Author: jsackmann

Tomas Machac’s Defiant Angles

Tomas Machac at the 2023 US Open. Credit: Hameltion

2024 is quickly turning into the year of Tomas Machac. The 23-year-old Czech reached his first grand slam third round in Australia, straight-setting Frances Tiafoe for a first top-20 win. A quarter-final showing in Marseille and a defeat of Stan Wawrinka at Indian Wells earned him a place in the top 60.

Now, in Miami, he has dispatched top-tenner Andrey Rublev and outlasted Andy Murray for a place in the fourth round. The live rankings place him precariously in the top 50; tomorrow’s match against fellow second-week surprise Matteo Arnaldi give him a chance to make it official. While Jiri Lehecka, a year younger and considerably higher in the rankings, is the poster boy for the resurgence of Czech men’s tennis, Machac is right behind him.

The key to the Machac game is a compact, versatile backhand that seems capable of anything. Inside-out backhands are usually little more than a curiosity, a miracle of timing that many players don’t even bother to try. The Czech hits one in ten of his backhands that way. Against Rublev, he cracked five: one for a winner and two more that forced errors. He won all five.

The tactics that surround Machac’s backhand are a joy to watch. Since he doesn’t serve big, every point threatens to become a rally. But the Czech angles for court position like a much bigger hitter. He approached the net 35 times in yesterday’s Murray match alone. Counting the times he was forced to come forward as well, he played 48 points in the forecourt, winning 38 of them. Combined with a court-widening slice serve, the net play makes Machac just as much of a threat on the doubles court. With Zhang Zhizhen, he reached the semi-finals in Australia and won the title in Marseille. He and girlfriend Katerina Siniakova would make a dangerous mixed duo at the Paris Olympics.

The unknowns that could limit Machac’s ceiling are, well, everything else. His forehand is a bit hitchy and it is nowhere near as effective as his backhand. By my Forehand Potency metric (FHP), he earns barely any points off that wing, ranking among the likes of Adrian Mannarino and Mikael Ymer.

And then there’s the serve. While he is capable of firing bullets–one of his serves in Australia registered at 128 mph (208 kph)–he rarely goes that route. His first serves in Miami have hovered around 110 mph, so he sets up points with slices wide, especially in the deuce court. He manages a respectable ace total thanks to a well-disguised delivery and the surprise that comes from his occasional bombs down the T.

The Machac serve is not a liability, exactly, but it is not the standard first-strike weapon for a prospect in today’s men’s game. Let’s take a closer look.

Lean right

Aside from keeping an eye on the radar gun while watching Machac’s progress in Miami, I don’t have a lot of data to put his serve speed in context. The only available point-by-point serve speed data these days comes from Wimbledon and the US Open, where the Czech has played just two career main-draw matches.

At Wimbledon last year, Machac’s first serves clocked an average of 115 mph (184 kph), faster than about one-third of the field. The Wimbledon gun might have been a little hot, as most players scored better there than in New York, and by a wider margin than you’d expect from more serve-centered tactics. When the Czech played a match at the US Open in 2022, his average first serve speed was 107 mph (171 kph). Four-fifths of the field hit harder; most of the names in his part of the list are clay-courters. Presumably he has gotten stronger since then, so while 115 mph may be an overestimate, 107 mph is probably low.

These numbers confirm that the serve won’t hold him back too much. Some other men in the same neighborhood are Casper Ruud, Tommy Paul, and David Goffin. Neither Carlos Alcaraz nor Novak Djokovic averaged much faster than Machac on the Wimbledon gun last year, and they did just fine. The Czech has only a bit of ground to make up with the rest of his game, and Ruud offers one example that it can be done.

What makes Machac’s serve look so pedestrian is the frequency with which he spins wide serves in the deuce court. Against Murray yesterday, he hit 54% of his deuce-court firsts to the wide corner. Fewer than 40% went down the T, and most of the remainder were also to the forehand side. He was even more extreme in the ad court, spinning 61% of those first serves down the T to the opponent’s forehand.

60/40 sounds rather undramatic, like most tennis stats. But few men favor one direction so strongly, at least until they reach critical situations like break point, when they lean more heavily on their favorite angle. Machac tries to balance it out by aiming for the backhand with his second serves, though by a slightly narrower margin. That does the job: The gap between his first- and second-serve results is about the same as tour average.

In the deuce court, at least, the tactic is working. Against Murray yesterday, Machac won 18 of 22 (82%) when his first serve went wide, though he was nearly as successful down the T. Against Rublev, he won 13 of his 14 wide deuce-court first serves. Understandably, he didn’t hit many deuce-court serves anywhere else. When Murray broke back yesterday to keep the third set alive, it wasn’t the serve itself that let Machac down. Twice at deuce, the Czech missed first serves when he tried to go down the T. His wide second serves drew weak replies on both occasions, but he lost both points with unforced errors.

The dis-ad-vantage

Wide serves in the deuce court are a gamble. You let your opponent take a swing at a forehand–probably his preferred wing–but you pull him out of position. Clearly it can work. Few men rely more heavily on their forehand than Rublev does, yet Machac attacked that side at every opportunity.

Murray was cannier and kept things much closer than Rublev did. But even he was fighting a losing battle. Machac won 80% of total first-serve points in the deuce court yesterday, compared to 69% in the ad court. So far, the Czech’s opponents have been more like Murray than Rublev, but still, the serve-to-the-forehand gamble pays off.

While he likes to aim for the same wing in the ad court as well, Machac doesn’t get the same court-position advantage. Across ten matches logged so far by the Match Charting Project, he has won 78% first-serve points in the deuce court against 71% in the ad court.

The difference lies largely in what Machac can do with his plus-one shot. In the deuce court, he wins about half of first-serve points with his serve or plus-one. In the ad court, that number falls below 40%. 50% is excellent: Djokovic hardly does better than that, and even an imposing server like Ugo Humbert does worse. But 40% is dire. Only clay-courters win so few short first-serve points overall. There’s less room to put away the second shot when you’ve left the returner standing in the middle of the court.

There’s nothing inherently wrong with a split between deuce-court and ad-court results. If asked, most players would probably prefer to win more points in the ad court, since most break points start in that direction. But the effect of winning more break points is mostly cancelled out by earning fewer break chances in the first place. Anyway, Machac doesn’t have any particular problem saving break points. He survived 13 of 15 against Murray. At tour level since this time last year, he has saved 64.5% of break points faced while winning 65.5% of serve points overall. That’s a closer margin that most players can boast.

The deeper we dig, the more we find weaknesses and unusual preferences in Machac’s game. Paired with each one, it seems, is a way in which it could work to his advantage. So far, he has succeeded despite the oddities. His results against Rublev and Tiafoe suggest that stronger competition might not break the spell, though the demands of yesterday’s gutbuster with Murray makes me wonder if brainier competition will raise the bar.

As the men’s game gets ever more powerful, there is less room at the top for playing styles that break the mold. Machac has already hinted that he can counterbalance brute force with the right set of angles, especially if they create opportunities for him to deploy his top-tier backhand. Countryman Radek Stepanek cracked the top ten with his own brand of unorthodox unpredictability. Machac has a different set of quirks, but based on his rapid progress this year, he may be able to do the same.

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More About Drop Shots: Alexander Bublik Edition

Alexander Bublik in 2022. Credit: Getty

If Carlos Alcaraz is the prince of the drop shot, Alexander Bublik is the court jester. We learned this week that Bublik hits droppers more than any other tour regular, about once every 14 points. That’s three times as often as tour average. No one else goes to the well more than once per 19 points.

Persistence aside, Sasha’s results are mixed: He wins about 45% of those points. That’s unimpressive compared to the ATP norm of 54%, and it’s particularly weak next to Alcaraz’s mark of 62%. Assuming that drop shots are, on average, hit from a neutral rally position, one in which each player has a 50% chance of winning the point, Bublik costs himself 3.3 points per thousand with his drop shot. In the last decade, only Benoit Paire has been worse.

On the other hand, the number rests on a big assumption. Alcaraz excels from the baseline; Bublik relies more on his serve. For any given situation–say, 5th stroke of a second-serve point, ball coming to the backhand side–Carlitos probably has a better chance of winning it, drop shot or not. Indeed, based on Match Charting Project data, Alcaraz wins 52% of points from that position. Bublik manages only 46%.

That’s typical. Here are the six situations in which Bublik hits the most drop shots, broken down by whether he is the server or returner, whether it’s a first- or second-serve point, the stage of the rally, and whether he’s faced with a forehand- or backhand-side shot. The table shows the probability that he wins the point if he doesn’t hit a drop shot:

Sv/Ret  Serve  Shot  Side  Exp W%  
Sv      1st    3rd   FH     57.4%  
Ret     2nd    4th   BH     42.8%  
Sv      2nd    3rd   FH     48.2%  
Sv      1st    3rd   BH     51.6%  
Ret     2nd    4th   FH     42.5%  
Sv      2nd    3rd   BH     46.1%  
Ret     1st    6th+  FH     42.2%

Only two of these scenarios favor Sasha: Plus-one forehands and plus-one backhands behind a first serve. Just about anything else and he’s the underdog.

Here are the same six situations, with expected point winning percentages for Alcaraz:

Sv/Ret  Serve  Shot  Side  Exp W%  
Sv      1st    3rd   FH     60.7%  
Ret     2nd    4th   BH     51.5%  
Sv      2nd    3rd   FH     57.3%  
Sv      1st    3rd   BH     54.1%  
Ret     2nd    4th   FH     53.6%  
Sv      2nd    3rd   BH     50.7%  
Ret     1st    6th+  FH     55.1%

When Carlitos opts for a drop shot, he’s trading in what’s already a positive expectation for one that he hopes is even rosier.

