Research – Heavy Topspin

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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Jelena Ostapenko In the Hands of Fate

Also today: Deciding tiebreaks, a MCP milestone, and assorted links.

*Jelena Ostapenko in 2023. Credit: Hameltion*

If you’ve ever spent five minutes watching Jelena Ostapenko play tennis, you know she’s as aggressive as it gets. She swings for the fences and sometimes knocks them over. Get her on a hot streak, and opponents can only hope its ends before the handshake. When she’s off her game, spectators in the first few rows duck for cover.

What you might not realize is just how aggressive she is. A few years ago I tuned Lowell West’s Aggression Score metric so that the numbers fell in a range between 0 and 100. In theory, 0 is maximally passive; 100 is go-for-broke, all the time. Ostapenko’s career Aggression Score in rallies is 175.

This sort of extreme style lends itself to all sorts of narratives. She can beat anybody, any time, as she showed when she won the 2017 French Open as an unseeded player, and again last year when she upset Iga Swiatek at the US Open–her fourth win in as many matches against the Pole. That makes her a perennial dark horse pick at majors. Even though she hasn’t reached a semi-final since 2018, neither Iga nor Coco Gauff–who exited the Australian Open after an Ostapenko barrage last year–would like her find her in their section.

(Sorry Iga: Guess who you might face in the quarters!)

Hyper-aggressive players also appear to be works in progress. Especially early in Ostapenko’s career, commentators would talk about her stratospheric potential if she could only improve her footwork, or play a bit more “within herself.” That is, not quite so many winners, not quite so soon, more point construction, fewer unforced errors. But players rarely change much, and as they age, they are more likely to become more aggressive, not less. The Latvian is now 26 years old, beginning her ninth year on tour. What you see is what you get.

What you get, it turns out, is a lot of close matches. Ostapenko played 30 three-setters last year, including four in a row to reach the Birmingham final and another four straight to start the US Open. Alona’s apotheosis came at Indian Wells, when she faced fellow super-aggressor Petra Kvitova in the third round. Both women tallied exactly 75 points; Kvitova won, 0-6, 6-0, 6-4. Tennis ball fuzz could be seen floating over the desert for days afterward.

That particular scoreline was an oddity, but the margin of victory was not. Ostapenko’s tight matches are not a result of streakiness, flightiness, or anything of the sort. They are an unavoidable function of her game style. It’s almost impossible to hit lots of winners without also committing piles of unforced errors. (We’ll come back to that.) When you do both in such numbers, you personally account for a substantial majority of point outcomes. The winners and errors (very approximately) balance each other out, and unless your opponent does something remarkable–or remarkably bad–with the limited influence you leave her, you end up winning about half the points played.

No one takes the racket out of an opponent’s hand like Ostapenko does. Once the return is in play, the Latvian ends nearly two-thirds of points herself, with a winner or unforced error, or by forcing an error. No one else comes close. Drawing on Match Charting Project data, I’ve listed the active players who end the most rallies:

Player                 RallyEnd%  
Jelena Ostapenko           65.9%  
Petra Kvitova              61.6%  
Madison Keys               60.8%  
Liudmila Samsonova         60.0%  
Camila Giorgi              59.7%  
Aryna Sabalenka            59.7%  
Veronika Kudermetova       57.5%  
Danielle Collins           57.5%  
Ekaterina Alexandrova      57.2%  
Ons Jabeur                 56.8%  
Peyton Stearns             56.5%  
Caroline Garcia            56.2%  
Naomi Osaka                56.2%  
Varvara Gracheva           55.0%  
Iga Swiatek                55.0%

Here’s another way to look at Alona’s extreme position on this list. The only other woman to grade out so far from 50% is Madison Brengle, who ends fewer than 34% of rallies. Ostapenko’s power turns the rest of the tour into Brengle.

Give and take

Ending even 57% of points on your own racket requires a lot of big swings. When you aim for a line, you might feel confidence about your chances, but you are taking a risk. A few players, like Swiatek, can generate winners without paying the unforced-error penalty, but that takes an unusual combination of patience and power that most players do not possess.

The 66% of points that Ostapenko ends on her own racket divides into roughly 37% winners (and forced errors) and 29% unforced errors. That’s worse than Aryna Sabalenka, who hits nearly as many winners with only a 23% error rate, but compared to the tour as a whole, the ratio is a solid one. For every unforced error she commits, she ends 1.25 points in her favor. Average among players represented in the Match Charting Project is 1.16, and the true mean is probably lower than that, since the MCP is more heavily weighted toward the best players.

