won 76% of their serve-and-volley points and men have won 66%. She also provides year-by-year numbers from the women’s Wimbledon draw showing that for more than a decade, the serve-and-volley success rate has hovered around the mid-sixties.

Sounds good, right? Well… not so fast. Through the quarter-finals in New York, men had won roughly 72% of their first-serve points. Most serve-and-volley attempts come on first serves, so a 66% success rate when charging the net doesn’t make for much of a recommendation. The women’s number of 76% is more encouraging, as the overall first-serve win rate in the women’s draw is about 64%. But as we’ll see, WTA players are usually much less successful.

Net game theory

When evaluating a tactic, we have to start by recognizing that players and coaches generally know what they’re doing. Sure, they make mistakes, and they can fall into suboptimal patterns. But it would be a big surprise to find that they’ve left hundreds of points on the table by ignoring a well-known option. If more frequent serve-and-volleying was such a slam dunk, wouldn’t players be doing so?

I dug into Match Charting Project data to get a better idea of how often players are using the serve-and-volley, how successful it has been. and, just as important, how successful they’ve been when they aren’t using it. The results are considerably more mixed than the serve-and-volley cheerleaders would have it.

Let’s start with the women. In close to 2,000 charted matches from 2010 to the present, I found 429 player-matches with at least one serve-and-volley attempt. After excluding aces, regardless of whether the server was intending to approach, those 429 players combined for 1,191 serve-and-volley attempts–95% of them on first serves–of which they won 747. Had those players not serve-and-volleyed on those 1,191 points and won at the same rate as their first- and second-serve baseline points in the same matches, they would have won 725 points. In other words, serve-and-volleying resulted in a winning percentage of 62.7%, and staying back was good for 60.9%. Just to be clear, this is a direct comparison of success rates for the same players against the same opponents, controlling for the differences between first and second serves.

A difference of nearly two percentage points is nothing to sneeze at, but it’s a far cry from the more than ten percent gap we’ve seen on the women’s side at the US Open this year. And it might not be enough of a benefit for many players to overcome their own discomfort or lack of familiarity with the tactic.

When we apply the same analysis to the men, the results are downright baffling. We have more data to work with here: In nearly 1,500 charted matches from 2010 to the present, more than half of the possible player-matches (1,631) tried at least one serve-and-volley. About four in five–once again excluding aces–were first serves. The tour-wide success rate was similar to what we’ve seen at the Open this year, at 66.8%.

Controlling for first and second serves, the same servers, at the same tournaments, facing the same opponents, won points at a 72.2% rate when they weren’t serve-and-volleying. That’s a five percentage point gap* that says men, on average, and serve-and-volleying too much.

* Technical note: These overall rates simply tally all the serve-and-volley attempts and successes for all players. Thus, they may give too much weight to frequent netrushers. I ran the same calculation in two other ways: giving equal weight to each player-match, and weighting each player-match by ln(a+1), where a is the number of serve-and-volley attempts. In both cases the gap shrunk a bit, to four percentage points, which doesn’t change the conclusion.

I was shocked to see this result, and I’m not sure what to make of it. It’s roughly the same for men who serve-and-volley frequently as for those who don’t, so it isn’t just an artifact of, say, the odd points that an Ivo Karlovic or Dustin Brown plays from baseline, or the low-leverage status of the occasional point when a baseliner decides to serve-and-volley. Since I don’t have a good explanation for this, I’m going to settle for a much weaker claim that I can make with more confidence: The evidence doesn’t suggest that men, in general, should serve-and-volley more.

Data from the women’s game is more encouraging for those who would like to see more serve-and-volleying, but it is still rather modest. Certainly, the 76% success rate in Flushing this year is a misleading indicator of what WTA players can expect to reap from the tactic on a regular basis. It’s possible that some women should come in behind their serves more often. But the overall evidence from a couple thousand matches suggests sticking to the baseline is just as good of a bet–if not better.

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.

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.