Repeat this exercise for every situation in which Bublik has hit a drop shot, take a weighted average, and we find that had he not hit drop shots, he would have won 46.5% of those points. With that in mind, his 45.4% drop-shot winning percentage doesn’t look so bad.

The recalculation doesn’t tell us that Bublik’s drop shot is good, but it does make the tactic look more viable. We’re assuming that in the aggregate, all shot opportunities with the same profile (i.e. second-serve point, ball to the backhand for the fifth shot of the rally) are about the same. That’s just an approximation, so a gap of one percentage point could occur because Sasha chooses lower-percentage moments to hit the drop. There’s even a sliver of evidence that he does so: Eight of his charted drop shots are backhands on the seventh shot of the rally or later of his own first-serve points. Those sound like desperate efforts to finish a point he’s given up on, and sure enough, he lost all eight. Take those out of the equation, and his win percentage on drop shots is exactly the same as when he hits something else.

Drops in expectation

Go through the same exercise for every player, and the drop-shot leaderboard takes on a different look.

Some players, like Kei Nishikori and Nicolas Jarry, win a very high percentage of drop shot points and exceed expectations by a wide margin. Others, like Alcaraz, see less of a benefit from their drop shot, in part because their other options are so good. Still others, like Daniil Medvedev, win more than half of drop-shot points, but because of the rest of their game and the moments they choose to deploy the drop, they may be sacrificing some points when they do so.

Call the new stat Drop Shot Wins Over Expectation, or DSWOE: the ratio of drop-shot success rate to non-drop-shot winning percentage, taking into account the situations in which the player chooses the drop.

Among the 60 players with the most charted points since 2015, here’s the top of the list–the men who gain the most per drop shot–along with a few notable names in Bublik’s section of the list, plus the most extreme laggards:

Player                       Drop W%  Exp W%  DSWOE  
Nicolas Jarry                  65.3%   50.4%   1.30  
Lucas Pouille                  60.3%   48.1%   1.25  
Kei Nishikori                  68.1%   54.5%   1.25  
Sebastian Baez                 63.2%   50.9%   1.24  
Richard Gasquet                60.7%   50.0%   1.22  
Kevin Anderson                 53.8%   44.6%   1.21  
Reilly Opelka                  52.1%   43.5%   1.20  
Marton Fucsovics               58.2%   49.5%   1.18  
Alejandro Davidovich Fokina    59.3%   50.7%   1.17  
Roger Federer                  59.5%   51.4%   1.16  
Robin Haase                    54.7%   47.8%   1.14  
Frances Tiafoe                 54.6%   48.0%   1.14  
Pablo Carreno Busta            58.9%   52.2%   1.13  
Dominic Thiem                  57.1%   50.7%   1.13  
Carlos Alcaraz                 62.1%   55.7%   1.12  
Rafael Nadal                   61.5%   55.4%   1.11  
Andy Murray                    55.7%   50.5%   1.10  
…                                                    
Holger Rune                    51.4%   51.3%   1.00  
Grigor Dimitrov                47.7%   47.9%   0.99  
Alexander Bublik               45.4%   46.5%   0.98  
Daniil Medvedev                53.0%   54.8%   0.97  
Novak Djokovic                 50.8%   52.9%   0.96  
…                                                    
Stan Wawrinka                  45.3%   48.9%   0.93  
Milos Raonic                   38.0%   41.3%   0.92  
Benoit Paire                   42.9%   46.8%   0.92  
Tommy Paul                     47.0%   51.5%   0.91  
Aslan Karatsev                 39.0%   49.9%   0.70

Surrounded by names like Rune and Djokovic, Bublik doesn’t seem so bad. Alcaraz, on the other hand, doesn’t stand out as much. He and list-neighbor Rafael Nadal are outrageously good in rallies whether they hit a drop shot or not. Even a world-class drop shot is only so much better than a standard Rafa or Alcaraz topspin groundstroke.

Tour average is around 1.05, meaning that the typical player does a bit better when they hit a drop shot than they would have had they chosen a different shot in the same situation. That tells us something that we probably suspected: Players are generally good at choosing the right moment to unleash the drop.

With this more fine-grained notion of expectations, we can re-calculate the number of points per thousand that each player gains or loses from drop shots. It is a function of both success rate (relative to expectations) and frequency. Nishikori and Jarry get great results from the drop but employ it rarely; men like Alcaraz and Sebastian Baez gain more points overall because they hit droppers so much more often.

Here are the players who gain the most points, along with the five tour regulars at the bottom of the list:

Player                       Freq%  W% - Exp%  DPOE/1000  
Sebastian Baez                3.9%      12.3%        4.8  
Alejandro Davidovich Fokina   5.2%       8.5%        4.5  
Lucas Pouille                 2.9%      12.2%        3.5  
Carlos Alcaraz                5.4%       6.4%        3.4  
Richard Gasquet               2.8%      10.8%        3.0  
Robin Haase                   3.9%       6.9%        2.7  
Kei Nishikori                 2.0%      13.6%        2.7  
Frances Tiafoe                3.2%       6.6%        2.1  
Pablo Carreno Busta           2.8%       6.7%        1.9  
Nicolas Jarry                 1.2%      14.9%        1.8  
Fabio Fognini                 3.7%       4.7%        1.8  
Andy Murray                   3.3%       5.2%        1.7  
Dominic Thiem                 2.6%       6.4%        1.7  
Marton Fucsovics              1.9%       8.7%        1.7  
Roger Federer                 2.0%       8.1%        1.6  
…                                                         
Novak Djokovic                3.3%      -2.1%       -0.7  
Alexander Bublik              7.2%      -1.0%       -0.8  
Lorenzo Musetti               5.1%      -2.3%       -1.2  
Aslan Karatsev                1.2%     -10.9%       -1.3  
Benoit Paire                  5.4%      -3.9%       -2.1

Five (or 4.8) points per thousand might not sound like a lot, but it represents the difference between Baez having a place in the top 20 and residing well outside of it. Alcaraz still grades well here, if not as much as he did before making all of the adjustments. Bublik scores closer to neutral too. His drop shot is probably more useful for earning him highlight-reel screentime than it is for winning points, but it isn’t hurting him that much.

Side matters

Armed with these adjustments, we can compare each player’s forehand and backhand drop shots, as well. Bublik has a fairly wide split. He wins just over 50% of points when he hits a forehand drop shot, next to only 39% behind a backhand drop shot. His expectations when faced with a backhand are worse in general, but not that much worse. His forehand drop shot success rate is two percentage points better than if he went with a standard groundstroke, while his backhand drop shot is five points worse.

So Sasha, if you’re reading this: We all love your drop shots. But maybe take it easy with the backhands.

The best forehand drop shots, compared to how the player would have fared with a different shot, belong(ed) to Kevin Anderson, Sebastian Baez, Lucas Pouille, Marton Fucsovics, and Nishikori, with Roger Federer not far behind. The most effective backhand droppers are those of Jarry, Reilly Opelka, Pouille, John Isner, and Richard Gasquet. “Expectations” is the key word for Opelka and Isner: They didn’t win a lot of points once a rally was underway, so a moderately good drop scores very well by comparison.

Here is the field of 60 regulars from the last decade. As usual, top right is good, bottom left is… yikes, Aslan Karatsev.

There are innumerable way to divide these numbers even further, and I know you’re tempted. But with drop shots, there is only so much data. Some of the outliers here, like Jarry and Anderson, are probably a bit aided by luck. Men who don’t hit many drop shots might only have a few dozen attempts on their weaker side. The standouts probably are better than average, but limits of our data lead us to overstate their advantage.

At least with the forehand/backhand division, adjusted for how players would have fared with something other than a drop shot, we can get some hints as to how our faves can improve their games. Taylor Fritz has a strong backhand, and I doubt the points he’s losing with his backhand drop shot are making it any more effective. Alexander Zverev isn’t doing himself any favors with his occasional forehand droppers. Karatsev, well… not everyone can excel at everything.

Bublik, despite his negative numbers in the aggregate, has an effective forehand drop shot. With the power of his serve and forehand, he’ll continue to earn plenty of opportunities to use it. If he resists the urge to showboat on his backhand side, the court jester of the drop shot could continue to show off his touch and still earn a more coveted position in the tactic’s royal house.

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Effects and After-Effects of the Carlos Alcaraz Drop Shot

Also today: Wild cards and doping bans; Miami preview podcast

Carlos Alcaraz in the 2022 US Open final

It is not easy to analyze the drop shot. Players don’t hit it very often, they sometimes hit it from very favorable or very unfavorable circumstances, and the goal of the shot sometimes extends beyond winning the point at hand. We can point to someone who hits droppers well and seems to win a lot of points doing so, but how much is the skill really worth?

Carlos Alcaraz is the poster boy for the modern drop shot. He loves to hit it–possibly too much–and when he executes, it’s one of the most stunning shots in tennis. At the business end of his Indian Wells campaign last week, he went to the well seven times against Alexander Zverev, ten times against Jannik Sinner, and three more in the final against Daniil Medvedev. He won 11 of those 20 points. That doesn’t sound so impressive, but Alcaraz could hardly complain about the end result.

To get a grip on drop shot numbers, we have a lot of work to do. What is a good winning percentage? Do any players suffer because they hit the drop shot too much? Is there a lingering effect from disrupting your opponent’s balance? Finally, once we have a better idea of all that, how does Alcaraz stack up?

Drop shot basics

To keep the data as clean as possible, let’s be specific about which strokes we’re looking at. While one can hit a drop shot in response to another drop shot (a “re-drop”), and it’s possible to hit a drop shot from the net in reply to a short volley or half-volley, those aren’t typically what we’re referring to. There are probably players (starting with Alcaraz!) who are better at that sort of thing than their peers, but those low-percentage recoveries aren’t today’s focus.

