Aryna Sabalenka Under Pressure

Also today: January 26, 1924

Aryna Sabalenka at Wimbledon in 2023. Credit: Adrian Scottow

It felt like a pivotal moment. Aryna Sabalenka had taken a 5-2 first-set lead in yesterday’s Australian Open semi-final against Coco Gauff. Gauff kept the set going with a strong service game for 5-3. Sabalenka lost the first point on her serve, but bounced back with a plus-one backhand winner.

At 30-15, the American struck again. She took advantage of a Sabalenka second serve to drag the Belarusian into a backhand rally, ultimately drawing an unforced error on the ninth shot and putting the game back in play.

Then, still just two points from the set, Sabalenka double-faulted.

The narrative practically writes itself. Aryna hits hard, aims for the lines, and keeps points short. Let her do that, and she will destroy you. Her first five opponents in Melbourne managed a grand total of 16 games against her. On the other hand, if you keep the ball in play, she’ll start pressing, trying too hard to dictate with her serve, going for too much when a smackable groundstroke presents itself.

Gauff, by this reading, is Sabalenka’s nightmare opponent. She won the US Open final by denying the Belarusian one would-be winner after another. Not only can she take Sabalenka’s game away from her, but Coco–at least on a good day–won’t give it back on her own serve. When she lets loose, Gauff wields just as much power as her more tactically aggressive opponent.

As it turned out, Sabalenka did lose that service game. Several twists and turns later, Gauff led the set, 6-5. Only then did Aryna regroup, winning four straight points from 30-love to force a tiebreak, then dropping just two more points to clinch the set. Gauff kept the second set close, but Sabalenka never allowed her to reach break point. The contest closed with a narrative-busting move: Facing match point, Gauff pulled out a 12-stroke rally, the kind of point that has been known to steer her opponent off course. But instead of compounding the damage, Sabalenka came back with two unreturned serves. Game over.

What to believe, then? Was the apparent first-set turning point a reflection of the true Sabalenka? Or is this the new Aryna, who slams the door when challengers sniff opportunity? Or is it something else, the all-too-common story in which someone looks like a clutch hero or a constant choker, only for us to discover, after crunching all the numbers, that she’s impervious to momentum and plays pretty much the same all the time?

Recovering at a disadvantage

Sabalenka’s serve games do follow a pattern after she loses a longish rally. But the results are not entirely straightforward.

On the next point (assuming the lost rally didn’t end the service game), Aryna is more likely to miss her first serve:

Year   1stIn%  post-rallyL-1stIn%  Change  
2019    61.2%               55.9%   -8.6%  
2020    61.5%               57.0%   -7.3%  
2021    58.6%               52.6%  -10.3%  
2022    60.0%               59.9%    0.0%  
2023    61.1%               61.3%    0.4%  
2024    63.3%               62.5%   -1.2%
----  
TOTAL   60.5%               57.6%   -4.8% 

Most of the effect is concentrated in the earlier years of her career on tour. Yesterday, the trend ran in the opposite direction: She made nearly 76% of her first serves overall, but after Gauff won a rally, she landed 88% of them.

The trend is clearer–and persisting to the present–when we look at double faults after losing a rally:

Year     DF%  post-rallyL-DF%  Change  
2019    8.6%            10.4%   20.8%  
2020    6.2%             8.4%   36.9%  
2021    7.9%            11.8%   50.3%  
2022   10.7%            10.1%   -5.5%  
2023    6.2%             7.2%   16.5%  
2024    3.4%             8.3%  144.7%  
----
TOTAL   7.9%             9.6%   22.5%

2022 was Aryna’s year of the yips; she was more likely to bunch double faults together than hit them in particularly nervy spots. (Put another way: Every spot was a nervy one.) The 2024 number will surely come back to earth, but it is still revealing: Sabalenka has made so much progress in this aspect of her game, but her second-serve struggles continue when she faces the threat of getting dragged into another rally.

Some of these effects persist even longer. From those service games that last long enough, here are Sabalenka’s first-in and double-fault percentages two points after losing a long rally:

Year   1stIn%  +2 1stIn%  Change    DF%  +2 DF%  Change  
2019    61.2%      55.8%   -8.8%   8.6%    8.7%    1.2%  
2020    61.5%      50.5%  -17.9%   6.2%    7.2%   17.1%  
2021    58.6%      56.0%   -4.5%   7.9%    8.7%   10.5%  
2022    60.0%      63.1%    5.3%  10.7%    7.8%  -27.1%  
2023    61.1%      59.2%   -3.2%   6.2%    8.4%   35.6%  
2024    63.3%      57.1%   -9.7%   3.4%    2.4%  -30.1%  
----
TOTAL   60.5%      57.1%   -5.6%   7.9%    8.0%    2.0% 

She continues to miss more first serves even two points after the rally setback. To some degree, the memory should have dissipated–after all, something else happened on the intervening point. On the other hand, she’s back in the same court. If a reliable serve didn’t work in the deuce court at 30-love, there’s reason to doubt it at 30-all.

