Category: Serve statistics

The Manufactured Attack of Caroline Garcia

Caroline Garcia in 2019. Credit: Peter Menzel

Last night, Caroline Garcia scored what many fans saw as an upset, straight-setting two-time Australian Open champion Naomi Osaka. While Garcia was seeded 16th and Osaka is just beginning a comeback, no one ever knows quite what to expect when the Frenchwoman takes the court. The former champ, for her part, has always been at her best on big stages.

The result was almost pedestrian. Garcia turned in a performance that exemplified the tennis of her late 20s: Serving big, returning pugnaciously, taking risks, and–on the rare occasions that Osaka left her an opening–net rushing. Osaka served well, but the 16th seed out-aced her, 13 to 11. More than three-quarters of points were decided in three shots or less, and Garcia stole a few more of those from her opponent than Osaka did from her. In a contest defined by small margins–one break of serve and a tiebreak–that was all it took.

The strange thing is, Caro didn’t use to play like this. She plays shorter points than any other tour regular, an average of 2.9 shots per point in charted matches from the last 52 weeks. It isn’t just about her powerful first serve: Her return points end even sooner than her serve points do. Back in 2018, when she first reached her career-best ranking of 4th on the WTA computer, she was averaging over four shots per point, a rally length that would put her in the range of Jessica Pegula and Maria Sakkari: in other words, a very different sort of player.

Here is the evolution of Garcia’s rally length, shown as a rolling 10-match average, for the 84 matches in the charting dataset:

Last night’s rally length was a blink-and-you’ll-miss-it 2.5 shots, the second-lowest figure I have on record for Garcia. Only a match against Donna Vekic last year comes in slightly lower, though last week’s match in Adelaide against Jelena Ostapenko may have been even more extreme. Osaka’s big game helped keep the number down, but it takes two to so comprehensively avoid the long-rally tango.

Garcia’s first serve has always been a weapon. But her tactical approach behind it has fluctuated wildly. The career trend of her Aggression Score in rallies illustrates how she has careened from one extreme to another. Aggression Score is scaled so that the most passive players rate around -100 and the most aggressive around 100, though Ostapenko and others have pushed the maximum figures further into triple digits. Here is how Garcia’s score has changed over time, again as rolling ten-match averages:

I don’t think there any other player in tennis–man or woman, past or present–who has followed a path like this. As she established herself as an elite on tour, even as she rose into the top five, she became more and more conservative. For reference, players who posted scores around zero in 2023 were Sakkari and Martina Trevisan, hardly styles that will remind you of Garcia’s. Eventually she reversed course, not only regaining her former style but surpassing it, ranking among Liudmila Samsonova and Aryna Sabalenka as one of the most aggressive players on tour, a rung below the class-of-her-own Ostapenko.

Is it working?

The oddest thing about the multiple phases of Garcia’s career is that she has reached the No. 4 ranking with two different styles. In each of her first three charted matches after achieving the peak ranking in 2018, she posted negative rally aggression scores. In two matches against Sabalenka, she averaged 3.9 and 3.7 shots per point; against Karolina Pliskova in the Tianjin final, the typical point lasted 4.3 strokes. When she returned to the No. 4 ranking at the end of 2022, after years in the wilderness, she was frequently posting triple-digit aggression scores and average rally lengths below 3.

The main effect of Garcia’s current style is that it makes the most of her serve. From 2015 to 2017, she won just over 66% of her first-serve points, a mark that is good but sub-elite. She fell all the way to 62% in 2021 before the big shift; since then, she has won more than 70% of her first-serve points. She ranked fourth in that stat heading into the Australian Open, and she converted nearly 90% of her first serves against Osaka. Her success behind the second serve hasn’t shown the same improvement, but the overall picture is a good one: She won more total serve points in 2023 than ever before.

The return game is a different story. This is where even a casual viewer can’t miss Caro’s new tactics: She’s not afraid to stand well inside the baseline to return serve, and yesterday she net-rushed one Osaka serve, SABR-style. Measured by court position, if not by winners and error stats, Garcia is even more aggressive than Ostapenko.

At her best, the Frenchwoman posted acceptable return numbers, if not great ones. Her best single-season mark, winning 42.7% of her return points in 2017, put her in the bottom third of top-50 players. As she has upped the intensity of her attack, this key number has headed south:

In the last 52 weeks, she has won just 38.3% of return points, worst among the top 50 by two full percentage points. Among the top 20, no one else is below 42%. She can get away with it because her own serve is so rarely broken, but such ineffectual return results will make it difficult to mount another assault on the top five. Breaking serve so rarely dooms her to a career of three-setters and narrow decisions. Those sorts of results can sometimes be encouraging–as in her pair of recent three-set losses to Iga Swiatek–but have a knack for halting winning streaks, too.

It doesn’t have to be this way. Players don’t sign contracts agreeing to deploy the same tactics on both sides of the ball. Garcia won return games far more often in her less aggressive days, breaking 33% of the time in 2017 compared to a dreadful 23% last year.

Some of Caro’s 2017 skills are still in evidence. She is solid enough in long rallies that she doesn’t need to so actively avoid them: In the last year, she has won a respectable 48% of points that lasted seven or more strokes, and if you remove the two Swiatek matches, she breaks even. While the Osaka match was primarily determined by short points, Garcia won 17 of 29 (59%) that went to a fourth shot.

Without any major changes, Garcia will remain the sort of player who aggravates fans and opponents alike, a dangerous lurker capable of delivering upsets, inexplicable marathons, and lame early exits in equal measure. Like any hyper-aggressive player, Caro’s results can be seemingly random, with all the frustration that entails. Unlike Ostapenko, Sabalenka, and the many ball-bashers on tour, though, Garcia has chosen to play this way, rebuilding her game into something that the 2018 version of herself would hardly recognize. If she can somehow join her late-career serve to her earlier return-game tactics, the randomness will disappear, and Caro may make yet another appearance in the top five.

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The Most Exclusive Clubs In Tennis

The new Big Two?

Tireless podcaster Alex Gruskin likes to talk about what he calls the “top-ten, top-15, top-20, and top-25 clubs.” He works out the membership of each one by consulting the Tennis Abstract ATP and WTA stats leaderboards, which display dozens of metrics for each of the top 50 ranked players on both tours.

To qualify for Alex’s “top ten club,” a player needs to be in the top ten in both hold percentage and break percentage–in other words, to be an elite server and returner. Even cracking the top 25 club is no easy task. In 2023, only 11 men were better than half of the top 50 on both sides of the ball. It’s more common to excel at one or the other. In 2022, the best returner (Diego Schwartzman) ranked 50th out of 50 on serve, and the best server (Nick Kyrgios) came in 40th on return.

The top-25 club is a high standard, and the top-ten club is a stratospheric one. This year, only three men–Novak Djokovic, Jannik Sinner, and Carlos Alcaraz–made the cut, and Alcaraz almost missed it, ranking 10th in hold percentage. Daniil Medvedev almost qualified, but he trailed Alcaraz by 0.7% in hold percentage and came in 11th in that category.

Three top-ten clubbers is, as it turns out, an unusual showing. In the 33 seasons for which we have the necessary stats to calculate hold and break percentage (back to 1991), only 13 men have ever managed the feat. Many of them did it several times, so there are a total of 49 player-seasons that qualify. For the two-plus decades between 1991 and 2011, there were only two seasons in which more than one player reached both top-ten thresholds. In 1992, the entire tour fell short.

By “club” standards (and most others), Djokovic’s 2023 season was particularly impressive. Alex usually classifies players into round-number clubs, occasionally giving credit to a near-miss who makes, for instance, the “top 26” club. We can extend the concept a bit further and place every season into its best possible club: If a player ranks in the top three by both hold and break percentage, he’s in the “top-three” club; if he ranks among the top four in both, he’s in the “top-four club,” and so on.