The ratio varies among players, but there is a fairly strong relationship. Here are the winner/forced error and unforced error rates–each as a percentage of all points where the return came back in play–for 140 current and recent players:

The correlation between the two rates (r² = 0.3) would be even stronger if it weren’t for net-rushers like Tatjana Maria–and to some extent Leylah Fernandez–who force their passive opponents into more aggression than they would otherwise produce.

As Sabalenka shows, it’s possible to seize as many points as Ostapenko does without giving quite so many away, but even that may be a mirage: Sabalenka racks up winners behind an overpowering serve that the Latvian can’t match. If the plot above is any indication, it would be difficult to bring her error rate down without also sacrificing some winners, not to mention the élan that she has ridden to seven tour-level titles.

So we’re left with something of a paradox. A hyper-aggressive player has more control over her fate than her peers do, but that control comes at a cost of a towering error rate, which keeps matches close. One result is a week like this one in Adelaide, where Ostapenko has reached the final by slipping through perilously tight battles with Sorana Cirstea (51.7% of points won) and Caroline Garcia (50.2%). Both matches could’ve gone the other way, something that is true so often when the Latvian steps on court. My tactical advice for Daria Kasatkina in tomorrow’s final: Cross your fingers.

* * *

Deciding-set tiebreak records

AbsurDB asks:

[A]m I right that Hurkacz’s 15 deciding sets going into tie-breaks in one calendar year is a historical record in ATP (10 such tie-breaks won is also probably a record?)?

Indeed, both are records. According to my data, the previous records came from Ivo Karlovic’s 2007 season, when he reached 11 deciding-set tiebreaks, winning eight of them. Here are all the player-seasons with nine or more.

Player              Season  Dec TB  Record  
Hubert Hurkacz        2023      15    10-5  
Ivo Karlovic          2007      11     8-3  
John Isner            2011      11     4-7  
John Isner            2018      11     6-5  
Ivo Karlovic          2014      10     7-3  
John Isner            2017      10     5-5  
Kevin Anderson        2018      10     6-4  
Mark Philippoussis    2000       9     5-4  
Marat Safin           2000       9     5-4  
Ivan Ljubicic         2002       9     2-7  
Ivan Ljubicic         2007       9     8-1  
Ivo Karlovic          2008       9     5-4  
Sam Querrey           2018       9     1-8  
Borna Coric           2019       9     6-3  
Hubert Hurkacz        2022       9     3-6

(Yes, I checked before 2000, as well, but no one reached nine until Philippousis did so that year. The first player-season with eight deciding-set tiebreaks was Tom Gullikson’s, in 1984.)

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MCP Milestones

Earlier this week, the Match Charting Project recorded its two-millionth point:

The milestone match was the Auckland second-rounder between Ben Shelton and Fabian Marozsan, which I charted as a warm-up for my article on Wednesday. We’re not resting on our laurels, of course: We’ve added another five matches (and 800 or so points) in the 48 hours since.

Also worth mentioning is another round number we reached in the offseason: 1,000 different ATP players. Apart from the name syou’d expect, it’s a healthy mix of lower-ranked active players and former tour regulars. #1,000 was Martin Jaite, via his 1987 Rome final against Mats Wilander. We’ve also now charted 800 different WTAers.

We stand about 200 charts away from 13,000 matches overall: approximately 7,000 men’s and 6,000 women’s. 2023 was our most productive year yet, and 2024 would be a great time to start contributing.

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Assorted links

Earlier this week I appeared on Alex Gruskin’s Mini-Break Podcast, in which he got overexcited about a number of week one trends, and I tried to talk him down from all the ledges.
I wrote about how GPT4 helped me make Tennis Abstract’s new navbar, because you had to know I didn’t do it myself.
The tours have introduced a new policy on late matches. I’m underwhelmed: There are an awful lot of exceptions, and there’s no acknowledgement of the underlying problem of longer and longer matches.
Two student projects worth a look: Pramukh’s Evaluating Tennis Player Styles in Relation to Tour Averages, based on MCP data, and Amrit’s Aces over Expected model.
If you can’t wait until Sunday for grand slam tennis, here’s the Clijsters-Henin 2003 US Open final.