In this post, when I say “drop shot,” I mean a drop shot from the baseline, excluding all shots from the net, including responses to earlier drops.

The Match Charting Project gives us over 4,600 men’s matches to work with since 2015. Those 750,000 points include almost 35,000 drop shots. That works out to a drop shot in about 4.6% of points. Or from the perspective of a single player, it’s 2.3%, 1 out of every 44 points. The player who hits the drop shot ends the point immediately (via winner or forced error) about one-third of the time, and 19% of the droppers miss for unforced errors. Overall, the player who hits the drop shot wins the point 53.8% of the time.

From the 60 players with the most charted points to analyze, here are the 15 who win the highest percentage of points behind their drop shots:

Player                       Drop Point W%  
Kei Nishikori                        69.6%  
Richard Gasquet                      66.2%  
Nicolas Jarry                        65.3%  
Sebastian Baez                       63.2%  
Carlos Alcaraz                       62.1%  
Rafael Nadal                         61.3%  
Lucas Pouille                        60.3%  
Roger Federer                        59.7%  
Alejandro Davidovich Fokina          59.3%  
Roberto Bautista Agut                58.9%  
Marton Fucsovics                     58.2%  
Pablo Carreno Busta                  58.1%  
Jannik Sinner                        57.7%  
Dominic Thiem                        57.5%  
Andy Murray                          56.7%

Alcaraz does well here! Despite the presence of Kei Nishikori at the top, the list is heavily skewed toward clay-courters. Drop shots are a more central tactic on clay than on other surfaces, which works in both directions: Clay-courters are more likely to develop good drop shots, and players who have dangerous droppers are more likely to succeed on dirt.

Another skill that contributes to a spot on the list is good judgment. Nicolas Jarry doesn’t hit many drop shots, so he is probably picking the ripest opportunities when he does. There’s almost zero correlation between frequency of drop shots and drop shot success rate. Call it the Bublik Rule. From the same group of 60 tour regulars, here are the top 15 ranked by frequency:

Player                       Drop/Pt  Drop Point W%  
Alexander Bublik                7.2%          45.4%  
Benoit Paire                    5.4%          41.7%  
Carlos Alcaraz                  5.4%          62.1%  
Alejandro Davidovich Fokina     5.2%          59.3%  
Lorenzo Musetti                 5.1%          50.7%  
Holger Rune                     4.8%          50.9%  
Sebastian Baez                  3.9%          63.2%  
Robin Haase                     3.9%          55.1%  
Fabio Fognini                   3.7%          54.7%  
Matteo Berrettini               3.5%          52.0%  
Nick Kyrgios                    3.3%          54.9%  
Andy Murray                     3.3%          56.7%  
Novak Djokovic                  3.3%          50.4%  
Botic van de Zandschulp         3.2%          51.4%  
Frances Tiafoe                  3.2%          54.1%

Bublik may be turning things around: In the Montpellier final last month, he attempted 18 droppers and won the point 14 times. For a consistent high-frequency, high-success combination, though, we’re back to Alcaraz. Only Carlos, Alejandro Davidovich Fokina, Sebastian Baez, and Andy Murray (barely) appear on both lists.

Here are all 60 players in graph form. The top right corner shows players who hit a lot of drop shots and win most of those points. The closer to the bottom, the lower a player’s success rate; the closer to the left, the fewer droppers he attempts:

As a percentage of all points played, Bublik wins the most behind his drop shot. But it comes at a cost, since he hits so many of them, often sacrificing points because of it. If we assume that each drop shot is struck from a precisely neutral rally position, meaning that the would-be dropshotter has a 50% chance of winning the point, Bublik is losing points by going to the drop shot so often.

That’s a big assumption, and it probably isn’t exactly true for Bublik, or for anyone else. But if we stick with that for a moment, we can combine frequency and success rate into one number. Take the difference between success rate and 50% (that is, the gain or loss by opting for a drop shot), multiply that by frequency, and you get the percent of total points that the player wins by choosing the drop. The resulting numbers are small, so here’s the top ten (and bottom five) list showing points gained or lost per thousand:

Player                       Drop Pts/1000  
Carlos Alcaraz                         6.5  
Sebastian Baez                         5.2  
Alejandro Davidovich Fokina            4.9  
Richard Gasquet                        4.5  
Kei Nishikori                          3.8  
Lucas Pouille                          3.0  
Pablo Carreno Busta                    2.3  
Andy Murray                            2.2  
Roberto Bautista Agut                  2.2  
Rafael Nadal                           2.0  
…                                           
Jo Wilfried Tsonga                    -0.8  
Feliciano Lopez                       -1.3  
Aslan Karatsev                        -1.3  
Alexander Bublik                      -3.3  
Benoit Paire                          -4.5

Reduced to one number, Alcaraz is our dropshot champion. Six points per thousand doesn’t sound like a lot, but to invoke the familiar refrain, the margins in tennis are small. Beyond the top five or ten players in the world, one single point per thousand is worth one place on the official ranking list. Stars of Alcaraz’s caliber are separated by wider gaps, but it’s still a useful way to gain some intuition about the impact of these apparently miniscule differences.

The after-effect

In the hands of someone like Carlitos, the drop shot is a reliable way to win points. But the impact can go further than that. All sorts of tactics–drop shots, underarm serves, serve-and-volley–can theoretically be justified by some longer-term effect. If your opponent is camped out six feet behind the baseline and you want him somewhere else, a drop shot will surely give him something to think about.

This is hard to quantify, to put it mildly. How long does the effect of a drop shot last? Does it decay after each successive point? Does it disappear at the end of a game? On the next changeover? Ever? Jarry might need to hit the occasional drop shot to remind his opponent that he can do it, but Alcaraz doesn’t even need to do that. Everybody knows he’ll dropshot them, so he’s probably in his opponent’s head even before he hits the first drop shot of a match.

The evidence is unclear. About two-thirds of drop shots are hit by the server. I looked at the results of points immediately after a point with a drop shot, points two points later, and all the points that followed within the same game. When the server hits the drop shot, his win percentage on those subsequent points is worse than his win percentage on other points throughout the match–that is, non-dropshot points that didn’t follow so closely after he played a dropper:

Situation          Win%  
Next point        63.3%  
Two points later  62.6%  
Same game         62.5%  
All others        64.2%

I suspect that the dropshot effect (if there is one) is swamped by all the other influences at work here. Droppers typically occur in longer rallies, which might tire the server. The server might go for a drop shot when he runs out of ideas, another thing that might go through his mind as he prepares for the next point. This seems to work against Alcaraz more than other servers:

Situation          Win%  
Next point        62.0%  
Two points later  62.1%  
Same game         63.2%  
All others        65.0%

The same pro-returner bias appears when we look at the results when it is the returner who goes for the drop shot. After seeing the numbers above, it’s tough to say that hitting a drop shot causes the higher success rate on subsequent points, but it is nonetheless a striking effect, especially for Carlitos:

Situation      Alcaraz W%     Tour W%  
Next point          44.0%       38.3%  
Two points later    41.8%       37.6%  
Same game           41.5%       37.9%  
All others          40.1%       35.8%

Whatever the mechanism here, it goes beyond “drop shot good, opponent confused.” More research is needed, and camera-tracking data would help.

Regardless of the after-effects (or lack thereof), the stats support the common contention that Alcaraz possesses a world-class drop shot. He might use it too often in some matches, and certainly there are individual situations in which he should have done something else. In the aggregate, though, the tactic is working for him. It produces more value than any other player’s dropper has done in the last decade. Tennis analytics is hard, but goggling at the game of Carlos Alcaraz is easy.

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Wild cards and doping suspensions

Simona Halep returned to action this week, thanks to a Miami wild card granted immediately after her doping suspension was reduced. Halep is well-liked, and there were few objections to her appearance in the draw. But Caroline Wozniacki, while careful to say she wasn’t specifically targeting Halep, said that she was against dopers getting post-suspension wild cards.

We’ve done this before. In 2017, Maria Sharapova returned from 15-month ban and immediately got a wild card to enter Stuttgart. The tennis world spent a few weeks in a dither about whether she’d get one to the French Open, too. She didn’t.

I wrote about the Sharapova situation at the time. I argued that Sharapova ought to get those opportunities. The reason I gave at the time was that it was better for the sport: She was one of the best players in the game, and fields would be more competitive with her than without her. Another reason is that without wild cards, it’s a long road back. Unranked after more than a year on the sidelines, a player needs to enter qualifying at ITFs, wait two weeks for those points to go on the official rankings (assuming they win!), and then use those rankings to enter (slightly) stronger events, with entry deadlines several weeks in advance of the tournaments themselves.

Climbing back up the ladder can take months. Is that part of the penalty? Is a 15-month suspension supposed to be 15 months of no competition, followed by 3-6 months of artificially weak, poorly remunerated competition? In team sports, this isn’t an issue, because coaches can put returning players in the lineup as soon as they’re ready.

As usual, the problem is that tennis doesn’t have unified governance. None of the various bodies in charge have an applicable policy. Sharapova was fine, and Halep will be fine, because stars get wild cards (if not as many as they would like), while lower-ranked players are stuck heading to Antalya to rack up ITF points. The discrepancy is particularly glaring in a case like that of Tara Moore, who missed 19 months but has been fully exonerated.

The WTA is apparently considering granting special rankings to players who have been cleared of doping charges or had their bans reduced, essentially treating them as if they are returning from injury. That’s better than nothing, but it wouldn’t address the more common scenario illustrated by Sharapova’s return.

I would go further and grant special rankings to any player returning from suspension. The term of the suspension is the penalty, period. Even better, and fairer to the field as a whole: Grant those special rankings in combination with a policy that restricts wild cards. For instance, Halep could have eight or ten entries into tournaments on the basis of her pre-suspension ranking, but no wild cards for her first year back. That way, individual tournament directors don’t need to re-litigate each doping ban, players have a predictable path to follow post-suspension, and superstars aren’t given any special advantages.