In 2023, Novak led the tour in hold percentage and was bested by only Alcaraz and Medvedev in break percentage. Thus, he’s a member of the top-three club. More exclusive categories are hard to find. Here’s the complete list of top-three clubbers since 1991, along with their ranks in hold percentage (H% Rk) and break percentage (B% Rk):

Year  Player          H% Rk  B% Rk  CLUB  
2023  Novak Djokovic      1      3     3  
1999  Andre Agassi        3      1     3  
1995  Andre Agassi        3      3     3

That’s it.

Sinner’s 2023 campaign was also sneakily great. He finished a deceptive fourth on the official ATP points table, but by ranking fifth in hold percentage and fourth in break percentage, he joined an absurdly elite group of top-five clubbers: only Djokovic, Agassi, Rafael Nadal, and Roger Federer.

Here’s the full list of top-ten club seasons since 1991:

Year  Player            H% Rk  B% Rk  CLUB  
2023  Novak Djokovic        1      3     3  
1999  Andre Agassi          3      1     3  
1995  Andre Agassi          3      3     3  
2021  Novak Djokovic        4      3     4  
2013  Rafael Nadal          4      1     4  
2008  Rafael Nadal          4      1     4  
2002  Andre Agassi          4      3     4  
2023  Jannik Sinner         5      4     5  
2019  Rafael Nadal          5      1     5  
2017  Rafael Nadal          5      2     5  
2015  Novak Djokovic        5      1     5  
2014  Novak Djokovic        5      2     5  
2012  Rafael Nadal          5      1     5  
2007  Rafael Nadal          5      2     5  
2006  Roger Federer         2      5     5  
2003  Andre Agassi          5      3     5  
                                            
Year  Player            H% Rk  B% Rk  CLUB  
2022  Novak Djokovic        6      4     6  
2013  Novak Djokovic        6      2     6  
2021  Daniil Medvedev       7      4     7  
2020  Rafael Nadal          7      2     7  
2019  Novak Djokovic        7      2     7  
2012  Novak Djokovic        7      2     7  
2011  Novak Djokovic        7      1     7  
2010  Rafael Nadal          2      7     7  
2008  Novak Djokovic        7      4     7  
2004  Roger Federer         2      7     7  
2021  Alexander Zverev      8      7     8  
2020  Daniil Medvedev       8      8     8  
2018  Novak Djokovic        8      5     8  
2016  Novak Djokovic        8      2     8  
2015  Roger Federer         4      8     8  
2005  Roger Federer         2      8     8  
2001  Andre Agassi          8      3     8  
1998  Marcelo Rios          8      2     8  
1991  Stefan Edberg         4      8     8  
                                            
Year  Player            H% Rk  B% Rk  CLUB  
2022  Daniil Medvedev       8      9     9  
2020  Andrey Rublev         9      5     9  
2018  Rafael Nadal          9      1     9  
2017  Roger Federer         2      9     9  
2009  Andy Murray           9      2     9  
2007  Roger Federer         3      9     9  
2000  Andre Agassi          8      9     9  
2023  Carlos Alcaraz       10      1    10  
2020  Novak Djokovic       10      4    10  
2019  Roger Federer         3     10    10  
2013  Roger Federer         7     10    10  
1998  Andre Agassi         10      3    10  
1994  Andre Agassi         10      5    10  
1993  Thomas Muster        10      4    10

The list is heavily weighted toward the Big Three and the current era. Whether it’s surface speed convergence or something about the players themselves, it’s tougher to reach the top with a lopsided game these days. Stefan Edberg was a top-eight clubber in 1991 (and might have been as good for several seasons before that), but Pete Sampras didn’t get anywhere close. His best showing by this metric came in 1997, when he cracked the top-14 club. Andy Roddick never even cleared the top 30.

Finally, here are the 15 men who reached both top-30 thresholds in 2023:

Year  Player            H% Rk  B% Rk  CLUB  
2023  Novak Djokovic        1      3     3  
2023  Jannik Sinner         5      4     5  
2023  Carlos Alcaraz       10      1    10  
2023  Daniil Medvedev      11      2    11  
2023  Andrey Rublev        17     11    17  
2023  Karen Khachanov      18     16    18  
2023  Alexander Zverev     15     18    18  
2023  Grigor Dimitrov      19     15    19  
2023  Taylor Fritz          6     19    19  
2023  Casper Ruud          21     17    21  
2023  Holger Rune          20     21    21  
2023  Frances Tiafoe        9     26    26  
2023  Ugo Humbert          29     23    29  
2023  Roman Safiullin      30     24    30  
2023  Sebastian Korda      14     30    30

Women’s clubs

The WTA gets the short shrift on topics like these, because much less historical data is available. I only have the necessary stats back to 2015, and even that season is incomplete.

Still, that doesn’t make some recent individual performances any less impressive. Iga Swiatek’s effort in 2023 predictably stands out: She came in third behind Aryna Sabalenka and Caroline Garcia in hold percentage, and she trailed only Sara Sorribes Tormo and Lesia Tsurenko in break percentage. By finishing third in both categories, she–like Djokovic–is a member of the top-three club.

Depending on how you define a full-season, Iga might be the first ever woman to reach such a standard, at least in the nine-year span for which we can do the math. Here is the full list of top-ten clubbers back to 2015:

Year  Player             H% Rk  B% Rk  CLUB  
2016  Victoria Azarenka      2      1     2  
2023  Iga Swiatek            3      3     3  
2022  Iga Swiatek            5      1     5  
2019  Serena Williams        1      6     6  
2015  Serena Williams        1      7     7  
2016  Serena Williams        1      8     8  
2016  Angelique Kerber      10      6    10

Azarenka’s run in 2016 was really a partial season: She hurt her knee and didn’t play again after retiring from her first-round match at the French. Her first four months of tennis put her on the path toward a historic campaign, but we’ll never know how it would have turned out. Those 29 matches can’t really be set along the same measuring stick as Iga’s 75-plus in each of the last two years. Serena’s three entries on this table were almost as abbreviated, but again we’re reminded of the limited data. Surely the list would be much longer, with many more instances of the Williams name, if we had better data.

Anyway, all hail the great Iga. May her reign last until Sabalenka figures out how to become a top-ten returner.

At least this year, it was slightly harder to crack the top-25 and top-30 clubs in the women’s game than it was in the men’s. Here is the full 2023 women’s list down to the top-32 threshold, which allows us to include a few names of interest who missed out on the top 30:

Year  Player               H% Rk  B% Rk  CLUB  
2023  Iga Swiatek              3      3     3  
2023  Cori Gauff              13      8    13  
2023  Jessica Pegula          16      5    16  
2023  Madison Keys             6     16    16  
2023  Barbora Krejcikova      12     18    18  
2023  Victoria Azarenka       19     17    19  
2023  Aryna Sabalenka          1     20    20  
2023  Marketa Vondrousova     22      6    22  
2023  Karolina Muchova         8     22    22  
2023  Leylah Fernandez        20     27    27  
2023  Jelena Ostapenko        28     12    28  
2023  Marie Bouzkova          29     21    29  
2023  Caroline Dolehide       23     30    30  
2023  Elina Svitolina         31     24    31  
2023  Beatriz Haddad Maia     18     31    31  
2023  Ons Jabeur              32      9    32  
2023  Belinda Bencic           5     32    32

More than ever, a well-rounded game is a necessity for players who hope to reach the top. For fans, “clubs” like these are a useful way to think about which stars are getting the job done on both sides of the ball.

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What If Jannik Sinner Made More First Serves?

Jim Courier thinks he should:

Among the current top 50, there’s actually a negative correlation between height and first-serve percentage–that is, taller guys make slightly fewer first serves, all else equal–but that doesn’t directly contradict what Courier said. There’s a whole lot that we could investigate in that couple of lines, but let’s stick with the question in the headline.

In the 52 weeks going into the current Miami event, Jannik Sinner made 57.3% of his first serves. That’s the lowest rate of the current top 50, and well below the average of 63%. When he makes his first serve, he wins 74.7% of points–slightly better than average–and on second-serve points, he wins 54.7%, which ranks 11th among the top 50. Altogether, he’s winning 66.2% of service points, again a little bit above top-50 average.