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Angelique Kerber in the New World

*Angelique Kerber in 2020. Credit: Rob Keating*

Angelique Kerber’s return to the tour has, so far, been a rocky one. She began Germany’s United Cup campaign with a narrow defeat to Jasmine Paolini, in which the Italian earned 21 break points against the German’s serve. Kerber took a set from the free-swinging Caroline Garcia but lost in three. Today, Maria Sakkari blew her off the court, winning nine games in a row before Kerber got on the board and split the remaining six.

The United Cup, in its new design, is not an easy place to make a comeback: The German faced top-30 players all three rounds. (Compare that to the tour event in Brisbane, where fellow returnee Naomi Osaka scored an opening-round victory against a player ranked 83rd.) Kerber surely didn’t expect to dominate immediately. It’s hard to get rolling again after an 18-month layoff, and she hasn’t been a truly elite player since early 2019. She turns 36 years old this month, a tough age even for players with three majors to their credit.

The Garcia match, in particular, highlighted another dimension of the challenge. The tour that Kerber rejoins is different from the one where she collected so many laurels. Angie is the very definition of a counterpuncher, a clever defender who uses anticipation and racket control to convert her opponent’s pace into winners of her own. It’s tough to counterpunch against someone like Garcia, who aims to end the point with nearly every shot.

The reckless Frenchwoman is hardly alone. Based on data from the Match Charting Project, here is the average rally length on the WTA tour since 2013:

It looks a bit fluky, but it’s noteworthy to find a peak in 2016, Kerber’s best year. Rally length has been essentially flat since 2021, perhaps since 2019 if we set aside the Covid-affected 2020 season. The German is plenty familiar with the landscape, having competed on tour until Wimbledon in 2022, but she developed her game back when the power of Serena Williams was an outlier. Now, Serena’s late-career bashing is the model for a new generation.

There are a number of ways to illustrate the trend. While the year-to-year differences are minor, the arrows all point in the same direction. In 2016, 49.6% of points were decided in three shots or less. Last year, it was 53.0%. (In 2021 and 2022, it was a bit higher still.) At Kerber’s peak, nearly 24% of points lasted at least seven strokes. Last year that figure had declined to 20.8%.

This is probably worse news for someone like Caroline Wozniacki than it is for Kerber. Woz keeps points alive and waits for errors, skills that Garcia (or Aryna Sabalenka, or Elena Rybakina, or dozens more players she might draw in the first round of the Australian Open) render meaningless. While Angie isn’t going to pile up aces–she’s hit a grand total of two in three United Cup matches–she is fully capable of redirecting a serve for a return winner, as she did a couple of times against Sakkari. Still, the shorter the point, the less likely that Kerber finds an opportunity to work her magic.

Throughout her career, the German lefty has rarely had a problem picking spots to end points with winners or forced errors. Match Charting data shows that 6% of her groundstrokes go for winners, right in line with tour average.

The catch, though, is when she hits them. Kerber is one of 58 players for whom the Match Charting Project has recorded at least 2,000 winners and forced errors since 2013. Only four of those players unleash their winners later in the rally. The average shot number of Kerber’s point-enders is 4.9–bad news in an era when nearly two-thirds of points are finished in four shots or less.

Here are the twelve players in the dataset whose winners occur latest in the rally:

Player                Avg Winner Shot#  
Daria Kasatkina                    5.1  
Viktorija Golubic                  5.0  
Yulia Putintseva                   5.0  
Carla Suarez Navarro               4.9  
Angelique Kerber                   4.9  
Sloane Stephens                    4.9  
Agnieszka Radwanska                4.9  
Simona Halep                       4.8  
Svetlana Kuznetsova                4.7  
Anastasija Sevastova               4.6  
Caroline Wozniacki                 4.6  
Su Wei Hsieh                       4.6

This isn’t a table where you want to find your name north of Wozniacki’s. It’s possible to survive on today’s tour playing this way, as Daria Kasatkina has proven, but it is much less likely to translate into a major title. Wimbledon champ Marketa Vondrousova didn’t miss the list by much, coming in at 4.4, but her aggression varies wildly from one match to another. Iga Swiatek and Coco Gauff appear closer to the middle of the pack, at 4.2, and Aryna Sabalenka ranks as the fourth most aggressive of the 58, at 3.4.

At the risk of belaboring the point, here’s another way of seeing the difference between Angie’s style and the brands of tennis that currently top the rankings. The following chart shows what percent of Kerber’s winners (and forced errors) happen at each point in the rally, compared to the same figures for Swiatek and Sabalenka:

The “1st shot” and “6th+” columns are virtual mirror images of each other. Even that understates the difference between the veteran and the two youngsters, because a point-ending serve from Kerber is more likely to be at least partially the fault of the returner–those errors are conventionally scored as forced regardless of the strength of the serve.