The Cost of a Double Fault

We all know that double faults aren’t good, but it’s less clear just how bad they are. Over the course of an entire match, a single point here or there doesn’t seem to matter too much, especially when a double fault creeps in at a harmless moment, like 40-love. Yet many missed second serves are far more costly. Let’s try to quantify the impact of tennis’s most enervating outcome.

To do this, we need to think in terms of win probability. In each match, a player wins a certain percentage of service points and a certain percentage of return points. If those rates are sufficiently dominating–say, Mihaela Buzarnescu’s 65% of service points won and 59% of return points won in last week’s San Jose final–the player’s chance of winning the match is 100%. No matter how unlucky or unclutch she was, those percentages result in a win. But in a close contest, in which both players win about 50% of points (often referred to as “lottery matches”), the result is heavily influenced by clutch play and luck. In Buzarnescu’s tour de force, flipping the result of a single point would be meaningless. But in a tight match, like the Wimbledon semifinal between John Isner and Kevin Anderson, a single point could mean the difference between a spot in the championship match and an early flight home.

My aim, then, is to measure the average win probability impact of a double fault. To take another example, consider last week’s Washington quarter-final between Andrea Petkovic and Belinda Bencic. Bencic won nearly 51% of total points–59% of her service points and 42% on return–but lost in a third-set tiebreak. Those serve and return components were enough to give her a 56.3% chance of winning the match: claiming more than half of total points usually results in victory, but so close to 50%, there’s plenty of room for things to go the other way.

I refer to this match because double faults played a huge role. Bencic tallied 12 double faults in 105 service points, a rate of 11.4%, more than double the WTA tour average of 5.1%. Had she avoided those 12 double faults and won those points at the same rate as her other 93 service points, she would have ended up with a much more impressive service-points-won rate of 67%. Combined with her 42% rate of return points won, that implies an 87% chance of winning the match–more than 30 percentage points higher than her actual figure! Roughly speaking, each of her 12 double faults cost her a 2.5% chance (30% divided by 12) of winning the match.

A double fault rate above 10% is unusual, but a cost of 2.5% per offense is not. When we run this algorithm across the breadth of the ATP and WTA tours, we find that the cost of double faults adds up fast.

Tour averages

Using the method I’ve described above–replacing double faults with average non-double-fault service points–and taking the average of all tour-level matches in 2017 and 2018 through last week’s tournaments, we find that the average WTA double fault costs a player 1.83% of a win. Put another way, every 55 additional double faults subtracts one match from the win column and adds one to the loss column.

In the men’s game, the equivalent number is 1.99% of a win. The slightly bigger figure is due to the fact that men, on average, win more service points, so the difference between a double fault and a successful service offering is greater.

There is, however, an alternative way we could approach this. By comparing double faults to all other service points, we’re trading a lot of the double faults for first serve outcomes. We might be more interested in knowing how a player would fare if his or her second serve were bulletproof–still eliminating double faults, but replacing them specifically with second serves instead of a generic mix of service points.

In that case, the algorithm remains very similar. Instead of replacing double faults with non-double-fault serve points, we replace them with non-double-fault second serve points. Then the cost of a double fault is a little bit less, because second serve points result in fewer points won than service points overall. The second-serve numbers are 1.61% per double fault in the women’s game and 1.70% per double fault in the men’s game. For the remainder of this post, I’ll stick with the generic service points, but one approach is not necessarily better than the other; they simply measure different things.

Building a player-specific stat

Odious as double faults are, they are not completely avoidable. Very few players are able to sustain a double fault rate below 2%, and tour averages are around twice that. Since the beginning of 2017, the ATP average has been about 3.9%, and the WTA average roughly 5.1%, as we saw above.

We can measure players by considering their match-by-match double fault rates compared to tour average. In Bencic’s unfortunate case, her 12 double faults were 6.7 more than a typical player would’ve committed in the same number of service points. In contrast, in the same match, Petkovic recorded only 3 double faults in 102 service points, 2.2 double faults fewer than an average player would have.