Courier presumably meant that Sinner’s first serve needs to be more reliable, not that he should take something off of it. In the hypothetical, then, he’ll continue to win roughly 75% of first-serve points. He’ll just have more of them.

If Sinner made 65% of his first serves instead of 57.3%, and he continued to win first and second serve points at the same rate, he’d improve his overall winning percentage on service points from 66.2% to 67.7%. That’s equivalent to increasing his hold percentage from 84.9% to 87.1%. (He’s currently holding 83.9% of the time, so he might be a bit unlucky.)

One and a half percentage points–how much does that really matter?

For starters, it would improve his position on the top-50 leaderboard from 24th to 11th. Now, he’s winning service points like Frances Tiafoe and Roberto Bautista Agut. Improved by 1.5%, he’d be in another league entirely, equal to Felix Auger-Aliassime and Taylor Fritz.

Another way of looking at it is within my framework of converting points to ranking places. As a rough rule of thumb, winning one additional point per thousand translates into a improvement of one place on the ranking table. That relationship doesn’t hold at the very top of the rankings, where players are not so tightly packed. But when I first introduced the framework in 2017, the relationship among players ranked 2nd to 10th was that–again, approximately–two points per thousand translated into one place in the rankings.

Back to Sinner. If he won 1.5% more service points, that’s a 0.75% increase overall. (We’re assuming his return game is unchanged.) Call it 0.8%, or eight points per thousand. According to the top-ten version of my rule, that’s worth four spots in the computer rankings.

Sinner is currently ranked 11th on the ATP computer, and after advancing to the Miami semi-finals yesterday, he ranks 9th on the live table. He could head back to Europe as high as 6th if he wins the title. From any one of those positions, a four-place jump would be significant.

Yet the Italian might be better even than that. My Elo ratings place him 4th, behind only Novak Djokovic, Carlos Alcaraz, and Daniil Medvedev. There’s no reliable relationship between points per thousand and ranking places at the very top of the table, but Elo hints at what an elite player Sinner already is. Tack on seven or eight more points per thousand and he might not be the number one player in the world, but he’s right there in the mix.

That is, at least as long as no one else improves even faster. Sinner isn’t alone in his 66.2% rate of service points won. Alcaraz entered Miami with exactly the same number. Sinner has more room to improve his first serve percentage than anyone else at the top of the game, but his rivals will hardly stand around and watch while he does.

The Underserved First Point

Not all points are created equal. Ask around, and you’ll get a variety of opinions as to which points are most important. Break points, obviously, are key. Pundits are fond of 15-30.

Then there’s the first point of the game. It’s been conventional wisdom for a long time that the opening points holds disproportionate weight. In a previous study, I disproved that. Of course it’s valuable to move from 0-0 to 15-0, and no one likes to start a game by dropping to 0-15. But the first point doesn’t have any magical effect on the outcome of the game beyond simply adding to one or the other player’s tally.

Yet here I am, talking about the first point again. While there still isn’t any magic, the first point is going to the returner too often. With a slight change in tactics or focus, this is a rare analytical insight that pros may be able to use to win a few more service games.

Point by point

The balance between the server and returner varies a great deal depending on the point score. In men’s singles matches at the US Open between 2019 and 2021, servers won 63.6% of points in non-tiebreak games. Yet at 40-love, the server won 67.7%, and at ad-out, the server won only 59.6%.

The point scores that generated such extremes hint at what’s going on here. If a game has reached 40-love, the server is probably a good one. It’s not always the case, but if you look at all the 40-love games in a large dataset, you’ll get far more John Isner holds than Benoit Paire holds. The opposite applies to ad-out, a score that Isner rarely faces. Thus, the difference in point-by-point serve percentage isn’t (entirely) because of the point score–it’s because of the servers who get there.

Other differences are more prosaic. On average, servers win more deuce-court points than ad-court points. In the same three-year dataset, the difference was 64.2% to 62.9%. There’s no selection bias component here. The typical ATPer is simply stronger in that direction. Some players–particularly left-handers–break the mold, but most will favor the deuce side. Both Novak Djokovic and Roger Federer, for instance, win nearly two percentage points more often when serving to that court.

Unbiasing

Because scores like 40-love and ad-out aren’t randomly distributed among servers, we need to do a bit more work to figure out which scores really do favor the server. The trick here is to compare each service point to the rest of the server’s points in the same match. A point like 40-love has a ton of Isners and Opelkas in it, so we’ll end up comparing it to a lot of other Isner and Opelka points. And in fact, the average player who reaches 40-love wins 65.0% of their service points and 64.3% in the ad court, two numbers that are well above average.

Working through the same exercise for every point score gives us a list of “actual” serve points won, “expected” serve points won, and differences. The “actual” column tells us what really happened at that score, bias and all; “expected” tells us how often that particular set of players won service points during the entire matches in question; and the difference gives us a first look at where servers are over- or under-performing.

The following table shows these numbers for each point score:

Score  Actual  Expected  Difference  
40-AD   59.6%     61.4%       -1.8%  
0-0     63.3%     64.6%       -1.3%  
15-0    62.7%     63.3%       -0.6%  
40-30   61.6%     62.2%       -0.6%  
15-30   62.3%     62.7%       -0.4%  
30-0    64.7%     65.1%       -0.3%  
40-40   62.6%     62.8%       -0.1%  
0-15    63.2%     63.3%       -0.1%  
                                     
Score  Actual  Expected  Difference  
40-15   64.6%     64.5%        0.0%  
30-15   62.8%     62.7%        0.1%  
AD-40   61.6%     61.4%        0.2%  
30-30   64.0%     63.6%        0.4%  
0-30    65.9%     65.2%        0.8%  
15-15   64.8%     64.0%        0.8%  
30-40   63.6%     62.2%        1.4%  
0-40    66.1%     64.7%        1.4%  
15-40   66.9%     64.5%        2.4%  
40-0    67.7%     64.3%        3.4%

The scores at the top of the table are the ones where we would expect servers to win more points. At the bottom of the list are those where the server seems to overperform.

Some of the results lend themselves to easy narratives. Servers really focus at 0-40 and 15-40, while returners know they have more break chances coming. 40-AD (ad-out) seems like a stressful time to serve, and the numbers back that up. Other results are a bit more baffling–shouldn’t 30-30 and 40-40 be the same, since they are logically equivalent? Why are servers performing so well at 30-40 if they ultimately struggle at 40-AD?

And to today’s topic: What about the first point? It ranks second only to 40-AD in how much the server underperforms, despite no obvious reason why it should lean one way or the other.

Second to none

When we consider a few more factors, this first-point underperformance has an even greater impact.

One useful way to measure the importance of a point is with win probability. Given any point score (or set/game/point score), combined with the likelihood that the server will win any given point, you can calculate the probability of a hold (or a match victory). If we assume that the server wins 64.2% of points, he’ll hold 81.6% of the time, so his win probability at the beginning of the game is 81.6%.

* 64.2% was the rate in non-tiebreak games at the 2021 US Open, while the overall rate for this 2019-21 dataset is a bit lower.

The next concept is volatility. A point’s volatility is determined by how much the result could swing the win probability. By winning the first point, the server’s win probability rises to 89.7%, the figure for such a server at 15-love. If he loses, it falls to 67.2%. The difference–22.5%–tells us how much is at stake in that single point.

In volatility terms, the first point isn’t particularly crucial. A 22.5% swing far outstrips, say, the 9.3% volatility at 30-love, but it pales next to the 76.3% volatility at 30-40. When the server faces break point, one swing of the racket can determine whether win probability drops to zero (because he loses the game), or bounces back north of 50% (because he gets back to deuce).

What the first point of the game gives up in volatility, it wins back in volume. The stakes are never higher than at 40-AD, but at the US Open in the last few years, barely one-fifth of games ever get that far. By contrast, there’s a love-love kickoff in every single game.