I don’t want to say that Kerber can’t succeed on her return to the circuit, but it’s clear that she faces a challenge. The tennis world of the mid-2010s is long gone, and even if she regains the form that took her to number one in 2016, it may not give her the same results in 2024. A new era requires a new Angie; we’ll see if she can produce one.

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Hubi’s Three-Set Magic

Also today: Torben Ulrich (1928-2023); What is this?

Hubert Hurkacz started the 2024 season right where he left off. In the round-robin stage of the United Cup, he played two singles matches, beating Thiago Seyboth Wild and losing to Alejandro Davidovich Fokina. Both matches went to a third set.

No one played more deciding third sets in 2023 than Hurkacz. Out of 55 best-of-three starts, he went the distance 32 times. That’s more three-setters–and a higher rate of them (58%)–than any player-season this century. On average, about 35% of ATP matches go three. Since 2000, only 16 players have posted a full season where they went to a third set more than half the time.

This is new territory for the 26-year-old from Poland. He reached a decider in only 35% of his three-setters in 2021, then increased that clip to 45% in 2022. The main difference between his 2022 and 2023 seasons was that his already small margins shrunk even further. He won matches at almost the same rate both years, even though he broke a bit less often and was less effective with his second serve in 2023. He converted his three-setters at exactly the same rate (62.5%) in both seasons. Hurkacz’s edge was still enough to keep him in the top ten, but only because he was willing to play so much tennis.

It’s a bit fluky to pile up so many three-setters, but we can get a hint at some trends by looking at the list of similar warriors:

Year  Player                  Bo3  Deciders   Dec%  
2023  Hubert Hurkacz           55        32  58.2%  
2018  John Isner               40        23  57.5%  
2022  Taylor Fritz             55        31  56.4%  
2010  John Isner               48        27  56.3%  
2019  Nikoloz Basilashvili     43        24  55.8%  
2014  Guillermo Garcia Lopez   42        23  54.8%  
2019  Fernando Verdasco        42        23  54.8%  
2018  Robin Haase              46        25  54.3%  
2009  Julien Benneteau         48        26  54.2%  
2005  Jurgen Melzer            39        21  53.8%  
2007  Dmitry Tursunov          41        22  53.7%  
2017  Jack Sock                51        27  52.9%  
2011  Stan Wawrinka            40        21  52.5%  
2013  John Isner               52        27  51.9%  
2017  Albert Ramos             54        28  51.9%  
2018  Joao Sousa               45        23  51.1%  
2000  Fernando Vicente         47        24  51.1%  
2013  Robin Haase              49        25  51.0%  
2003  Gaston Gaudio            55        28  50.9%  
2006  Dmitry Tursunov          61        31  50.8%

There are plenty of clay-court grinders on the list; that doesn’t really apply to Hubi. What pops out to me are the three appearances of John Isner. While Hurkacz isn’t as one-dimensional as Big John, he has the same sort of profile. Only four other players in the current top 50–none of them in the top 15–break serve as rarely as he does. When breaks are scarce, sets go to tiebreaks and matches go three. An incredible 14 of Hubi’s 32 three-setters went to a sudden-death tiebreak. He won ten of them.

None of this is sustainable. In one sense, that’s bad news: If Hurkacz somehow lands in 14 more deciding-set tiebreaks this year, he’ll end up closer to 7-7 than 10-4. On the other hand, three-set stats are just trivia–exhausting trivia, at that. There wasn’t much to separate his top-line 2022 and 2023 results, and he’s surely be happy with another top-ten finish regardless of whether he needs to play 30-plus deciding sets to get there.

If Hubi does force so many third sets, is he likely to keep winning so many? That’s a more complicated question.

What is a good three-set record?

This is a great example of what’s missing from the tennis discourse. People talk about three-set records all the time, especially on broadcasts whenever two players head for a deciding set. We expect that top players win more one-set shootouts than journeymen do, but how many more? For a fringe top-tenner like Hurkacz, is 62.5% good? Great? Boringly in line with expectations?

What makes this tricky is that, anecdotally, there are so many different types of three-setters. Last year, Hurkacz went three with four different players ranked outside the top 100. We’d expect him to win those; it’s a bit disappointing he didn’t win them even more quickly. Hubi also went to three deciders against a number one: two with Carlos Alcaraz, one with Novak Djokovic. We wouldn’t expect him to win those (and he didn’t), but simply taking a set is a moral victory. Any list of 32 three-setters is going to include a bunch of matches that should never have gotten that far. There might be 32 different levels of expectations, if we want to break it down that far.