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Miami preview podcast

I had a fun conversation yesterday with Alex Gruskin, talking about my recent Iga Swiatek piece and previewing the men’s and women’s draws in Miami. Click here to listen.

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All Hail the Iga Swiatek … Serve?

Iga Swiatek at the 2023 US Open. Credit: Hameltion

There are a million things to praise about Iga Swiatek’s tennis these days. This puts commentators in a quandary, because her matches are often so short that there isn’t time to list them all. She is world-class at nearly every aspect of the game.

If there is an exception, it is her serve. While it is not a liability, it doesn’t appear to stand out as a weapon, and Swiatek continues to make technical tweaks to improve it. She doesn’t dominate first-serve points the way that Qinwen Zheng or Elena Rybakina does; she doesn’t pile up aces like Rybakina, Karolina Pliskova, or Aryna Sabalenka. The longer a point lasts, the more time she has to take control, so who needs a standout first strike?

A look at the bigger picture, though, tells us that Iga’s serve is just fine. She was broken just five times in six matches en route to her second Indian Wells title. In the last 52 weeks, she has held 81.6% of her service games, best on tour.

To quote myself when Alex Gruskin threw that stat at me a couple of weeks ago: Wait, WHAT?!

Here’s the top ten since Miami 2023:

Player              Hold%  
Iga Swiatek         81.6%  
Aryna Sabalenka     79.4%  
Elena Rybakina      78.5%  
Caroline Garcia     76.4%  
Madison Keys        76.4%  
Petra Kvitova       75.8%  
Katie Boulter       74.3%  
Qinwen Zheng        73.2%  
Liudmila Samsonova  73.1%  
Maria Sakkari       73.0%

I can already hear everybody sputtering out their “yeah but” explanations, and we’ll get to some of them in a moment. First, though, we need to acknowledge just how elite this is. Sabalenka held at 80.8% last year, her best campaign so far. In 2015, when Serena Williams went 53-6 and won three majors, she held 80.9% of service games. Ash Barty peaked at 80.1%. Pliskova has twice cracked 79% for a full season, but never 80%. Same for Kvitova.

WTA match stats are sparse before the mid-2010s, so I don’t have numbers for Navratilova, Graf, Davenport, Venus Williams, and the rest. (Navratilova won 75% of total games in 1983, so… wow.) Suffice it to say, hold percentages that start with an eight are the province of all-time serving greats. Iga has muscled her way into that group.

The all-rounder

The simplest explanation of Swiatek’s serve stats is that she wins a lot of all kinds of points. As long as she doesn’t double fault, she’s in a rally, and she doesn’t lose many rallies.

This is true, sort of. In the last 52 weeks, Iga has won almost half of her return points, good for a break percentage of 49.5%. That leads the tour as well, granting her a spot in the hyper-exclusive Top One Club.

The average player in the WTA top 50 has a hold percentage about 33 points higher than her break percentage. Iga’s difference of 32 points, then, is not far from the norm. Despite winning so many service points, she is an entirely different sort of player than Rybakina (43 point gap) or Caroline Garcia (55 [!] point gap). Swiatek tacks an average serve onto a game that is otherwise outlandish.

On the other hand, it’s easy to underrate average. Most players who are extremely good at one thing are lucky if the rest of their game can pull enough weight to keep them on tour. The biggest servers are often indifferent (at best) on return; the best baseline players are rarely blessed with world-beating serves. Here are the current top ten returners among the top 50 (plus #52 Sara Sorribes Tormo), shown with their hold percentages and the differences between their serve and return results:

Player               Break%  Hold%   Diff  
Iga Swiatek           49.5%  81.6%  32.1%  
Lesia Tsurenko        48.1%  56.4%   8.3%  
Sara Sorribes Tormo   47.5%  58.4%  10.9%  
Clara Burel           45.4%  61.3%  15.9%  
Coco Gauff            44.7%  71.2%  26.5%  
Daria Kasatkina       44.5%  62.4%  17.9%  
Marketa Vondrousova   44.0%  68.7%  24.7%  
Jessica Pegula        43.1%  72.0%  28.9%  
Elise Mertens         41.0%  65.2%  24.2%  
Katerina Siniakova    40.2%  61.3%  21.1%  
Ons Jabeur            40.1%  67.0%  26.9%

If we approximate “serve-specific skill” as the difference between hold and break percentage, we find that the best returners are–unsurprisingly–generally weaker servers. Everyone on this list is below average in serve-specific skill. Among this group of elite returners, though, Iga is the best server. Only a few women–familiar names like Pegula and Gauff–come close.

Here is the relationship in visual form:

Iga clearly occupies a world of her own.

What works

One thing Swiatek does well is that she can hit her serve hard. At least year’s US Open, 40 different women had at least 100 first serves that landed in the box and registered on the radar gun. The top of the list are the names you’d expect: Sabalenka, Qinwen Zheng, Samsonova, Gauff, and Keys. Next up were Elise Mertens and… Iga Swiatek. Iga’s average first serve was a rounding error away from Keys’s and just 2.5 km/h slower than Gauff’s.

Speed matters, obviously. All else equal, a faster serve means more aces, more short points, and more service points won. The spin that Swiatek generates may make her first serves more difficult than the radar gun indicates, as well. When five-foot, four-inch Yulia Putintseva challenged the Iga serve at Indian Wells, she often found herself making contact at or above head level. Putintseva, I suspect, would have preferred to take on a flatter hitter like Samsonova, even if it meant handling a few more miles per hour.

Raw speed might also be underrated. When I dug into some ATP numbers to tease out the effects of speed and precision last month, I found that speed seems to matter more than accuracy. Equivalent data isn’t available for the women’s game (and the men’s data itself was exceedingly sparse), but it seems reasonable to assume that the relationship would be similar.

The relative effects of speed and precision are particularly important to Swiatek, because she hits a lot of her serves down the middle of the box. (Technically, those serves could still be “precise,” in the sense that they land close to the service line, but they won’t be as unreturnable as the equivalent deep serve close to a sideline.) Match Charting Project data tells us that the average WTAer hits 21% of their first serves down the middle. Iga comes in at 32%. Returners start the point on the back foot, even if they don’t have to move their back foot very far.

Swiatek gets away with all those down-the-middle serves, partly because she is better than her peers in general, and partly because she sacrifices less effectiveness than average by choosing a more conservative target. Here are her first-serve winning percentages by direction:

Direction   Iga W%  Tour W%  
Deuce-Wide     68%      65%  
Deuce-Body     64%      57%  
Deuce-T        74%      67%  
Ad-T           69%      64%  
Ad-Body        63%      56%  
Ad-Wide        69%      64%

(I use “down the middle” and “body” interchangeably here, because that’s how Match Charting Project logs are coded. Within tennis, the term “body serve” often refers to a narrower category of balls aimed directly at the returner. Iga hits some of those, but an awful lot of her serves–even her first serves–are neither that sort of body serve nor a delivery aimed at a corner.)

The average player gives up eight percentage points when they go down the middle. Iga sacrifices only six. It also helps to be so good in general. A winning percentage of 63% or 64% will keep you in a service game; 56% or 57% will put it much more at risk.

82%, here we come

One benefit of scoring so many points with down-the-middle serves is that it allows Swiatek to save the angles for when it matters most. It’s tough to pinpoint exactly what the key moments are for Iga, since her matches are often so lopsided. Serving at 4-all in the first set against Maria Sakkari yesterday, she built a 30-15 advantage with three first serves to the body. She served wide on the next point and down the T at 40-15. Neither one came back. She didn’t lose another game the rest of the way.

My hypothesis, based on watching her recent matches, was that this was a recurring pattern, that Iga goes to the corners more on key points and thus holds serve even more often than her serve-point success would indicate. But this is wrong, at least facing break points over the last 52 weeks. Since Miami last year, she has won 64.6% of serve points, but only 60.6% against break point. Most women save break points less often than they win other serve points, because break points tend to be generated by stronger returners. But a margin of two percentage points is typical. Iga’s four-point gap is not.

In fact, Swiatek was dreadful facing break point last year. A few years ago I built a metric to measure each player’s success rate at break point, comparing their break points saved to the number of points they’d be expected to win based on the other serve points played in those matches. By Break Points Over Expected (BPOE) in 2023, Iga was dead last among tour regulars. She faced 311 break points, and if she had served as well on those points as she did in the rest of those matches, she would have saved 184 of them. Instead, she saved 165, a difference of -19. No other top player had a negative result worse than -5.

Fortunately for the Polish star, this is the kind of clutch (or anti-clutch) performance that tends not to persist. Either it’s bad luck, or the choking turns out to be temporary. And indeed, in 2024, Swiatek has turned things around. She has saved 76 of 109 break points faced instead of the expected number of 66. She probably won’t sustain that level of break point overperformance, but even a neutral score would further improve her tour-leading hold percentage. If she could prove out my hypothesis and win more break points than expected by saving her best serves for those moments, she would head further into untouchable territory.

No one will ever mistake the Swiatek serve for the cannon of Sabalenka or Rybakina. But Iga’s overall game means she wins more points than the heavier hitters. Her serve doesn’t have to be great, it just needs to stick around tour average. She has achieved that, and–pity her poor opponents–there is room for her to improve even more.

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The Clutch Defense of Emma Navarro

Emma Navarro at the 2023 US Open. Credit: Hameltion

The dizzying rise of Emma Navarro continues. She finished 2023 at a career-high 32nd in the rankings, rose to 23rd before Indian Wells, and now, on the back of yesterday’s upset of Aryna Sabalenka, she could crack the top 20 on Monday.