By combining volatility and volume with the degree to which servers under- or over-perform, we can put together a top-level view of what players are gaining or losing at each point score.

Multipliers gone wild

In a tour de force of mathematical derring-do, I’m going to take these three numbers and multiply them together.

The “difference” from the previous table tells us how much better or worse players are serving at a specific point score, compared to their overall performance. If two differences are similar, the one that matters more is the one with higher volatility, right? So we multiply by volatility. And all else equal, the more often a situation occurs, the greater its impact on the end result. So we multiply by the number of occurrences in the dataset.

The final tally is volatility * occurrences * difference, cleverly dubbed “V*O*D” in the table below. The product of three percentages is tiny, so I’ve multiplied those figures by 10,000 to make the results easier to read.

Here are the results:

Score  Volatility  Occurrences  Difference  V*O*D  
40-AD       76.3%          22%       -1.8%  -29.9  
0-0         22.5%         100%       -1.3%  -29.2  
15-30       44.9%          34%       -0.4%   -5.8  
15-0        16.5%          50%       -0.6%   -4.9  
40-30       23.8%          26%       -0.6%   -3.6  
40-40       42.5%          43%       -0.1%   -2.6  
0-15        33.2%          50%       -0.1%   -2.3  
30-0         9.3%          27%       -0.3%   -0.9  
                                                   
Score  Volatility  Occurrences  Difference  V*O*D  
40-15        8.5%          24%        0.0%    0.1  
30-15       20.7%          34%        0.1%    0.6  
AD-40       23.8%          22%        0.2%    1.1  
40-0         3.0%          16%        3.4%    1.7  
30-30       42.5%          32%        0.4%    5.9  
0-40        31.4%          16%        1.4%    7.1  
0-30        40.0%          27%        0.8%    8.2  
15-15       29.4%          46%        0.8%   11.0  
30-40       76.3%          25%        1.4%   26.3  
15-40       49.0%          24%        2.4%   28.2

With all factors taken into account, we see that servers are giving up about as much on the first point of the game as they are when faced with nerves at 40-AD. Two point scores also stick out at the other end of the spectrum, where 30-40 puzzlingly continues to be a time when servers find their best stuff.

Exploiting the mundane

The exact V*O*D numbers are far (far!) from natural laws, but when I ran the same algorithm on data from other grand slams, the contours were nearly the same. In the 2017 and 2018 US Opens, for instance, 40-AD and 0-0 were again the standout “underperforming” points, and 0-0 was the one that topped the list.

* I took a rudimentary look at this topic very early in the blog’s history, using data from 2011. 0-0 didn’t stick out to the same degree, but I didn’t control for the deuce/ad difference, as I have today. When accounting for deuce-court strength, 0-0 performance looks relatively worse.

All of which is to say: I can’t explain why this is a thing, but it sure looks like it’s a thing. And if it’s a thing, it looks like an opportunity for savvy players and coaches.

I’m perfectly happy to accept that servers struggle to maintain their focus (and perhaps their ability to surprise) at 40-AD. More importantly, I’m sure that players and coaches are very aware of the necessary mental gymnastics so deep in a game.

On the other hand, there’s no good reason that servers should underperform at the start of every game. In fact, I’d be more ready to accept the idea that servers would have the edge. The opponent hasn’t seen a serve for a few minutes (or more), and the server’s arm is (relatively) fresh. While it’s not a recipe for domination, it sounds like a recipe for a tiny edge that the server can build on.

That’s why I believe there’s something to be exploited here. Perhaps players–or at least some of them–are taking a bit off their first-point first serves, using the opening salvo as a mini-warmup. Maybe they are more willing to hit their second-best serve, or aim to the returner’s stronger side, as a tactical move to set up more effective serves later in the game. As I’ve said, I don’t know why the numbers are turning up this underperformance, but it’s clear there’s a gap to be closed.

There’s no magic in the first point, but there’s an awful lot of value. Players who serve up their best stuff at the beginning of the game are getting an edge that their peers ought to be developing, too.

The Best at Getting Better

Here’s a stat you probably didn’t know*. Since the restart, the WTA top five in first-serve points won are Naomi Osaka, Serena Williams, Ashleigh Barty, Jennifer Brady, and … Maria Sakkari.

** unless you’ve been listening to me podcast lately.

The first four names are to be expected: Osaka, Williams, and Barty are probably the top three offensive players in the game, period, and Brady makes her money with big serving. Sakkari is the one who stands out. She does many things well, but I would never have thought to put her in this group, ahead of the likes of Karolina Pliskova, Aryna Sabalenka and, well, everybody else.

Sakkari’s first serve might be the best-kept secret in the women’s game, in large part because it hasn’t been around to keep secret for long. When she started playing tour events, her serve was quite weak, and it has only gradually improved since then. That’s what I marvel at. In six seasons at tour level, all with at least 18 matches played, here are her rates of first-serve points won:

Year     1st Win%  
2016        58.6%  
2017        59.7%  
2018        63.7%  
2019        65.2%  
2020        66.5%  
2021        69.9%

This probably doesn’t need further explanation. Fewer than 60% of first serve points isn’t very good, 70% is excellent, and improving from one to the other is a massive accomplishment. But in case you’re not convinced, here’s the same progression along with percentile rankings, showing that Sakkari started her career better than only 13% of her peers, and this year is outperforming 93% of them:

Year     1st Win%  Percentile  
2016        58.6%          13  
2017        59.7%          20  
2018        63.7%          53  
2019        65.2%          67  
2020        66.5%          79  
2021        69.9%          93

Players can and do improve, but they usually retain the same relative strengths and weaknesses throughout their career. The Greek star has broken that mold, and there’s a natural follow-up question: Has there been anyone else like her?

Meet Kiki

Here’s the simple filter I used to identify players who had substantially improved this aspect of their game. For every player with a full season in which they won fewer than 60% of first-serve points (almost exactly the 20th percentile), I identified those who eventually recorded a full-season in the top half of WTA players, roughly 63.3% or better.

From 2010 to 2021–yes, an awfully short span, due to the limited availability of historical WTA match stats–112 different players posted a sub-60% season. 26 of them went on to an above-average year. One example is Carla Suarez Navarro, who won 59.0% of first-serve points in 2010, and peaked at 64.0% (56th percentile) in 2016. That’s a respectable progression, but far from Sakkari’s standard.

Here are the 10 players who improved on a sub-60% season to eventually manage a season of 65% or better, ranked by the best level they attained:

Player       Weak   1st%  %ile  Strong   1st%  %ile  
K Bertens    2015  59.5%    18    2019  71.9%    97  
M Sakkari    2016  58.6%    13    2021  69.9%    93  
D Kasatkina  2017  59.0%    15    2021  66.4%    78  
S Halep      2012  56.4%     3    2014  66.4%    78  
Y Shvedova   2011  59.4%    17    2016  66.1%    75  
A Cornet     2011  58.9%    14    2020  66.1%    75  
M Linette    2016  59.9%    21    2020  65.8%    73  
Y Wickmayer  2012  60.0%    22    2017  65.8%    72  
A Sasnovich  2016  58.4%    11    2018  65.1%    67  
S Stephens   2011  59.7%    19    2015  65.0%    66

Kiki Bertens wasn’t quite as bad as Sakkari at her worst, but she wasn’t getting much benefit from her first serve. Like the Greek, she had back-to-back seasons below 60%, but unlike Sakkari, her improvement was instant. She leapt from sub-60% in 2015 to almost 68% (86th percentile) a year later. You won’t be surprised to hear that her ranking catapulted upwards as well, from 104th at the end of 2015 to 22nd a year later.

Kiki’s several years since also bode well for Sakkari. Her first-serve winning percentage of 67.4% last year was her worst since crossing the 60% barrier. A slightly less optimistic story comes from Simona Halep, whose 78th percentile mark in 2014 remains her career best. Coming from such an abysmal starting point, it’s remarkable that Halep has improved as much as she has, but she remains firmly in the range of good-but-not-great in this dimension of her game.