We don’t need to make it that complicated. What I want is a shorthand way of looking at a player’s three-set record and knowing whether he’s likely to keep it up.

It turns out that you get pretty close with a simple formula. Tour regulars–defined here as players with at least 50 ATP main-draw matches in a season–tend to win between 50% and 60% of their third-set deciders. (On average, they clean up against lower-ranked players with less time on tour, as you’d probably expect.) We can estimate what a player’s three-set record “should” be as follows:

Three-set win% = 45% + (20% * Two-set win%)

That’s it. A player’s winning percentage in straight-set matches is a decent approximation of their current level: While it’s possible to luck into a two-set victory, it’s unusual. Here’s what the model implies as likely three-set records at various skill levels:

Two-set W%  Three-set W%  
40%                52.9%  
50%                54.9%  
60%                56.9%  
70%                58.8%
80%                60.8%

Three-set records are rarely so extreme as two-set records. Djokovic, for instance, went 20-2 (!) in two-setters last year. The model predicts that he would win 63% of his three-setters. In reality he went 11-4 (73%), outperforming the estimate but still coming in much closer to 50%, as logic would suggest. Three-setters tend to occur between more closely-matched players, and once the outcome comes down to a single set, luck plays a larger part. Deciding sets aren’t as coin-flippy as tiebreaks, but as Hurkacz’s 14 third-set shootouts remind us, the margins can be equally slim.

So, back to Hubi. Last year, he won 70% of his two-setters. A typical performance for a player like that would be a three-set winning percentage of 58.8%–a 19-13 record in deciders instead of his actual 20-12. Odd as his 2023 season was, he won the close ones about as often as he should have. Even if luck turns against him, he could finagle another top-ten finish with a stronger performance at the majors–but that’s a subject for another day.

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Torben Ulrich (1928-2023)

In 1955, Torben Ulrich invited a couple of visiting South African tennis players, Gordon Forbes and Abe Segal, to come see his band at a jazz club in Copenhagen. Ulrich, manning the clarinet chair, sat out the first several numbers. Forbes wanted to see his friend in action and encouraged him to join in.

“I must wait,” Ulrich said, “until something happens inside me. So far nothing very much has happened.”

The red-headed, bearded Dane died last month at the age of 95. In his near-century on earth, a whole lot happened. Yet he always operated on his own timetable. He once walked off the court when an opponent wouldn’t stop lobbing. (“I had asked him nicely several times to stop it, but he told me to mind my own business.”) Gene Scott told another story:

There was this recent time in Richmond. There was this girl who was wearing a very short miniskirt. The whole house, including the players, could not keep their eyes off of her. Now, Torben is getting ready to serve when he suddenly freezes in midair, then walks over to the stands. Everybody is wondering where he’s going. He stops behind the girl and quickly drops a ball down her back. I know of no other player who has ever coped with a distraction in such a gentle, colorful way.

Forbes recalled a club member who was impatient for Ulrich to vacate a practice court:

‘Have you been playing long?’ [the member] said.

‘As long as I can remember,’ said Torben.

‘How much longer will you play?’ asked the member.

‘We may go on for many years,’ said Torben.

Ulrich did, indeed, go on for many years. He won his first tournament, the Danish Nationals, in 1948, when he was 19 years old. Three years later he picked up his first international singles title in Antwerp. He remained capable of top-level tennis for another two decades after that.

“Over the years, it seems he has never lost the key,” a fellow player told Sports Illustrated in 1969, when Torben was 40 years old. “When it looks like he is ready to come apart, he comes up with that one big match. He remains respectable.”

Ulrich was never a top-tenner; he failed to reach the quarter-finals of a major in 43 tries. Yet he piled up dozens of smaller tournament victories in singles, doubles, and mixed. He contested over 100 Davis Cup rubbers for Denmark, many of them alongside his younger brother, Jørgen.

The Dane was perhaps more at home in the world of art. At various times, he wrote poetry and music criticism, painted, and made films. This side of him had a greater influence on his legacy. His son, Lars, was a promising junior tennis player, but he was probably made the right decision when he shifted his focus to music and co-founded the band Metallica.

Torben, it seemed, was as happy with one pursuit as any other. He was a seeker–it didn’t much matter what. Tennis, with its whirlwind schedule and ever-changing mix of fellow-travelers, fit the bill.