The double fault trends are less clear, in part because our sample size is shrinking and double faults are blessedly rare. If nothing else, it’s safe to conclude that the explosion of double faults on the point after the lost rally doesn’t continue to nearly the same degree.

Tallying the cost

Now, this all seems bad. Sabalenka possesses one of the best first serves in the game; her whole attack is built around it. Her emergence as a superstar came after she got control of the service yips and cut her double faults down to manageable levels. After losing a long rally, she needs her serve more than ever, and–at least by comparison with other situations–it isn’t there for her.

Except… it doesn’t matter! At least not on the first point. Here is the bottom-line figure of service points won:

Year    SPW%  post-rallyL-SPW%  Change  
2019   59.6%             63.8%    7.2%  
2020   60.3%             56.6%   -6.0%  
2021   61.5%             61.3%   -0.3%  
2022   57.2%             59.9%    4.7%  
2023   63.7%             63.9%    0.4%  
2024   66.7%             70.8%    6.3%  
----
TOTAL  60.7%             61.7%    1.6% 

Fewer first serves, but more serve points won. It isn’t supposed to work like that, but Sabalenka bounces back strong from lost rallies. A shift of +1.6% in her favor is solid enough, and it’s even better if you look solely at the last three years.

Part of the explanation is that she tightens up the rest of her game–exactly the opposite of what my off-the-cuff narrative suggests. Under pressure, I hypothesized, she would try too hard to end points. Instead, after losing a long rally, she’s more willing than usual to play another one: She commits 14% fewer plus-one errors than her usual rate, implying a lower rate of aggression when she has an early chance to put the point away.

On the second point after losing a long rally, the bottom-line outcomes are more mixed:

Year    SPW%  +2 SPW%  Change  
2019   59.6%    53.9%   -9.5%  
2020   60.3%    55.3%   -8.3%  
2021   61.5%    58.5%   -4.9%  
2022   57.2%    61.5%    7.4%  
2023   63.7%    60.7%   -4.7%  
2024   66.7%    71.4%    7.1% 
---- 
TOTAL  60.7%    58.2%   -4.0%

While these aren’t as rosy as the next-point results, focus on the last few years. Since the beginning of 2022, Aryna has won more service points than usual when she returns to the serving direction where she recently lost a long rally–despite landing fewer first serves. She is even stingier with plus-one errors on these points, coughing up 29% fewer than usual.

These trends did not hold in yesterday’s semi-final. While Sabalenka made more first serves on the two points after Gauff outlasted her in a rally, fewer of them ended in her favor: 4% less on the first point, 12% less on the second. We can’t read too much into single-match totals with stats like these: 4% is a difference of one point. And Gauff is a far superior returner and baseline player than the typical WTAer, one who is unlikely to lose focus after going toe to toe with Sabalenka for a point or two. The average player pushes Aryna to a seventh shot barely one-tenth of the time; Gauff did so on one of every six points yesterday.

All of this leads us to an unexpected conclusion: Does Aryna Sabalenka have nerves of steel? First serves and double faults are just components in a larger picture; when we measure her results by points won, Sabalenka serves more successfully right after an opponent makes her uncomfortable. The yips are gone, and the on-court histrionics are a diversion that deceived us all. Aryna under pressure may be even more fearsome than her typical, terrifying self.

* * *

January 26, 1924: Suzanne’s longest day

Suzanne Lenglen wasn’t accustomed to spending much time on court. In eight tournaments since the 1923 Championships at Wimbledon, she had lost just ten games. Her doubles matches, especially with net maven Elizabeth Ryan at her side, were often just as lopsided. She never missed, she could put the ball anywhere on the court, and most opponents were lucky just to win a single point.

Lenglen and Ryan in 1925 at Wimbledon. Colorization credit: Women’s Tennis Colorizations

In January 1924, Lenglen eased her way back onto the circuit. Battling some combination of illness, anxiety, and hypochondria, she didn’t return to singles action until February. (She’d win her first three matches before dropping a game.) But she was a celebrity on the French Riviera, and she was prevailed upon to compete in doubles. She won the mixed at the Hotel Beau-Site tournament in Cannes to ring in the new year, and she entered both the women’s doubles–with Ryan–and the mixed at the Hotel Gallia tournament a few weeks later.

On the 26th, Lenglen and Ryan completed their waltz through the draw, defeating a British pair, Phyllis Covell and Dorothy Shepherd-Barron, 6-3, 6-4. Suzanne’s most aggravating foe was another Brit, a line judge with the temerity to call a foot-fault on the five-time Wimbledon champion. She tried to get the man removed and ultimately had to settle for his “voluntary” departure. “It is unfair,” she said. “The English are pigs.”