Steady improvements

There’s no particular advantage to spreading out one’s gains over a half-decade, like Sakkari has. If she had been given the option of picking up eight percentage points in a single year, like Bertens did, she would’ve taken it.

Still, the fact that the Greek keeps marching upwards is what makes her ascent so fascinating to me. In the decade-plus of data available, no other woman has improved her first-serve win percentage for five years running. Only two players–Yulia Putintseva and Saisai Zheng–have enjoyed positive bumps for four consecutive seasons, and neither situation really compares. Zheng’s improvement took her from 53.2% in 2015 to 59.3% in 2019, and Putintseva rose from 57.9% in 2017 to 62.4% so far this year. While both are making the most of what they have, neither has fundamentally transformed the type of threat they bring on court the way that Sakkari has.

In search of a better comparison–any comparison–with this five-year streak of gains, I turned to the more extensive set of ATP match stats, which go back to 1991. In those three decades, I found exactly 10 players who improved in this department for five (or more) consecutive years. It’s a decidedly diverse group, with a few names you might recognize:

Player            Streak  Start %ile  End %ile  
Renzo Furlan           6           2        73  
Slava Dosedel          6           2        16  
Julien Benneteau       5          16        55  
Arnaud Clement         6          18        70  
Michael Chang          5          18        92  
Roger Federer          5          47        94  
Thomas Enqvist         5          58        94  
Boris Becker           6          79        99  
John Isner             7          82        98  
Marc Rosset            5          87        98

The starting and ending percentiles indicate that this list includes players who began bad and ended a bit less bad, servebots who started great and eked even more out of their biggest weapon, and then a handful of Sakkari-esque figures who steadily went from considerably below average to far above it.

Michael Chang is the closest parallel of the group, even if we don’t have complete match stats for the first few years of his career. In 1991 he was one of the best returners in the game, but winning barely two thirds of his first serve points wasn’t enough to keep him in the top ten in an offense-dominated era. Five years later he was winning 77% of his first deliveries and ended the season at his peak ranking of #2. He couldn’t sustain the elite-level serving stats, but he did have a few more above-average years.

And then there’s Roger Federer. I’ll leave it to Sakkari fans to work out whether his presence on this list can tell us anything about her future.

Ave Maria

This is all just a long way of saying “wow!” There are other aspects of Sakkari’s game that she has improved, though none so consistently and dramatically. Once you start looking at year-to-year trends for individual stats, future projects start to multiply: identifying peak ages for different parts of the game, determining which stats are more or less likely to regress to the mean, finding which ones best predict ranking climbs, and so on.

We’ll get to some of those answers eventually. In the meantime, I’ll be watching Sakkari with new, better-informed eyes.

Jannik Sinner’s Missing First Serve Points

In Sunday’s Miami Open final, Jannik Sinner posted some very odd stats in his straight-set loss to Hubert Hurkacz. He won a respectable 48.4% of his second serve points–three points behind the the ATP top 50’s average since the restart–but only 55.3% of his first serve points. First serve points are the bread and butter of the offensive game, and Sinner got only as much out of that as Casper Ruud derives from his second serve.

It’s not that Hurkacz has magical anti-first-serve powers, either–it was only the second time since the restart that he won more than 40% of first-serve return points. He barely won 30% against Denis Kudla in the Miami first round.

Sinner’s first serve is not typically so ineffectual, but that isn’t to say it’s particularly good. While the tour wins well over 70% of its first-serve points, the Italian won only 63.5% in the quarter-finals against Alexander Bublik (another man who would never be confused with Andre Agassi), and 64.6% in his semi-final match with Roberto Bautista Agut. In both of those contests, he held on to 57% of his second serves–an outstanding mark for a player’s weaker offering.

I keep returning to second-serve points won and the difference between firsts and seconds to emphasize that Sinner is doing a lot of things right. Winning so many second-serve points suggests that he understands the tactics that go into playing service points when the ball comes back. Yet he hardly reaps any extra benefits from landing his first serve.

If it looks like a clay-court specialist…

I calculated the difference between first-serve and second-serve points won–let’s call it WinDiff–for every men’s tour-level player-season between 2000 and 2021 with at least 15 completed matches. That gives us almost 2,500 data points. At one extreme is 2019 Sam Querrey, who won over 80% of his first serve points but only 47% of his seconds, for a WinDiff of 33.2 percentage points. At the other end is Juan Carlos Ferrero 2011 campaign, when he won 65.5% of his firsts and 57.0% of his seconds, for an 8.5-point WinDiff.

Querrey’s season was mediocre and Ferrero’s was pretty good, suggesting that there’s a sweet spot somewhere in the middle. Yet it’s possible to have outstanding seasons near either end of the spectrum. Last year, Alexander Zverev’s WinDiff was 32 (77%/45%), and he won 28 of 39 matches. And in 2008, a young Rafael Nadal had a WinDiff of 11.5 (71.9%/60.4%), which was good enough to give him his first year-end #1 ranking.

Finding Ferrero and Nadal in Sinner’s neighborhood starts to give us an idea of what kind of players have low WinDiffs. Out of 2,460 player-seasons, only 33 had smaller WinDiff’s than Sinner’s 11.4 percentage points for 2021 so far, and you might be able to identify a few common traits among the players who posted narrower gaps:

Yoshihito Nishioka, Juan Monaco, Filippo Volandri, Potito Starace, Flavio Cipolla, Albert Montanes, Pablo Cuevas, Diego Schwartzman, Damir Dzumhur…

Clay courters, short guys, Italians… you get the idea. Ferrero and Nadal offer profitable career paths for Sinner, but I’m not sure that “be like Rafa” is practical advice for anyone, no matter how talented.

Room for improvement?

When I mentioned the extreme stat from Sunday’s final in my Expected Points podcast yesterday, I concluded on an optimistic note. Sinner is 19, he just reached a Masters final, he’ll continue to work on his first serve, and as we’ve seen, the rest of his game is already top-notch.

But does the data bear out such a rosy outlook? Are there players who have emerged from the purgatory of a low WinDiff to get more out of their first serves?

The average WinDiff of the top 50 since the restart is about 21.5 points. The bad news is that only a few low-WinDiff players eventually reach that level. The good news is that a disproportionately weak first serve is apparently correctable, or–at least–the stat is noisy enough that some players regress toward the mean.

Going back to my set of 2,460 player-seasons, the 5th percentile was a WinDiff of about 14 points. 71 different players had at least one season below that threshold, and 20 of those guys have played at least 10 full seasons since 2000. Drawing the line at a decade’s worth of play is some serious selection bias, but if Sinner doesn’t stick around for another 7.5 seasons of 15 or more matches, that’s probably a sign of something else gone very wrong.

The following table shows those 20 players. For each, I’ve shown their highest single-season WinDiff since 2000 and the average across their 21st-century career. Remember that tour average is a bit above 20 points, and Sinner’s 2021 so far sits at 11.4.

Player                 Seasons MaxWD  AvgWD  
Juan Martin Del Potro       10  24.8   21.2   
Pablo Cuevas                11  22.5   20.0   
Fernando Verdasco           17  23.0   20.0   
Albert Montanes             15  24.1   19.5   
Philipp Kohlschreiber       16  23.9   18.2   
Juan Ignacio Chela          13  22.1   17.7   
Tommy Robredo               15  21.1   17.6   
Jarkko Nieminen             14  21.4   17.4   
David Nalbandian            12  22.2   17.1   
Fabrice Santoro             10  21.0   17.1   
Nikolay Davydenko           14  20.3   17.0   
Dudi Sela                   10  21.9   16.4   
Albert Ramos                10  19.6   16.3   
David Ferrer                17  19.2   16.2   
Juan Carlos Ferrero         13  18.3   15.1   
Mikhail Kukushkin           10  18.0   14.9   
Rafael Nadal                18  17.5   14.8   
Olivier Rochus              12  17.8   14.7   
Filippo Volandri            10  16.2   13.2   
Juan Monaco                 13  15.9   12.7

Juan Martin Del Potro offers the brightest path, if one can emulate the results without the injuries. His WinDiff as as 17-year-old tour newbie was roughly 13 points, but he quickly landed near tour average. Sinner isn’t nearly as tall, so a better comparison might be David Nalbandian, who didn’t win nearly as many first-serve points as his fellow Argentine, but held on to enough. It’s certainly easier to look at Sinner and imagine a Nalbandian-like future than it is a Monaco- or Volandri-like one.