He didn’t care about results. Once, he told Forbes that he didn’t win. “I simply played in the usual way,” he said. “It was my opponent who lost.”

Perhaps Ulrich’s career-best result came at the 1968 US Open, where he upset 15th seed Marty Riessen before falling to John Newcombe in a fourth-round nailbiter, 5-7, 4-6, 6-4, 10-8, 6-4. Newk’s serve could overpower a much younger man, but it was no match for Torben’s mind. “What is speed?” he mused. “If I am concentrating properly, really seeing, a big serve will be coming at me in slow motion.”

The match could have gone either way. At a crucial moment, Ulrich flubbed an easy volley when a butterfly darted in front of his face. Was he distracted? He silenced the press with a question of his own: “Was I then a man dreaming I was a butterfly, or am I now a butterfly dreaming I am a man?”

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What is this?

After the Tennis 128 in 2022 and 1973 Redux last year, my plan is to return to contemporary tennis, with the usual hefty dose of analytics.

My goal is to write as much as possible about the game between the white lines, as opposed to forecasts, ratings, previews, business, and–heaven forbid–tennis personalities and politics.

I will also continue to look back to events from 50 years ago–and 100, and perhaps the occasional non-round number. 1974 was every bit as fascinating a season as 1973. I won’t do 100-plus installments, as I did last year, but I’ll revisit various pivotal moments as their anniversaries roll around, especially to commemorate the birth of World Team Tennis this summer.

You can expect to find a new post a couple of times a week, probably more often during the majors. Your suggestions for topics are always welcome. Comments are open (provisionally! I cannot emphasize enough how provisionally!), and I’ll add a “suggestion box” to the sidebar one of these days.

If you want to keep up with everything I’m doing here, please subscribe. Links to new article will also appear on the Tennis Abstract home page. I can’t promise I’ll always post links on Twitter.

Happy new year!

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The Underserved First Point

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

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

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

Point by point

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

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

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

Unbiasing

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

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

The following table shows these numbers for each point score:

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

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

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

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

Second to none

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

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

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

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

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

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

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

Multipliers gone wild

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

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

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

Here are the results:

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

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

Exploiting the mundane

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

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

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

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

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

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

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

So You’d Like To Do Some Tennis Research

Great! Here’s some data.

Maybe you’ve got a class project that will allow to you pick your own dataset. Or perhaps you just think that tennis analytics are cool, and you’d like to jump in. One of the more common questions I get is from people in this situation who are looking for a little guidance in choosing a subject. Here are a few tips.

1. Scratch your own itch

I try not to pick topics for others, because I generally find that people do better work (and are more likely to stick with it) when they are “scratching their own itch,” working on what they find particularly interesting. If nothing comes to mind, keep reading.

2. Get skeptical

When you’re watching tennis or reading about it, get in the habit of questioning everything. Does that player really hit more wide serves on break points? Does that guy really play better when he’s leading? If you listen with this type of mindset, you can come away from watching a single match with half a dozen new ideas.

This tip presupposes what might be step 0 — watch and read about tennis! I assume that if you’ve found my blog and want to do analytics, you’re already a pretty big fan. Keep it up–any analyst can benefit from attentively watching more tennis. Reading analytical work is also key, both to get ideas, and to learn what effective studies look like.

3. Think analogically

Many of us who do tennis analytics also work in other sports. Others are academics such as economists and statisticians whose “real jobs” have them working in fields far from athletics. Non-tennis subjects aren’t irrelevant–quite the contrary! If you do an interesting hockey study, or read about an interesting experimental design in development economics, think about how else you could apply a similar approach. Sometimes it’s a dead end with no direct application to tennis, but the exercise itself has value–practicing this kind of thinking eventually pays off.

This tip can be particularly useful for those of you doing a class project. If your professor provides examples of the type of work they’d like to see, consider if there’s a close cousin in tennis analytics. That first thought might not be where you end up, but it’s a good way both to get ideas and to ensure that you’re doing roughly the sort of work that’s asked of you.

4. Chart a match (or ten)

The Match Charting Project is the largest public dataset of shot-by-shot tennis data. It can be overwhelming at first, so if you are considering doing research with the dataset, I strongly recommend charting a match or two as a way to get familiar with it.