Not long ago, many fans thought of Navarro as a vulture, riding a bunch of small-tournament victories to an inflated ranking. Now, with back-to-back wins over Elina Svitolina and Sabalenka on one of the sport’s biggest stages–and not on clay, her favorite surface–the doubters are quieting down. The American already ranks 19th on the Elo table, another list she’ll continue to climb when this week’s results go in the books.

Yesterday’s triumph was less straightforward than it looks at first glance. The scoreline–6-3, 3-6, 6-2–hides just how close it was. Navarro won just 83 points to Sabalenka’s 80. The second-seeded Belarussian lost the match despite winning return points at a slightly higher clip than her opponent. Sabalenka’s ratio of winners to unforced errors was 38:28, the type of attack that has won her innumerable matches, and one that looks better than Navarro’s 21:16.

The underdog appeared to be the clever, resourceful player on court, making improbable returns and outlasting her more aggressive foe on the long points. Yet the numbers don’t bear out much of that, either. 20 points lasted at least seven strokes, and each player won 10. Sabalenka won five of the longest eight. Navarro’s returning won the day, as we shall see in a moment, but it was not particularly impressive against a far-from-peak Sabalenka. In the last year, opponents have gotten 70% of Aryna’s serves back in play. Navarro managed 67%.

Despite all that, Navarro walked off court with a smile on her face. What worked?

Timing is everything

The top-level answer is that Navarro converted break points, and Sabalenka didn’t. The underdog seized four of her five chances. In each game that she generated a break point, she secured the break. Sabalenka, on the other hand, earned more opportunities but took advantage of just two. She squandered a chance to put the first set back on serve at 5-3, and she could have erased Navarro’s break advantage at 3-1 in the decider. In neither of those games did the American slip again.

Break points, like points in tiebreaks, tend to be more complicated than average. Servers are a bit more careful to put balls in the court–and thus more conservative–and returners are hyper-focused. A high-pressure point is less likely to end with an unreturned serve; long rallies are more common. Navarro–with some help from her opponent–took this to an extreme.

The American, despite putting slightly fewer serves back in play than Sabalenka’s average opponent, kept the point going on each one of her five break points. She also returned every serve at 15-30, three of four at 30-30, and both at deuce. Here’s how Sabalenka’s rate of unreturned serves looks when separated by whether she was in trouble–defined as whether Navarro had already won two points in the game:

Situation       Points  Unret  Unret%  
Not In Trouble      51     16   31.4%  
In Trouble          22      4   18.2%

Even that distinction understates things. Two of Sabalenka’s unreturned serves in the “in trouble” category came at 40-30. When the second seed was really on the ropes, Navarro got the ball back on 15 of 17 tries. Pressure points are less likely to end quickly, but not by such an enormous margin.

Whether Sabalenka became uncharacteristically shaky under pressure, Navarro morphed into a return savant, or it was pure dumb luck, those few points determined the outcome of the match. In extended rallies, as we’ve seen, the American was not the overwhelmingly superior player, but that’s not the point. Sabalenka dominates most of her opponents by winning more cheap points than they do. If she wins just half of the rest of the points–on her serve and her opponent’s–she comes out on top. Take away most of the cheap points, and her edge is gone. Navarro won 24 of 49 return points–roughly half–when she put the ball back in play. Because she was so resourceful at key moments, she held Sabalenka to just 54% of serve points at 30-all or later.

Lessons

There are so many ways this match could have ended differently. Sabalenka could’ve served a little better under pressure, or Navarro could have returned a little worse. The whole scenario was made more likely by the conditions, slow-playing Indian Wells courts and balls, combined with wind that distracted the favorite more than the underdog.

Another culprit on the Belarussian side was Aryna’s plus-one. Eleven of her unforced errors came on the first shot after her serve, many of them wild and inexcusable, one of them two points away from defeat. It is to Navarro’s credit that she got so many serves back, but a more typical Sabalenka performance would have put away more of the desperate returns.

This is all a description of what happened last night, not speculation about a trend, or any kind of prediction. Sabalenka usually hits about as many unreturnable serves in pressure situations as she does at other times. In the limited data we have so far on Navarro, there’s no evidence that she is much better returning at key moments. Clutch performance in tennis is only rarely persistent: It’s easy to identify matches or tournaments when a player was particularly good or bad when it mattered most, more or less impossible to forecast it. If we hit rewind and replayed the match from the start, Navarro might still pull the upset, but it wouldn’t develop the same way.

What the match does give us is a little more evidence that Navarro is here to stay. She drew even with the second-best player in the world, staying calm enough throughout the proceedings to deliver her best tennis when the stakes were highest. She might not win a rematch with Sabalenka, but her position in the top 20–whether or not the WTA makes it official next week–is no fluke.

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The Downward Slide of Stefanos Tsitsipas’s Backhand Return

Stefanos Tsitsipas ahead of the 2023 US Open. Credit: Hameltion

Yesterday in Indian Wells, Jiri Lehecka knocked out Stefanos Tsitsipas with a masterclass of precision power hitting. The Czech tallied 27 winners to Tsitsipas’s 8, and that’s only after a belated burst of energy from the Greek in the second set. When I wrote about Lehecka in January, I chided him for an “excess of self-restraint,” hitting too many balls down the middle to take full advantage of his baseline weapons. He avoided that trap yesterday, and Tsitsipas paid the price.

Still, Lehecka didn’t seize upon every exploitable edge. The Tsitsipas backhand, pretty as it is, is a bit cumbersome, often leaving him slow to react. The time he needs to unleash the one-hander is a key reason why Stef is one of the most surface-sensitive players on tour, preferring courts that give him an extra split-second to prepare. Indian Wells plays slow for a hard-court event, but it’s hardly the same as the Monte-Carlo dirt. Combined with Lehecka’s power, a hard court has the potential to expose the Greek’s weaker side.

Lehecka generally stuck to the routine, sending both forehands and backhands cross-court, rarely doing anything in particular to force his opponent to hit a backhand. Still, the Czech made one concession to his opponent’s tendencies: He hit more serves than usual to the backhand. Lehecka’s favorite serve is the deuce-court slider wide, and he scored a few points blasting balls that Tsitsipas’s forehand couldn’t reach. But more often, he forced Stef to hurry the backhand, or chip a return.

The results were devastating. The Czech typically hits about half of his serves to each wing. 51% of his first serves and 52% of his seconds go to the backhand. Yesterday, he went that way 61% and 58% of the time, respectively. When Lehecka hit a first serve to the backhand, Tsitsipas got it back less than 60% of the time… and he won only 12% of those points. When a second serve went to the backhand, Stef got a more respectable 71% back, but still won just 14%. It was a short match, so we’re not talking about that much action: In nine return games, Tsitsipas won just four points when he had to make a backhand return.

The word is out–not that it was ever really a secret. Two weeks ago in the Acapulco quarter-finals, Alex de Minaur hit 90% of his serves to Tsitsipas’s backhand, beating the Greek for the first time at tour-level in eleven tries. While de Minaur’s persistence was unusual, it made a useful point. Stef–not long ago the third-ranked player in the world–has fallen out of the top ten, and one of the causes is something that every opponent can attack until he patches it up.

Serve this way

Yesterday’s match notwithstanding, Tsitsipas remains an elite server. He held 88.8% of his service games last year, the best mark of his career. His return numbers, though, are sinking. In 2021, he broke one-quarter of the time; last year, that number fell to 19.3%. By that metric, he’s in the bottom third of the ATP top 50.

It’s hard to pinpoint just one element of his return game that has gone astray, because everything is trending downwards. According to Match Charting Project data, he gets 66% of serves back in play–a below-average if acceptable figure–but wins just 42% of those points, one of the lowest marks on tour. Both rates are worse than his career averages of 68% and 44%, respectively.

The decline can’t be entirely blamed on a tour-wide tactical consensus, though Stef’s opponents aren’t helping. Here is a ten-match rolling average of the percentage of first serves hit to the Tsitsipas backhand on hard courts since late 2018:

(Clay courts add another wrinkle to the question, because everyone tends to get more serves to the backhand side on dirt. Four of Tsitsipas’s five most extreme matches by this metric were on clay.)

As always, it can be tough to gain an intuition with an unfamiliar tennis metric. 60% may not sound like a lot, but most servers cluster around the tour average of 52.5%. The servers who most frequently target the backhand side are clay-courters: Albert Ramos tops the list at at 63.5%, with Fernando Verdasco right behind him. At the other extreme, around 45%, are some right-handers, often those who can use height and/or wrist action to open the court with lots of slice. Daniil Medvedev and Andy Murray are two of the best-known proponents of this approach, and Medvedev is partly responsible for some of the troughs in Tsitsipas’s trend line above.

More to the point, the tour is taking aim at Stef’s backhand as much as it does anyone’s. Only Ivo Karlovic was faced with more backhand returns on hard courts. Denis Shapovalov, another one-hander, is in the same range. Again, the message about Tsitsipas’s backhand isn’t new, but it’s no accident that servers are picking on it at the same time that his return numbers take a nosedive.

Crash

Anyone who doesn’t attack the Greek’s backhand return these days is leaving points on the table. Here is another ten-match rolling average, this one showing Tsitsipas’s rate of return points won when his opponent lands a first serve to his backhand:

If you’ll forgive me some technical jargon, that’s… not good.

As we’ve seen, Tsitsipas won just 12% of those points against Lehecka. He won only 14% against Taylor Fritz in Australia and 16% in Los Cabos against Casper Ruud. Daniil Medvedev held him to 11% last fall in Vienna. And at the Tour Finals, Jannik Sinner hit 21 first serves in that direction. Tsitsipas won none of them.

Across 125 career charted hard-court matches, Stef has won 23.1% of return points on first serves to his backhand and 24.7% to his forehand. Since the start of 2023, those numbers have fallen to 20.6% and 23.4%. Every important return stat is trending downward, and the backhand numbers are declining fastest of all.