Another reason for optimism is that Sinner himself has already posted a 21-point WinDiff season last year, and this year’s weirdness is in large part due to his improvement against second serves, not a drastic drop in first-serve effectiveness. Maintaining his 56.5% rate of winning second-serve points seems unlikely only because it is so good. If he can manage that, he can survive with a modest first delivery so long as it’s in his typical high-60s range instead of the mid-50s that proved his undoing against Hurkacz.

Finally, the clay-centricity of the list above might be reason to pause before pegging Sinner as an eventual #1. But it also suggests that the teenager is developing exactly the right kind of game to excel on dirt. For the next couple of months, Italian fans will have plenty to get excited about.

Hsieh, Errani, and a Match That Broke Everybody

In their third round match today at the Australian Open, Sara Errani and Su Wei Hsieh played 232 points. The fastest serve either one hit registered at 93 mph (149 kmh), Hsieh’s first serves averaged 85 mph, and Errani’s mean first serve speed was 75 mph. I use the word “mean” here as more than just a way to avoid saying “average” so many times.

The two veterans are crafty–dare I say tricky–players with an arsenal of weapons once the ball is in play. But the serve is mostly just a stumbling block to make the best of. Hsieh won 62 of her 115 return points, good for 54% of Errani’s serves. This is more impressive than it sounds–the Italian double faulted only four times today. It’s fairly common for a winner on the women’s tour to win more than half of her return points, but what makes this match so weird is that Errani did the same. She won 63 of her 117 return points, also a 54% clip.

About half of WTA losers fail to convert better than 50% of their service points. But only 2.4% of winners miss the mark. And there’s a huge gap between 50%–mediocre and survivable–and Hsieh’s 46%. A 46% rate of service points won translates to a 40% likelihood of holding. Coincidentally, that’s exactly what both players did, each hanging on to their service games in 6 of 15 tries.

I have the relevant stats for just under 25,000 tour-level, main draw women’s matches since 2010, and only about 80 winners–0.3%, or less than once per 300 contests–won service points at a lower clip than Hsieh did today.

** I say “about” because the stats I have from the early 2010s aren’t perfect. A match with 60% of return points won is a prime candidate to be a mistake. I checked these 80 for obvious errors, like matches with a small number of service breaks, but those numbers aren’t perfect either.

There’s no grand analytical insight to be gleaned from a match like this. It’s just a glorious oddity that reminds us how many different ways there are to win matches. (And to be honest, you only need to watch Hsieh for about 90 seconds to recognize that.) In that spirit, here’s some more trivia:

  • Since 2010, this is only the 12th Australian Open main draw match in which neither player won half of her service points.
  • The only AO match in which neither player won 46% of their service points was the 2018 third-rounder between Anett Kontaveit and Jelena Ostapenko. They both held about 45.5% of their points, and 68% of total games (17 of 25) were breaks.
  • There have been about 400 tour-level matches since 2010 in which neither player wins half of their service points. Before today, 21 of those involved Errani, and she won 17 of them.
  • The other players who have been involved in at least 12 such matches are Monica Niculescu (16), Alize Cornet (14), and Carla Suarez Navarro (13). Today was only Hsieh’s 5th appearance on the list.

Perhaps oddest of all, this the first time in four tries that Hsieh avoiding getting bageled by Errani. Last time they played, in Istanbul in 2017, the Italian won, 6-0 6-1, needing only 55 minutes and a total of 87 points. Errani was so on-form that day that she won a whopping 66% of her service points. Hsieh finally turned the tables, even if she still hasn’t figured out how to stop this dogged opponent from breaking her serve.

The Underhand Serve: When and Why?

An underhand serve functions in two ways–one short term, one long term. The short-term goal is to win a single point. Your opponent is standing way back, and the service equivalent of a drop shot could go for a 50 mile-per-hour ace. The long-term goal is to give your opponent something to worry about, perhaps distracting him or changing his return position for games, or sets to come. It’s not about winning a single point, but about slightly improving your odds in many future points.

In his second-round match yesterday against Ugo Humbert at the Australian Open, Nick Kyrgios opted for both. He unleashed the underhander twice, once at 40-love in his second service game, and again at 5-5, 40-30 in the fourth set.

The first dropper was on as meaningless a point as he could ask for. Kyrgios’s probability of winning a service game from 40-love is about 99.6% (really!), so the risk of losing the game after throwing away a point is essentially nil. He won the point with a backhand winner on his next shot, but the object of the exercise–assuming there was a tactical one, and I’ll give Nick the benefit of the doubt here–was more long-term oriented.

He delivered the second underarm serve on a much higher-pressure point. Kyrgios is still heavily favored to hold serve from 40-30, but he could be forgiven for feeling some nerves and wishing for a free point. This time he netted the underhand attempt and ended up winning the point after a (conventional) second serve.

A drop of data

When the underhand serve first started to go mainstream a couple of years ago, I updated the Match Charting Project spreadsheet to allow us to track these attempts. Counting the Kyrgios-Humbert match, we’ve now gathered the results of 35 drop-serve attempts across 20 different men’s matches. (We’ve recorded many women’s underhand serves as well, but most of those belong to Sara Errani, who has a different set of goals when she goes that route.)

35 points is awfully far from big data, but it is enough to get a taste of how a handful of players are deploying this unorthodox weapon.

The most common point score for an underarm serve is 40-love. Of the 35 attempts, 40-love accounts for 12 of them. Another 4 occured at 40-15, plus two more at 30-love, so roughly half of the recorded drop serves came with a service game more or less secured. A few of the remaining points were also relatively unimportant ones, like Daniil Medvedev’s underhander at love-40 toward the end of a 2019 US Open match against Hugo Dellien, and Alexander Bublik’s back-to-back tries at 0-5 and 1-5 in a tiebreak against John Isner.

Bublik is the major source of unimportant-point underarm serving. He’s responsible for 19 of the recorded points, 16 of which were at 40-love, 40-15, 30-love, or those two tiebreak points I just mentioned.

Inferring tactics

Since so many underarm serves are deployed at low-pressure moments, it’s tempting to conclude that players are thinking long term.

On the other hand, our handful of recorded underhand deliveries–even the ones on 40-love points–don’t skew toward the beginning of matches. We have two charted matches in which Robin Haase tried an underhander: a 2019 Budapest tilt against Borna Coric in which he made his first attempt in the third game, and a 2020 Davis Cup rubber when he waited until the 32nd game of the match.

Poster boy Bublik is inconsistent on this as well. Twice he has brought out the underhander in his second service game–once in the Newport match versus Isner, and another time the same summer in Washington against Bradley Klahn. Yet at the US Open against Thomas Fabbiano the same year, he didn’t unleash the secret weapon until 40-love in the 32nd game of the match.

I’ll admit, it might be foolish to try to detect the grand plan underlying the behavior of Alexander Bublik.

But it works!

Yeah, our 35 points make up tiny sample, but… the server won 27 of these 35 points! That’s 77%, and it includes underarm first-serve attempts that missed. When players had to hit a conventional second serve, they still won 7 of 10 points–a rate of second serve points won that any player would happily accept.

These numbers–cautiously as we must treat them–suggest that the underarm serve trend has plenty of room to run. The rare players who dare to risk ridicule are still only using the drop serve less than twice per match, and of course the vast majority of men on tour are never hitting them at all. The more common the underhand delivery becomes, the less effective it will be, but there’s a lot of space between the current drop-serve win percentage of 77% and the typical player’s success rate on serve. Tour average is around 65%, and only the most dominant servers exceed 70%.