Charting a match is also a great way to generate more questions. It forces you to watch closely, so you’ll notice tactics that you might not have otherwise seen. As you chart, you might find yourself dreaming up hypotheses–say, that a player’s service return is particularly effective when she steps inside the baseline. The rest of the match will offer more data to confirm or contradict, and it might help you develop more ideas about where to go from there.

5. Collect your own data

There’s more than enough tennis data out there to keep you busy for a very long time. But don’t be afraid to strike out in a new direction. Perhaps you’d like to study whether certain players are more effective under the lights, which would require tracking the start time of matches. Maybe you’d like to see if certain coaches are particularly good at extracting better performances from their charges, which means you’d need to build a database of coaches, look up when they worked with each of their players, and how the players fared during that time.

Many analysts think that their job is just that–analysis. But in some areas, there more to be gained from better data than from better analysis. Plus, building a new dataset doesn’t have to be a monumental task. The coaches example I gave might include only a few dozen coaches, who worked with a handful of players each.

6. Start small

Following some of my suggestions above can lead you into a huge, ambitious project. the most common result of taking on a huge project is an unfinished project, as I can tell you from experience. Before going big, try to find a “proof of concept” both to get your feet wet, and to see whether you’re on a useful track.

In the coaches example I just gave, you might look at what happened to the WTA rankings of Wim Fissette’s players when they worked with him. I don’t know if there’s a “Fissette effect,” and now that I mention it, I’m curious! That’s a mini-project you could do in an afternoon, and it gets you started on the path of a more thorough study.

Ok, ok, here’s a list

Still stuck? A few years ago, Carl and I put together a list of potential research topics. I’ve since taken it down, but Peter forked it, so it still exists on GitHub.

Some of the topics have already been done, and several others are beyond the scope of what’s possible with publicly-available data. That still leaves you with dozens of ideas.

Finally, once you’ve completed a study–big or small–be sure to post it on twitter and share with other tennis analysts. Your work might be the key that gives the next graduate student or hobby analyst the spark to start a project of their own.

Are Tournament Draws Giving Us Suspiciously Many Venus-Serena Clashes?

This week in Lexington, top seed Serena Williams faces her sister, Venus Williams, in the second round. They are both among the all-time greats, and they have played each other nine times in grand slam finals, so it’s always jarring to see them turn up in the same section of a draw and play on a Thursday.

Lately, their encounters seem to always happen long before the business end of a tournament. Their three matches between the 2017 Australian Open final and this week in Lexington all happened in the round of 32, including a planned 2019 Rome meeting from which Serena withdrew. Venus is usually unseeded, no longer the world-beater she once was, so it is at least possible that the Williams sisters would be bracket neighbors in any given week.

But should it happen quite so often? It is an understatement to say that Serena and Venus were not universally embraced upon arrival in the tennis world. If you’re conspiracy minded, every tournament draw is an opportunity to commit dastardly deeds. Perhaps early in the Williams era, it was the work of racist or otherwise misguided tournament officials who wanted to avoid all-Williams finals. Or nowadays, event honchos recognize that Venus is unlikely to reach the final, so they tinker with the bracket to make a headline-grabbing Williams-versus-Williams clash more likely.

I’m sure that most draws are conducted on the up-and-up, but the process is sufficiently opaque that it’s easy to get suspicious. It’s also easy to make mistaken generalizations from insufficient data. Let’s see what the numbers can tell us.

150 tournaments!

Lexington is the 150th tour event with both Serena and Venus in the field.*

* I think. My WTA data isn’t perfect for the early years of their careers, and there was an uncomfortable amount of manual tabulation involved in this post. Their TennisAbstract player pages are missing the 1999 Grand Slam Cup, but I’ve included it in all the numbers here. For the purposes of doing analytics, it doesn’t matter much if the total is 148 or 151, but if you’re printing a banner or making a cake, you should double-check.

Thursday’s match in Lexington will be their 31st, plus one withdrawal apiece. In 13 of the 150 events, the Williams sisters were either the top two seeds or the 3rd and 4th seeds, meaning that draw shenanigans were out of the question–they could not face each other until the final. 4 of those 13 times, that’s exactly what they did.

What are the odds?*

* Of me being able to use this sub-heading in any given blog post?

I went through the remaining 137 tournaments and identified the round in which they either did meet or could have met. For the purposes of analyzing draws, there isn’t really a difference. For instance, Serena and Venus have landed in the same half 73 out of a possible 137 times, a bit more than the 68 or 69 times that we would expect.