The only question remaining for Tsitsipas’s opponents is this: How much is too much? De Minaur set a new standard by going to the backhand with 90% of his serves, both first and seconds. That’s not unheard of on clay courts (Lorenzo Musetti has come close in two previous meetings with Stef), but it’s very unusual on a hard court. Only a handful of Tsitsipas’s opponents have topped even 70% in one direction.

Against most players, such a balance is probably appropriate. Too much to one side, and you lose the element of surprise. But because so much serving is split 50/50 (or 53/47), we don’t have much data to test the hypothesis. If there’s a 30% chance the server will go one way, will a returner really have an edge in the more likely direction? Against de Minaur, Tsitsipas figured things out quickly enough and inched over toward the backhand side. But not for long: The Aussie cracked one of his few forehand-side serves for an ace, far out of Stef’s reach. Tsitsipas is a good test case for servers looking to experiment: His success rate when he gets the return back in play is near the bottom of the table, so he’s unlikely to turn a match around just because he guesses right a few times.

I have no idea whether, at this point in the Greek’s career, his backhand return is something that can be fixed. In the short term, it will be easier for opponents to expose it than it will be for him to find a solution. Tsitsipas’s return numbers, already dire, could get worse before they get better.

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Yuan Yue Will Return Your Serve Now

Yuan Yue at Wimbledon last year. Credit: si.robi

Here’s an impressive stat for you: Last week in Austin, champion Yuan Yue won more than half of the return points she played. In fact, had she picked up just one more point against Wang Yafan’s serve in the quarter-finals, she would have won at least 50% of return points in each of the five matches she played.

This isn’t earth-shaking stuff: There are about a dozen tournaments every year where the champion wins more than the 51% of return points than Yuan did in Texas. Iga Swiatek won 56% at the French; Aryna Sabalenka cleared 52% in Australia. Lauren Davis won 53% in Hobart last year. The average single-match loser on the WTA tour loses about half of their return points, so it’s not far-fetched that a titlist would rack up these numbers for five or six days running.

Still, this is Yuan Yue we’re talking about. Not only was the 25-year-old Chinese woman a longshot to win the title–it was her first on tour–she has hardly established a reputation as a steady returner. A dangerous one, perhaps: In last year’s Seoul final against Jessica Pegula, Yuan turned one out of six of the American’s deliveries into a return winner or forced error. But the overall results weren’t so impressive, as she won fewer than 40% of return points in the match. For all of those big swings, there were lots of swings and misses. Out of five matches in an otherwise encouraging week in Seoul, she won more than 46% of return points only once.

The game Yuan brought to Austin was something different. Like San Diego champ Katie Boulter, she took fewer risks than usual, trusting that she could win points a shot or two later. Facing Pegula, and in another losing effort to Emma Navarro in the Hobart semi-finals, Yuan’s average return point lasted four strokes. Against Wang Yafan on Friday, return points took six. Yuan hit just three return winners in that match; in the final against Wang Xiyu, she didn’t hit any. Presumably she’s ok with that.

The magnitude of Yuan’s achievement isn’t quite the same as Boulter’s: The Brit beat five opponents ranked in the top 40, and Yuan didn’t face anyone in the top 60. Yet the week marks a major step forward. The 25-year-old cracked the official top 50, and Elo now rates her as the second-best Chinese woman on tour. If she continues to put returns in play the way she did in Austin, she could climb even higher.

One more ball

Returns in play are good, but they come at a cost. Do you aim to stay in as many points as possible, accepting that a lot of your returns will be weak, or do you swing big, piling up errors in exchange for a handful of return winners and better odds when your returns find the court?

While the pros and cons are different for every player, no one escapes the tradeoff. Even across players, there is a persistent negative correlation between returns in play and in-play returns won. If you make more, you win fewer of them. The following plot shows those two numbers for every woman with at least five matches in the Match Charting Project dataset from the last 52 weeks:

The best place to be is the upper-right corner, with a lot of returns in play and a lot of those points won. Except… that sector is mostly empty. The women who get the most serves back–Kasatkina, Avanesyan, Sorribes Tormo–win those points at an average rate. Even that success rate is boosted a bit by the slower courts where those players tend to succeed. By contrast, the players who win the most in-play return points–Swiatek, Ostapenko, Yastremska–achieve that by missing a lot, or by being an all-time great. Even Swiatek doesn’t put an above-average number of returns in play.

With our new sense of what these numbers mean, let’s take another look at Yuan’s step forward. The limited data at hand includes five of her matches from before this week, which we can compare to the quarter-final and final from Austin. Here’s the same graph, but with points added for Yuan’s sample of previous matches (Yuan-Prev) and for the two in Austin (Yuan-ATX):

Um, yeah. Wow. There are caveats, of course: It’s just two matches, and neither Wang is a particularly stellar server. (On the other hand, Yuan’s previous opponents were middling servers as well.) If this shift is even a little bit sustainable, Yuan will no longer be just a fringe figure on tour.

Runaway momentum

While we’re extrapolating from too-small sample sizes, I’ll give you another one, one that doesn’t paint such a rosy picture for last week’s champion.

Break points go to the returner more often than return points in general, because more break points are generated against weaker servers (or by stronger returners, or both). The women currently ranked in the top 50 win 44.4% of their return points, and they convert 46.3% of break points.

Yuan, in 33 tour-level matches since this time last year, has won 44.3% of her return points, but only 43.2% of her break point chances. A gap of three percentage points (between 43% and the expected 46%) is statistical shorthand for too many missed opportunities. I checked those numbers only because the Austin champ, in both the quarters and the final, showed signs of letting momentum get away from her. Against Wang Yafan, she got broken right after securing the first set, then struggled to regain the advantage. In the final, she served for the title at 5-2 in the second set, dropping serve twice before finishing the job in a tiebreak.

As I say, these are small samples. We tend to ascribe too much importance to hot and cold streaks–they would arise even if every point were decided by a roll of the dice. (I suffered through an epic Chutes and Ladders slump yesterday, probably because of the clutch play of my four-year-old opponent.) Still, there’s some evidence that Yuan struggles under pressure, even if she overcame it several times last week.

In this context, there’s a bit of negative spin we can put on all those returns in play. I’ve written before that momentum (and clutch, and streakiness, all that stuff) is tough to measure in tennis because the structure of the sport is anti-streak. If you hit a good serve in the deuce court, you have to hit one in the ad court. Four aces in a row? Congrats, you get to do something else now–you might even have to sit down for a couple of minutes. And that’s to say nothing of your opponent’s ability to give you shots other than the ones you’re hitting well.

But against her compatriots last week, Yuan inadvertently created conditions in which streaks could take root. All those returns in play–combined with a fair number of longer points that developed on her own serve–reduced the separation between serve and return. From 5-2 in the second set of the final, Yuan’s backhand went awry, and there was little she could do to avoid it. Her own serve wasn’t imposing enough to end points quickly, and she was out of the habit of taking big cuts on return. It was easy to get into a rut.

The momentum eventually shifted, of course. Yuan won 12 of the last 15 points of her quarter-final, and in the final, she won 10 of 12 points from 5-6 in the second set to reach 6-1 in the tiebreak. She pried herself out of one pattern and immediately found a different one, one that still largely avoided short points but ended in her favor. Yuan’s conservative returning paid off on paper, but the unending string of long(ish) points may have made it harder for her to regain control on the few occasions that she lost it.

Yuan’s fellow champion last week, Katie Boulter, already stumbled at her next obstacle, losing a straight-setter yesterday in Indian Wells to Camila Giorgi. Yuan’s first test in the desert is Varvara Gracheva, a middling server who could prove susceptible to the Chinese woman’s improved game. Next up would be a tantalizing second-rounder with China’s number one, Qinwen Zheng. Zheng’s intimidating–if erratic–serve could tell us a lot more about just what Yuan is now capable of.

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Can Sebastian Baez Find Success on Hard Courts?

Sebastian Baez in Cordoba last month. Credit: jmmuguerza

Sebastian Baez is a marvel. In an era dominated by tall, all-court sluggers, the five-foot, seven-inch Argentinian has carved out a place on the circuit as a throwback clay-court specialist. Just a couple of months past his 23rd birthday, he has already won six tour-level titles and reached a new career-best ranking of 19th on the ATP computer.

The obvious comparison is Diego Schwartzman, another Argentinian on the small side who won titles and reached a French Open semi-final by grinding out victories and swinging above his weight. Schwartzman eventually cracked the top ten, but when he was Baez’s age, such a milestone looked extremely unlikely. When he turned 23, he stood outside the top 60, heading back to South America for another cycle through the continent’s late-season Challenger swing. He wouldn’t reach the top 20 for another two and half years.

If we assume Baez continues to improve throughout his mid-20s in the same way that Schwartzman did, a single-digit ranking seems achievable. He’s already 11th on tour in clay court Elo. Only a few players ahead of him on the official ranking table are younger.

The main stumbling block is the natural ceiling on dirtballers. There are far more ranking points available on hard courts than on clay, and one of the prime opportunities on the Argentinian’s favorite surface, in Madrid, plays fast because of its altitude. (Baez has competed there only once, losing in the second round last year to another sterling clay-courter, Stefanos Tsitsipas. Schwartzman never won more than two matches there, either.) For Schwartzman to gain a top-ten place, he needed more than a Roland Garros semi-final: He had recently reached indoor finals in Vienna and Cologne, and he was 14 months removed from defeating Taylor Fritz for a hard-court title in Los Cabos. Diego’s magic somehow worked on all surfaces. Even in a year when he posted outstanding results on clay, that was his only route to a single-digit ranking.