As Bublik and friends have discovered, there’s little risk in mixing things up. Strong servers like him and Kyrgios have plenty of low-leverage opportunities to remind their opponents that surprises could be in store later in the match, when the stakes are raised. Our very early indicators suggest that where Kyrgios has gone, the rest of the tour could profitably follow.

Serving In an Empty Stadium

The pandemic offers a wealth of natural experiments. Ever wondered how the presence of fans affects players? Before last March, we were mostly limited to speculation, because fans were almost always there. The tours have made various compromises to keep the action going, so we have a wealth of data from all sorts of different scenarios–with or without linespeople, with or without towelkids, and of course, with or without fans.

The closest thing we have to a “pure” natural experiment concerning the effect on fans on tennis players is the 2020 US Open. Flushing Meadows is usually packed with spectators on most courts, while in 2020, it was empty save a handful of support staff. There are confounding variables aplenty, such as the aforementioned lack of linespeople (on most courts) and towelkids, and we also must keep in mind that players entered the 2020 US Open with less recent match play than usual. It isn’t a perfect natural experiment–such things are exceedingly rare–but it is better than tennis usually offers.

What should we expect from spectator-free tennis? One suggestion comes from Ben Cohen and Joshua Robinson, who found in August that both basketball and soccer players were shooting more accurately in empty stadiums:

NBA players are making a higher percentage of their free throws and hitting corner 3-pointers at rates the league has never seen. Soccer players are striking dead balls more precisely than they did before the pandemic. Without the distraction of screaming fans, one part of their games seems to have improved: shooting.

We can already speculate that tennis won’t be so clear cut. For one thing, there weren’t screaming fans before the pandemic. For another, everything in tennis is a tradeoff: If you’re serving more accurately, you might be tempted to try for a bit more power or aim closer to the corners. The “accuracy” effect, then, wouldn’t show up as accuracy, but as increased speed, or some mix of several measures. But let’s not rush to throw in the towel (as it were)–let’s look at the numbers.

US Open, now and then

We’ll check four different stats for an empty-stadium effect: first serve in, double faults per second serve (the inverse of second serves made), first serve points won, and average first serve speed.

For each stat, we’ll calculate averages for men and women from 2019 and 2020 US Open single main draw matches, adjusted for player. (I’m using the data available in my slam_pointbypoint GitHub repository.) That is, we’ll limit our focus to those players who appeared in both tournaments and weight each player’s effect by the year they played the least. A player who served 300 points in 2019 and 100 points in 2020 will have a weight of 100 points in both calculations; a player who served 250 points in both years will have a weight of 250 points in both. This corrects for the different mix of players (and the amount that each player competed) in the two adjacent years, which might otherwise affect the numbers in a misleading way.

Here are the results:

WOMEN        2020   2019  Change  
First in    61.8%  61.5%    0.5%  
DF/second   13.7%  13.4%    2.0%  
First won   66.4%  62.2%    6.6%  
First KM/H  158.6  155.2    2.1%  
                                  
MEN          2020   2019  Change  
First in    61.7%  59.5%    3.7%  
DF/second   10.7%  11.3%   -5.4%  
First won   72.9%  71.2%    2.3%  
First KM/H  186.2  184.8    0.8%

The women didn’t really improve their accuracy: a slight uptick in first serves in, and a bigger decrease in second serves made. On the other hand, they won way more of their first-serve points in 2020 than in 2019, and they served 3.4 KM/h faster. That puts the accuracy figure in perspective–no, they didn’t make more first serves, but it appears that they traded speed for accuracy. They did quite well in the bargain.

The men, on average, took a different approach. They made more first serves and committed fewer double faults (Alexander Zverev notwithstanding), but they didn’t increase their first serve speed as much. Men also won more first serve points, though their gain was not the enormous boost seen by the women.

Improvements in context

Based on these year-to-year comparisons, it looks like both men and women served better without spectators. The women’s giant boost in first serve points won suggests that there are other factors beyond those we can easily measure–perhaps players were missing first serves at a typical rate not only because they were hitting harder, but also because they were aiming for the corners. It’s also possible that post-restart rustiness affected returns more than serves–in lockdown, it’s easier to drill your own serves than to keep in practice against elite-level first serves.

Another consideration is the usual year-to-year fluctuations. For women, the small changes in first serves in and second serves missed are less than half the magnitude of the year-to-year changes at the US Open between 2015 and 2019. These numbers will always drift up and down for a variety of reasons, sheer randomness not least among them.

The 6.6% jump in the women’s rate of first serve points won, on the other hand, is quite unusual. The average fluctuation in the previous four pairs of years is 1.7%. The serve speed increase is also unusually large. It’s a 2.1% jump, compared to a typical movement of about 0.7%.

The 2019-to-2020 changes in men’s rates are less noteworthy in context, even if they do tell a suggestive story. The rate of first serves made is surprisingly noisy, fluctuating an average of 2.7% in each pair of years between 2015 and 2019, so the fans-to-no-fans shift of 3.7% doesn’t prove much of anything. The double fault and serve speed changes are no greater than previous fluctuations.

The only slightly convincing “pandemic effect” on the men’s side is the percentage of first serve points won. As we’ve seen, men won 2.3% more such points in 2020 than in 2019, adjusted for the mix of players–an increase half-again as large as the typical fluctuation of 1.5%. That’s hardly a slam-dunk case for better post-restart serving. It could be pure luck, or it could be attributed to a mix of the many confounding variables I’ve already mentioned.

Serving isn’t shooting

This stuff is complicated. Penalty kickers in soccer have an objective that is clear to all–to score a goal. While tennis servers have a similarly simple aim–to win the point–the only part of the point they can completely control is the serve, and given the tradeoffs between speed, precision, and keeping the ball in the box, there’s no single variable that tells us whether a player is serving better.

Things get even hairier when we look for data beyond the US Open. We could do the same exercise for the last few years of French Opens, but remember that the post-restart Roland Garros had a sprinkling of paying fans. Is that halfway between an empty stadium and normalcy? Is it worse than a full stadium, because individual voices are easier to discern? Is it a mix, because the French fans filled up the stands for their native players and left other courts empty? I have no idea.

It is clear that women served harder than usual at the 2020 US Open, and they won way more first serve points than in recent years. Men served more accurately, even if their success rate didn’t translate into the same whopping success than the women’s adjustments did. What we can’t say for sure is how much of those shifts can be attributed to the empty stands in Flushing last year. Even the purest natural experiments don’t always return bulletproof findings.

Charting Aryna Sabalenka’s Win Streak

Aryna Sabalenka has won 3 titles and 14 matches in a row. Let’s dig into the data and see if we can identify any improvements that would account for her success.

For the Match Charting Project, I’ve logged every shot of each of the Belarussian’s tour-level matches. (There are a few exceptions where I haven’t found video.) We’ll look at hard-court matches only today. With that constraint, we have 140 Sabalenka matches, dating back to early 2017 (including the current streak), and another 1,121 women’s tour-level contests over the same time period for reference.

Big serving?

Aryna always brings a powerful serve, but it remains a work in progress, at least tactically. The key metric for pure serve dominance is unreturned serves–quite simply, serves that don’t come back. While some are aces, they don’t have to be, and the distinction doesn’t really matter.

This first graph has a lot going on, but as I’ll use the same basic template for several more figures, it’s worth taking a moment to understand what we’re looking at. The two dotted lines show tour average rates of unreturned serves (the lower average is for all players; the higher one is for match winners), the thin jagged line shows Sabalenka’s rate of unreturned serves for each individual match, and the thicker red line shows her five-match rolling average.

Her five-match rolling average has been above 30% for the entire win streak. It’s not an unprecedented level for her, though–she sustained similarly high levels at various points over the last three years. (We should also be a bit cautious ascribing serve effectiveness to a player when the Ostrava, Linz, and Abu Dhabi courts might have been faster than average.) Consistently powerful serving has certainly helped Sabalenka’s cause, but it probably isn’t the whole story.