We know that each WTA double fault affects a player’s chances of winning the match by 1.83%, so compared to an average service performance, Bencic’s excessive service errors cost her about a 17% chance of winning (6.7 times 1.83%), while Petkovic’s stinginess increased her own odds by about 6.6% (2.2 times 1.83%).

Repeat the process for every one of a player’s matches, and you can assemble a longer-term statistic. Let’s start with the WTA players who, since the start of last season, have cost themselves the most matches (“DF Cost”–negative numbers are bad), along with those who have most improved their lot by avoiding double faults:

Player                   DF%  DF Cost  
Kristina Mladenovic     7.7%    -3.84  
Daria Gavrilova         7.9%    -3.77  
Jelena Ostapenko        7.7%    -3.58  
Petra Kvitova           8.1%    -3.01  
Camila Giorgi           8.3%    -2.63  
Oceane Dodin           10.2%    -2.51  
Donna Vekic             7.0%    -1.91  
Venus Williams          6.7%    -1.71  
Coco Vandeweghe         6.4%    -1.60  
Aliaksandra Sasnovich   6.7%    -1.55  
…                                      
Agnieszka Radwanska     2.3%     1.27  
Sloane Stephens         2.1%     1.43  
Caroline Wozniacki      3.2%     1.43  
Barbora Strycova        3.5%     1.47  
Elina Svitolina         3.9%     1.48  
Simona Halep            3.5%     1.53  
Qiang Wang              2.6%     1.54  
Anastasija Sevastova    3.1%     1.57  
Carla Suarez Navarro    2.1%     1.67  
Caroline Garcia         3.6%     1.82

And the same for the men:

Player                  DF%  DF Cost  
Benoit Paire           6.2%    -4.51  
Ivo Karlovic           5.8%    -3.63  
Fabio Fognini          5.0%    -2.38  
Denis Shapovalov       6.3%    -2.26  
Grigor Dimitrov        5.1%    -2.25  
Gael Monfils           5.0%    -2.22  
David Ferrer           5.2%    -2.06  
Jeremy Chardy          5.3%    -2.00  
Fernando Verdasco      4.8%    -1.94  
Jack Sock              4.8%    -1.73  
…                                     
Roger Federer          2.1%     0.88  
Tomas Berdych          2.9%     0.89  
Juan Martin del Potro  2.8%     0.93  
Albert Ramos           3.1%     0.97  
Pablo Carreno Busta    2.2%     1.07  
Richard Gasquet        2.6%     1.12  
John Isner             2.6%     1.23  
Dusan Lajovic          1.9%     1.23  
Denis Istomin          1.9%     1.23  
Philipp Kohlschreiber  2.5%     1.24

Situational double faults

These aggregate numbers have the potential to hide a lot of information. They consider only two things about each match: how many double faults a player committed, and how close the match was. This statistic would treat Bencic the same whether she hit nine of her double faults at 40-love, or nine of her double faults in the third-set tiebreak. Yet the latter would have a colossally greater impact.

While this is an important limitation to keep in mind, it appears that double faults are distributed relatively randomly. That is, most players do not hit a majority of their double faults in particularly high- or low-leverage situations. The player lists displayed above show both the most basic stat–double fault percentage–along with my more complex approach. For players with at least 20 matches since the beginning of last season, double fault rate is very highly correlated with the match-denominated cost of double faults. (For men, r^2 = 0.752, and for women, r^2 = 0.789.) In other words, most of the variance in double fault cost can be explained by the number of double faults, leaving little room for other factors, such as the importance of the situation when double faults are committed.

That said, there’s plenty of room for additional analysis into those specific sitations. Instead of taking a match-level look at win probability, as I have here, one could identify the point score of every single one of a player’s double faults, and see how each event affected the win probability of that match. I suspect that, for most players, that would amount to a whole lot of extra complexity for not a lot of added insight, but perhaps there are some players who are uniquely able to land their second serve when it matters most, or particularly prone to double faults at key moments. This match-level look has made it clear how costly double faults can be, and it’s possible that for some players, missed serves are even more damaging than that.