Baez owns one hard-court championship, from last year’s US Open warmup in Winston-Salem. But apart from that week, his story diverges from Schwartzman’s, with a career record on the surface of just 17-33. He has never won two completed matches at any other tour-level hard-court event. (His two third round appearances at majors were aided by retirements.) The Argentinian can be a star and a national hero without all-surface success, but surely he wants more. Can he achieve it?

Surface and speed

When I wrote about surface sensitivity a couple of weeks ago, Baez didn’t stand out as an extreme. Tsitsipas and Lorenzo Musetti were the men whose results were most dependent on slow courts. The numbers showed that Baez does better with a slower bounce, but the effect is less than half of what it is for Tsitsipas. The 23-year-old is more closely comparable in this department to Daniil Medvedev, who doesn’t like to play on clay–or eat it.

However, that analysis left out one major factor. I simply rated tournaments by the degree to which they helped servers end points quickly, regardless of surface. Indian Wells, on hard courts, came out as just barely speedier than Rome and slower than Madrid. Miami and the US Open were roughly equivalent to the Caja Magica as well.

Intuitively, there is more than one dimension to player preferences. Some men might just want more time to prepare, as could be the case with Tsitsipas and his one-handed backhand. But others–Baez among them–are much more comfortable on a certain type of surface, because of the type of bounce, the footing, or both. When we reduce surface type and speed to one variable, Baez and Medvedev come out equal. When we separate type from speed, they look very different.

This scatterplot shows 56 players on the two dimensions:

(The units are regression coefficients and essentially meaningless out of context. They do, however, show direction and magnitude of each player’s preferences.)

Among players with at least 100 tour-level matches since 2021, Baez ranks third in the degree of his preference for clay courts, behind Albert Ramos and roughly tied with Alexander Zverev. Once surface type is controlled for, he prefers faster courts. Santiago, where he won the title last week, is one of the quicker clay courts on the circuit, giving servers as many quick points as Wimbledon (really!). Rio de Janeiro, the site of his triumph the week before, is also faster than the average dirt, rating about the same as Indian Wells.

Medvedev is the exact opposite. Only Adrian Mannarino has a stronger demonstrated yen for hard courts. Once his choice of surface is secure, though, the Russian wants it as slow as possible. Only a few players (including Musetti and another slow-hard-specialist, Alex de Minaur) are so extreme.

Schwartzman–the model for a potential all-court Baez–prefers clay, and he likes all of his courts slow. His performance is even more speed-dependent than Medvedev’s, but his surface type preference isn’t nearly as strong as that of his younger countryman.

This is all rather abstract, and to some degree, it’s just a fancy way of saying that Baez struggles on hard courts. Let’s make things more concrete by looking at what happens when the Argentinian shifts to the tour’s more popular surface.

Translations

Hard-court tennis is more serve-dominated than the clay-cout variety. The typical tour regular wins, on average, 3% more service points on hard than on clay: 4% more first-serve points and 1% more second-serve points. They win 7% fewer return points. (That sounds like a paradox, since the serve and return numbers are different. The catch comes from specifying “tour regulars”–part-timers on hard courts have bigger serves than their equivalents at clay events.)

Here are the player-specific numbers for each man in the top 20 (except for Ben Shelton, who hasn’t played much on clay). The figures are ratios of each hard-court metric to the corresponding clay-court metric–serve points won, first-serve points won, and return points won–so the higher the number, the bigger the difference in favor of hard courts.

Player               SPW  1st SPW   RPW  
Ugo Humbert         1.10     1.08  0.95  
Novak Djokovic      1.09     1.11  0.91  
Alex de Minaur      1.08     1.08  0.99  
Daniil Medvedev     1.06     1.07  0.98  
Jannik Sinner       1.06     1.08  0.95  
Tommy Paul          1.06     1.08  1.08  
Grigor Dimitrov     1.06     1.04  0.95  
Holger Rune         1.05     1.06  0.92  
Taylor Fritz        1.05     1.09  0.93    
Alexander Zverev    1.05     1.03  0.89

Player               SPW  1st SPW   RPW  
Alexander Bublik    1.05     1.04  1.04  
Karen Khachanov     1.05     1.09  0.96  
Andrey Rublev       1.05     1.05  0.94  
Hubert Hurkacz      1.04     1.02  1.00  
Frances Tiafoe      1.03     1.05  0.95  
- ATP Regular -     1.03     1.04  0.93  
Carlos Alcaraz      1.02     1.02  0.92  
Stefanos Tsitsipas  1.02     1.03  0.89  
Casper Ruud         1.01     1.04  0.91  
Sebastian Baez      0.94     0.96  0.85

Baez is… different. Everyone in the top 20 wins more serve points on hard courts than on clay except for him. Only a few other men on tour have the same “backwards” split, and only Federico Coria is close to Baez in the degree of his weaker hard-court service performance. What costs the Argentinian even more is how his return numbers suffer away from clay. Almost everyone wins fewer return points on hard, but Baez takes the cake here too.

Perhaps needless to say, there’s no way that this can work. Baez wins about 62% of service points on clay, a respectable number and an impressive one for someone his size, but still below the average of a top-50 player on the surface. To win even fewer on hard suggests that he would struggle even at Challenger events. At Winston-Salem last August, Baez won 63.5% of his serve points and over 43% on return. That’s a combination that will win matches; he just hasn’t provided any evidence that he can pull it off once he crosses back out of North Carolina.

Growth rate

The one reason for optimism is that Baez is young, inexperienced on surfaces other than clay. Like Schwartzman, he grew up playing on dirt, and he rose through the rankings by winning South American Challengers, then picking up victories on the continent’s Golden Swing. Maybe there’s a necessary transition period?

Here are the same ratios as above, now by season for our two Argentinian heroes:

Player  Year   SPW  1st SPW   RPW  
Diego   2015  1.01     0.99  1.01  
Diego   2016  1.04     1.07  0.94  
Diego   2017  1.08     1.09  0.91  
Diego   2018  1.03     1.03  0.89  
Diego   2019  1.08     1.09  0.94  
Diego   2020  1.03     1.03  0.85  
Diego   2021  1.02     1.03  0.95  
Diego   2022  1.01     1.04  0.89  
Diego   2023  1.09     1.08  0.88  
                                   
Player  Year   SPW  1st SPW   RPW  
Baez    2022  0.91     0.94  0.82  
Baez    2023  0.96     0.99  0.88

Baez did close the gap between his hard-court and clay-court performances in his second year on tour. But he still shows a more marked surface preference than Schwartzman ever did. As soon as Diego arrived on tour, he was able to win more service points on hard courts–roughly the same ratio as the typical tour regular. Baez isn’t even close. Schwartzman had to retool his game to succeed on hard courts, and Baez will need to do so even more.

The 23-year-old truly is a throwback, an undersized grinder who spins in his serves, plays defense, and constructs points. It’s a joy to watch, and the package makes him one of the best players on tour for the 14 weeks or so each year when there are top-level clay events on offer. It doesn’t, however, work so well when there’s no dirt to kick out of his cleats. Fortunately Baez is young, and he has many years left to figure it out. He’ll need to.

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Katie Boulter’s Game of Patience

Katie Boulter in 2021. Credit: Chris Czermak

You can be forgiven if you didn’t have Katie Boulter on your radar going into the 2024 season. Her career-best ranking in the top 60 was a bit misleading, stemming largely from a debut title on the grass at Nottingham, where she picked up the championship without facing a single top-130 player. Nothing she can do about that, of course, but when it came to things she could control, the results were not always so encouraging. She wrapped up 2023, at 27 years of age, with a career total of just 25 hard-court victories.

Since then, it’s been a whole new Katie. She opened her campaign with an upset of 5th-ranked Jessica Pegula at the United Cup, and counting qualifying, she has won at least one match at six straight events. To solidify her new status, she won the title in San Diego last week, knocking out four seeded players in the process. Nothing cheap here: All five of her opponents were ranked in the top 36, and the weakest among them–Lesia Tsurenko–had won each of their three previous meetings.

After years in the ITF wilderness, relying on British grass-season wild cards for tour-level appearances, Boulter has earned a place in the WTA top 30. Thanks to the giant-killing in Southern California, her Elo rating backs it up, placing her 28th on tour, 26th on hard courts. The Brit has always had a first serve and forehand that made it possible to dream big. It has just been a matter of harnessing the big weapons and filling out her game with complementary parts that wouldn’t leave her exposed.

The results from San Diego suggest that she has finally done so. Commentators like to talk about the importance of playing “within” oneself, waiting for opportunities instead of swinging for winners when none are on offer. Boulter hasn’t always done that, and she has the unforced error totals to prove it. She found a better balance against last week’s barrage of top-40 foes, playing a bit more conservatively and cutting down mistakes without sacrificing too many winners. Now, she’s on everyone’s radar.

Katie bolt the door

Boulter ascended through the ranks with what might best be described as low-percentage tennis. In her 100+ matches on tour, she has landed just 57% of her first serves, racking up more double faults than aces. 13% of her groundstrokes are unforced errors, well above tour average. Her typical return point lasts just barely three strokes.

In twelve matches logged by the Match Charting Project before last week’s run in San Diego, a mixed bag ranging from ITFs in 2017 to her final-round victory over Jodie Burrage in Nottingham last year, her Rally Aggression Score worked out to 84, putting her in the same range as free swingers such as Caroline Garcia and Camila Giorgi. Against Burrage, her Rally Aggression Score was 267, a remarkable figure for a stat that I initially scaled so that it would max out around 100. Just about every possible shot–plus a few impossible ones–was a winner or unforced error. The average point in that match lasted just 2.9 shots.

It’s possible to win with numbers like these–just ask Aryna Sabalenka, Petra Kvitova, or Jelena Ostapenko. But the margins are slim. It’s particularly tough to thread the needle while making as few first serves as Boulter does. Surprisingly, she struggled on that front in San Diego, making just 54% of her first deliveries for the week, including a mere 51% against Emma Navarro in the semi-final. When only one-quarter of total points begin with your best shot, you can’t risk missing so much with the rest of your arsenal.