We might gain from breaking down Aryna’s serve effectiveness into first and second serves. First, let’s look at something else:

Serve plus one

There are two ways we could look at “serve plus one” effectiveness, and we’ll do both. First, let’s count Sabalenka’s opportunities to hit a second shot behind her serve, and see what percentage she puts away. (As with aces and other unreturned serves, the “winner” concept is a distraction: I’m counting second-shot winners together with shots that force errors. If you end the point, it doesn’t matter much whether your opponent touches the ball.)

The second figure shows us that, on hard courts, when women are faced with a second shot behind their serve, they finish the point about 20% of the time. Sabalenka’s career average is 28%. She far exceeded that over a string of four matches to finish Ostrava and start Linz, maxing out at 42% against Jennifer Brady in the Ostrava semi-final. Since then, her rate returned to roughly her (impressive) career average.

This measure is something of a “key to the match” for Sabalenka. When she converts at least 30% of second-shot opportunities behind her serve, she wins 91% of her matches. When she doesn’t, she wins 62%. Of course, 62% is nothing to be ashamed of, and the dip visible in early 2020 coincides with her Doha title, the one time in her career that the five-match rolling average fell below 20%.

Serve plus serve plus one

These first two measures are related, of course. A big server should post good numbers in both. But a great “pure” serving day might mean a worse-looking serve-plus-one day, because fewer weak returns are coming back at all. The reverse holds as well: A strong server might not hit as many unreturned serves as usual because her opponent is managing to just barely put them back in play–easy sitters for second shots.

To identify the combined benefits of good serving and efficient serve-plus-one’ing, we simply count how often Sabalenka wins service points in two shots or less.

We’ve already seen the two components of this, so there are no surprises here. The typical player wins about 40% of her service points this way, and Aryna has historically averaged 46% on hard courts. This number looks as good for her recent winning streak as we’d expect. But as with the previous graph, it suggests weakness during her 2020 Doha title, so the predictive power here is limited.

First and second serves

The combined metric of unreturned serves plus second-shot putaways gives us a good snapshot of when the offensive game is working. Let’s break down the previous graph into first- and second-serve specific numbers:

These track the overall numbers. Aryna has generally been good lately on both first and second serves, but with neither one has she been more successful or consistent than in previous hot streaks. Second serves are particularly hard to rate because the per-match sample size is so small–fewer than 30 second serve points per player per match, and some of those end up as double faults.

Before moving on to the return game, let’s look at one more indicator of service-point success:

Longer points on serve

As I said at the outset, Sabalenka has always been a good server. While her current momentum might owe a bit to fewer mental lapses on serve, it would be logical to look elsewhere for an explanation, simply because there was more room to improve in other areas.

We’ve seen how her serve and second shot rate. What about serve points that go deeper? This metric considers all points where the returner’s second shot comes back, and then counts how often the server goes on to win the point.

The average hard-court WTA match winner claims almost exactly half of her service points when the rally reaches five shots. Over her career, Sabalenka has won 48%, worse than the typical match winner but better than the overall tour average.

Aryna has done better lately. To cherry-pick a starting point, she has won 51% of these points in her last 24 matches, dating back to the Doha second round. Her average over the first five matches in Abu Dhabi was 55%, the best she has managed since her breakout run in late 2018, when she pushed Naomi Osaka to three sets at the US Open and hoisted the Wuhan trophy a few weeks later.

Return winners

We’ll walk through the dimensions of her return performance in a similar manner, starting with return winners (and point-ending non-winners), then on to “return-plus-one” putaways, followed by the combination of the two.

First, return winners. I use the number of point-ending return winners divided by in-play serves–that is, excluding double faults.

Veronika Kudermetova had a rough day last Wednesday, so Sabalenka’s current five-match rolling average is as high as it’s been since early 2018. Apart from that last-minute burst of return dominance, her recent return winner rates look a bit like the serve stats: consistently solid, if not spectacular.

Return plus one

How about when the serve return doesn’t finish the job? This “return plus one” metric counts opportunities when the server puts her second shot in play and measures how often the returner hits a winner or forces an error with her own second shot. The sample sizes are a getting a bit small here (each player has 43 such opportunities in an average hard-court match), so the per-match rates are rather spiky:

The small single-match samples, combined with the relationship between return-plus-one and return winners–almost interchangeable ways to respond successfully to a mediocre serve–render conclusions a bit tough to come by. Sabalenka was average by this measure in Ostrava, great in Linz, and all over the place in Abu Dhabi.

Short return points won

Will things be clearer when we combine both methods of quickly winning a return point?

Aside from a weak return performance against Elena Rybakina in Abu Dhabi, Sabalenka has been comfortably above average in this metric in every match since she faced Victoria Azarenka in the Ostrava final.

Like “serve plus one,” this is a good indicator of overall success for the Belarussian. If we use this metric to split her 140 charted hard-court matches in half, the dividing line is 27.5% of return points won with a return winner or a return-plus-one putaway. Above that mark, she has won 62 matches, or 88.6%. Below it, she has won only 41, or 58.6%. She was above the line in nearly all of her matches in Linz and Abu Dhabi, and she sat at 25% or higher in every round of her 2020 Doha triumph, clearing 30% in three of five matches there.

First and second serve returns

Has she been particularly devastating against first or second serves? Let’s see:

Few women feast on second serves the way Sabalenka does, and she’s been particularly relentless of late. The typical tour player wins about 30% of second-serve return points with a first- or second-shot putaway, and over her last 15 matches, Aryna has won 41% that way. 41% is a respectable total percentage of return points won against many servers, and Sablaenka would be winning that many even if she refused to hit more than two shots per rally.

Granted, Sabalenka doesn’t hit that many fifth or sixth shots. How does she fare when her return points extend that far?

Long return points

You’ll be glad to know that the code for this final* graph didn’t throw any divide-by-zero errors–Aryna has played at least one “long” return point in each of her hard-court matches. This metric tallies up all return points in which the server puts her third shot in play, then calculates how often the returner won the point.

** Yes! It’ll be over soon!

This is another spiky mess, with an average of only 20 points per match. Still, if we’re looking for a category in which Sabalenka is newly excelling–not just thriving as usual–this could be our smoking gun.

Tour average for match winners on this stat is 46.7%. The server has an advantage by definition, because she has just put the ball back in play. The Belarussian’s career mark is 44.4%, only a bit better than the overall average. Yet in her last 15 matches, she has won 48.0% of these long return points, her best 15-match span since early in her career, when she faced a weaker mix of opponents.

I don’t want to overemphasize this: When there are only 20 points of this type per match, an improvement of 3.6 percentage points translates to a gain of less than one point per match. That doesn’t explain the magnitude of Sabalenka’s recent gains. But it does indicate that she is shoring up one of her few weaknesses, and in combination with her solid play on long serve points, it suggests that she no longer needs to rely on a one-two punch, even if her one-two punch is as dizzying as anyone’s.

Don’t make me say consistency

Tennis matches are decided by a handful of points: While Sabalenka has been dominant lately, she lost more points than she won against Coco Gauff in the Ostrava opening round. As such, improvements always look minor when we try to quantify them, if we can quantify them at all.

I’ve pointed out some areas where Sabalenka may be improving, others where a good statistical showing usually coincides with a W, and still others where an excellent performance doesn’t seem to matter much. All of these categories have one thing in common: She is putting up stellar numbers right now.

Remember, in the twelve graphs above (yes, twelve, sheesh), the dotted yellow lines indicate the average performance of match winners. In every single one of the categories, Aryna’s five-match rolling average is above that line. Every single one! In most cases, it has been above the line for some time.

It doesn’t take any statistical savvy to see that if a player is better than the average match winner in every category, she’ll be awfully tough to beat. The rest of the Australian Open field can only cross their fingers that Sabalenka’s current form won’t survive two weeks of quarantine.