Her nerves would be tested even more severely in the mixed doubles final. Lenglen partnered Charles Aeschlimann of Switzerland, while Ryan teamed with the 43-year-old Canadian Henry Mayes. Both men were better known on the Riviera than in the tennis world at large, more clubbable than talented. Lenglen and Ryan–herself one of the top few woman players in the world–would be the stars of the show.

Lenglen and Aeschlimann took the first set, 6-4; Ryan and Mayes came back with a 6-1 frame of their own. The underdogs–that is, the team without Suzanne–built up an early lead in the third, thanks to Aeschlimann’s inconsistency and Ryan’s glittering play. Mayes served for a 4-2 advantage, but a lucky netcord halted their momentum, and the deciding set settled into a rhythm it wouldn’t break for 20 more games.

Only at 13-14 did Ryan finally give in. She gifted a double fault to her opponents, and Mayes’s fatigue–he had played a four-set men’s doubles final beforehand–began to tell. Lenglen and Aeschlimann broke serve, securing the 6-4, 1-6, 15-13 victory. It would stand as the longest set of Suzanne’s unparalleled career.

* * *

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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.

How Servers Respond To Double Faults

Italian translation at settesei.it

In the professional game, double faults are quite rare. They sometimes reflect a momentary lapse in concentration, and can negatively impact a server’s confidence. Players are sometimes particularly careful after losing a point to a double fault, taking some speed off their next delivery, or aiming closer to the middle of the box.

Let’s dig into some data from last year’s grand slams to see what players do–and how it affects their results–immediately after double faults. IBM’s Slamtracker provided point-by-point data for most 2017 grand slam singles matches, including serve speed and direction, and the available matches give us about 5,000 double faults to work with. (I’ve organized the data and made it freely available here.)

For each server in each match, I’ve tallied their results on points immediately following double faults. (That means that we exclude after-double-fault points when the double fault ended the game.) Then, for each player, I compared those results with match-long averages. Because double faults are so unusual, and because we only have this data for the majors, the sample isn’t adequate to tell us much about individual players. But for tour-wide analyses, it’s more than enough.

Serve points won: As we’ll see in a moment, men and women have different overall tendencies on the point following a double fault. But by the most important measure of simply winning the next point, gender plays little part. Men, who in this sample win 65.1% of service points, fall just over one percentage point to 64.0% on the point following a double fault. Women, who average 57.8% of service points won, drop even more, to 56.1% after a double.

First serve percentage: I expected that servers become more conservative immediately after a double fault. For women, that hypothesis is correct: In these matches, they land 63.3% of their first serves, while after a double fault, that number jumps to 65.4%. On the other hand, men don’t seem to change their approach very much. On average, they make 62.3% of their first offerings, a number that barely changes, to 62.5%, after double faults.

First serve points won: Here is additional evidence that women become more conservative after double faults, while men do not. In general, women win 63.7% of their first serve points, but just after a double fault, that number drops to 62.9%. For men, there is a decrease in first serve points won, but it is almost as small as their difference in first serve percentage: 72.7% overall, 72.4% after a double fault.

First serve speed: With serve speed, we run into a limitation of the Slamtracker data, which gives us speed only for those serves that go in. So when we look at the average speed of first serves, we’re excluding attempts that miss the box. Even with that caveat, the data keeps pointing in the same direction. Contrary to my “conservative” hypothesis, men serve a bit faster than usual after a double fault–183.3 km/h following doubles, versus 182.8 km/h in general. Women do seem to change their tactics, dropping from an average speed of 155.5 km/h to a post-double-fault pace of 152.2 km/h.

First serve direction: Slamtracker divides serve direction into five categories: wide, body-wide, body, body-center, and center. After a double fault, men are less likely than usual to hit a wide serve (24.1% to 25.8%), and those serves get split roughly evenly between the body and center categories. The difference in body serves is most striking: They account for only 3.5% of first serves overall, but 4.4% of post-double first serves. This may be the one way in which men opt for the conservative path, by maintaining speed but giving themselves a wider margin of error.

Women move many of their after-double-fault serves toward the middle of the box. On average, over 44% of serves are classified as either “wide” or “center,” but immediately after a double fault, that number drops below 41%. It’s not a huge difference, but like all of the other tendencies we’ve seen in the women’s game, it suggests that for many players, caution creeps in immediately after missing a second serve.

Tactics

As usual, it’s difficult to move from these sorts of findings to any sort of tactical advice. Even the first data point, that both men and women win fewer service points than usual right after they’ve double faulted, can be interpreted in multiple ways. By one reading, players may be serving too conservatively, missing out of the benefits of big first serves. On the other hand, if confidence is an issue, perhaps serving more aggressively would just result in more misses.

When in doubt, we have to trust that the players and coaches know what they’re doing–they’ve honed these tradeoffs through decades of experience and thousands of hours of match play. For fans, these numbers add to our understanding of the conclusions that players have reached. For the pros, perhaps a more detailed look at what happens after a double fault would help tweak their own strategies, both bouncing back from their own double faults and taking advantage of the lapses in concentration of their opponents.