The Brit’s most effective step forward, especially against Kostyuk in Sunday’s final, was to keep herself in more return points. She has traditionally swung big on return, ending 11% of second-serve points with a return winner or forced error, and even finishing 6% of first-serve points that way. She didn’t sustain those numbers in the final, but the tradeoff was worth it. In those previous 12 charted matches, she put just 60% of first-serve returns in play, compared to a tour average closer to 75%. Facing Navarro, she kept the point alive on 65% of first serve returns; against Kostyuk, she put the ball back in play 79% of the time.

The result, more or less by definition, was longer return points. While the Burrage match was extreme, it is not uncommon for Boulter to average in the neighborhood of three strokes per point on return–still in Ostapenko territory. The San Diego semi was a wholly different animal, with her average return point lasting 4.5 shots. In the final, it was 4.1 shots. Such a radical shift would be a bad sign for many big hitters: Ostapenko and her ilk end points early because that’s the way they want to play. Yet Boulter thrived on her newfound patience.

The 27-year-old won 47% of her return points in San Diego, five percentage points better than her tour-level average and about the same as a typical performance from Pegula or Coco Gauff. On Sunday against Kostyuk, Boulter played 81 return points and won 40 of them.

Winners, slightly delayed

Even though she did not smack as many return winners as usual over the weekend, Boulter still won plenty of points from the baseline. She just took fewer risks in the process. Excluding aces and double faults, here’s a top-level comparison of the frequency with which she hit winners (plus forced errors) and unforced errors in her last two matches, compared with her previous charted matches and WTA average:

Match(es)    W+FE  UFE  
vs Kostyuk    14%   9%  
vs Navarro    19%   8%  
Previous      16%  13%  
WTA Average   12%  10%

The Navarro match was an unalloyed triumph, as you might expect from the 6-3, 6-1 scoreline. But even the Kostyuk numbers point to a major step forward. It’s not easy to cut down unforced errors from one side of tour average to the other, especially against someone like the Ukrainian, who feeds opponents an ever-shifting mix of speeds and depths. In the past, the Brit might have lost her rhythm and gone on an error spree. Instead, she was even steadier. On 28 key return points–game point, deuce, or break point–Boulter committed just one unforced error.

Facing women without the weapons to quickly end points themselves, Boulter discovered that a winner on the fourth or fifth shot of the point is just as effective, and less risky, than a big swing on the second or third shot. In her previous charted matches, she won about 49% of points that lasted four to six shots. Against Kostyuk, she won 76%, dictating play the way she has always preferred to do, just one or two shots later.

Presumably, it won’t always be quite this easy. Boulter won’t keep her unforced error rate in single digits forevermore; more aggressive opponents will tempt her into playing her old game. (Though the Brit did straight-set Donna Vekic in the quarters.) Still, she appears to have discovered new capabilities, seven years after her first appearance at Wimbledon. This year, she’ll likely return to the All-England Club as a seeded player, with all the expectations and pressure that entails. A decade into her pro tennis career, Boulter has earned herself a lot more attention.

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Alex de Minaur’s Adequate Inaccuracy

Alex de Minaur at the 2024 Australian Open. (Getty Images: Julian Finney)

Last week, Tennis Insights posted a graphic showing the average first serve speed and accuracy–distance from the nearest line–for the ATP top 20. There’s a ton of fascinating data packed into one image.

Hubert Hurkacz is fast and accurate, Novak Djokovic is nearly as precise, and Adrian Mannarino defies logic as always. The most noteworthy outlier here, especially just after his run to the Rotterdam final, was Alex de Minaur. The Australian gets plenty of pop on his first serve, hitting them faster than tour average, if slower than most of the other men in the top 20. This comes at a cost, though. As one of the shortest guys among the elite, he doesn’t hit the lines. He’s by far the least accurate server in this group:

Via @tennis_insights

Precision is great: It’s certainly working for Hurkacz and Djokovic. But everything is a tradeoff. Any pro player could hit more lines if there was no reason to serve hard. Or vice versa: If the goal was simply to light up the radar gun, these guys could add miles per hour by aiming at the middle of the box. Standing a modest six feet tall, De Minaur is even more constrained than his typical peer. No technical tweak is likely to move him into Hurkacz territory. He might make small improvements or swap some speed for more accuracy.

Small gains would be enough, too. De Minaur wins fewer first-serve points than the average top-50 player, but in the last 52 weeks, he has outpaced Carlos Alcaraz, Holger Rune, and Casper Ruud. He trails Alexander Zverev by about one percentage point. This isn’t Sebastian Baez (or even Mannarino) we’re talking about. Whatever the cost of de Minaur’s inaccuracy, he’s able to overcome it. It’s just a matter of what gains he could reap by making returners work a bit harder.

Here’s the question, then: How much does accuracy matter?

Speed first

For this group of players over the last 52 weeks, speed is by far the most important factor in first-serve success. Speed alone–ignoring accuracy or anything else–explains 72% of the variation in first-serve points won. Accuracy alone accounts for 43%. (The players who are good at one thing are often good at others, so most of those 72% and 43% overlap.) 43% might sound like a lot, but isn’t that far ahead of something as fundamental as height, which explains 33% of the variation.

Surprisingly, precision is even less critical when it comes to unreturnable first serves. Using unreturned serve counts from Match Charting Project data, accuracy explains just 30% of the variation in point-ending first serves, less than we could predict from height alone. (Speed alone explains 60% of the variation in unreturned serves.) I would have expected that accuracy would play a big part in aces and other unreturned serves, since a ball close to the line is that much harder to get a racket on. But while precision may increase the odds of any individual serve going untouched, average precision isn’t associated with untouchable serving.

The story is the same for any metric associated with first-serve success. Speed matters most. There’s immense overlap between the factors I’ve discussed: Taller players find it easier to hit the corners, and all else equal, they take less of a risk by hitting bigger. There is probably some value of height that isn’t captured by speed or accuracy, such as the ability to put more spin on the ball, but the main benefit shows up on the radar gun.

To tease out the impact of each variable, I ran a regression that predicts first-serve points won based on speed, accuracy, and height. The results should be taken with an enormous grain of salt, since we’re looking at just 20 players, some of them the game’s most outrageous outliers. Still, the findings are plausible:

  • Speed: Each additional mile per hour translates to an improvement of 0.43 percentage points in first-serve points won. (1 kph: +0.27 first-serve points won)
  • Accuracy: Decreasing distance from the line by 1 cm results in an improvement of 0.2 percentage points in first-serve points won.
  • Height: At least for these twenty players, the value of height is entirely captured by speed and accuracy. The margin of error for the height coefficient spans both positive and negative values. It is unlikely that height is a negative, though I suppose it’s possible, if speed and accuracy capture the height advantage on the serve itself, and height is a handicap on points that develop into rallies. Either way, the impact is minor, if it exists at all.

Approximately, then, one additional mile per hour is worth the same as two centimeters of accuracy. The height of the graph–110 to 130 mph–represents a variation of nearly 9 percentage points of first-serve points won. The width–70 to 52cm–represents a range of 3.6 percentage points. Broadly speaking, speed remains more important than accuracy, though a particular player might find it easier to improve precision than power.

Just one example of what the numbers are telling us: De Minaur has won 72.8% of his first-serve points over the last year, compared to the top-ten average of 75.3%. If this model were to hold true–a big if, as we’ll discuss shortly–that’s a gap he could close by improving precision by about 12 cm, to a tick better than tour average.

Drowning in caveats

For every question we answer, we’re rewarded with ten more questions.

I’m most interested in the choices that individual players could conceivably make, and the analysis so far offers only hints to that end. For this group of servers, we can say that a player who serves faster will win more points than his slower-serving peers. But we don’t know whether a specific player, if he was able to juice his serve by a mile or two per hour, would enjoy the same benefits. Hitting harder, or placing the ball more accuracy, is better, but by how much?

(I dug into the speed question way back in 2011 and found that one additional mile per hour–for the same player–was worth 0.2 percentage points. More recently, I found that for Serena Williams, an additional mile per hour was worth 0.5 percentage points. One of these days I’ll revisit the initial study with the benefit of many more years of data and perhaps a bit more wisdom.)

De Minaur was unusually precise in Rotterdam. Another Tennis Insights graphic indicates that his accuracy improved to about 55 cm for the week, an enormous gain of 15 cm from his usual rate, even more remarkable because his average speed was a bit quicker as well. (Playing indoors probably helped.) The model suggests that 15 cm is worth three percentage points. His boost of two miles per hour should have been worth nearly one more percentage point itself. Yet he won “only” 73.9% of his first-serve points–about one percentage point better than his non-Rotterdam average.

It’s just one week, so it isn’t worth fretting too much over the discrepancy. Still, it illustrates the value of the data we don’t have. (By “we,” I mean outsiders relying on public information. The data exists.) If we knew de Minaur’s accuracy and speed for every match, we could figure out their value to him specifically. Perhaps an uptick of one mile per hour is worth 0.43 percentage points only if you start serving like the players who serve faster–guys who are generally taller and can put more slice or kick on the ball. Those weapons aren’t available to the Aussie, so a marginal mile per hour may be less valuable. For him, accuracy might have a bigger payoff–relative to speed–than it does for other players. We just don’t know.

Sill, we’ve extracted a bit of understanding from the data. We’ve seen that accuracy translates into more first-serve points won, and we have a general idea of how many. De Minaur showed himself capable of hitting the lines as precisely as Andrey Rublev or Grigor Dimitrov, at least under a roof for one week. Just half that improvement, if he could sustain it–even if he didn’t get the full gains predicted by the model–would shore up a mediocre part of his game and lay the groundwork for a longer stay in the top ten.

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