Because of their seeds, they had the chance of ending up in the same quarter 116 times, and that’s how it worked out 28 times, just under the 29 times that an exact one-in-four rate would’ve given them. The smaller the draw section, the fewer tournaments that Serena’s and Venus’s seeds made it possible for them to meet.

I counted the number of tournaments with a possible meeting on or before a certain round, and then the number of events in which the draw delivered that meeting, regardless of whether both Williamses got that far. Here are the results, along with the probability of that many or more actual meetings:

Section  Possible  Actual  Chance  
Half          137      73     25%  
Quarter       116      28     62%  
Eighth         85      17      3%  
16th           64       5     37%  
32nd           42       1     74%

There’s a one-in-four chance that Serena and Venus would’ve landed in the same half as many times as they have throughout their entire careers. That’s a bit of bad luck, but it’s hardly a smoking gun. The same is true for the same quarters, as well as very early meetings that would pit them against each other in the round of 32 or 64.

That leaves one eyebrow-raising number to discuss. On 85 occasions, at least one of the two women was seeded outside the top eight, making possible a meeting in the round of 16 or earlier. Given random draws, we’d expect 10 or 11 brackets in which they could face each other so early. Instead, we got 17.

A 3% chance of so many early encounters isn’t quite as bad as it sounds. I’ve tried to walk you through this process in the way I approached it. While I wondered if Serena and Venus have met more often than random draws would normally deliver, I didn’t have a particular round in mind. As you’ve seen, I generated a bunch of numbers, and one of the five looked suspicious. You might be able to construct a story that explains why the round of 16 is different from the others (such as my theory that tournament directors want mid-week headlines), but because we generated so many numbers, we were that much more likely to end up with an extreme percentage simply by chance.

The smoking (nerf) gun

Thus, we’re able to raise the possibilities that some draws weren’t random, but we can hardly prove it. One problem–one that we could’ve foreseen from the get-go–is that some draws are definitely not tampered with. Probably most draws. And even if they were, most tournaments wouldn’t have any reason to mess with Serena’s or Venus’s placement in the bracket. Or if they did, they might prefer an all-Williams final, and thus alter the bracket in the opposite direction of what we’re hunting for.

If you like conspiracy hunting, I’ve got a tiny sample for you. Since the beginning of 2018, Venus and Serena have played in the same tournament 15 times, and their seedings (or lack thereof) made it possible for them to be drawn in the same eighth 14 of those times. Of the 14, they were placed in position for a round-of-16 or earlier meeting 5 times. There’s only a 2% chance of that … if you set aside the fact that I’m checking all sorts of subsets of matches looking for (probably spurious) patterns. If nothing else, the 5-of-14 figure explains why it seems like Serena and Venus keep landing in the same draw sections lately. They do!

Broadly speaking, then, this is all much ado about nothing. (I don’t even know if these conspiracy theorists exist, so maybe I just invented a conspiracy and spent my evening debunking it. Hooray?) It’s possible that a few tournament directors are producing non-random draws … but it would take a very different kind of investigative work to prove it. Worst case scenario, we get a few more Serena-Venus matches. It may not be fair to the older sister, but it’s a pretty good deal for tennis fans.

Visualizing Trends in Net Play Across Five Decades of Grass Court Tennis

Earlier this week, I wrote about one aspect of the long-term decline in net play: the widespread belief that approaching the net is more difficult now because fewer players have a weaker side. I presented evidence indicating that most players still have a weaker side, which suggests that all groundstrokes–on both strong and weak sides–have gotten stronger, making net play a riskier proposition.

If that is true, it is reasonable to assume that passing shot winners are more frequent (relative to the number of net approaches), and perhaps that volleys are more aggressive, resulting in more first-volley winners and first-volley errors. More powerful and precise strokes should, on balance, make net points shorter than they used to be.

We can begin to test these theories using the extensive shot-by-shot records assembled by the Match Charting Project (MCP). MCP data includes every men’s Wimbledon final and semi-final back to 1990, as well as many elite-level grass court matches from the 1970s and 80s. For the purposes of today’s study, I will use only Wimbledon semi-finals and finals, plus a handful of other grass court matches from 1970-89 to complement the sparser Wimbledon data. This way, we know we’re comparing the elites of various generations to one another.

Contemporary net approaches

Let’s start by looking at what happens in a 2010s Wimbledon’s men’s final or semi-final when a player approaches the net. I’m excluding serve-and-volley points, and will do so throughout. I’m also excluding approach shot winners, which are often little more than gestures in the direction of the net following a big shot. (Even when they’re not, it can be difficult for charters to distinguish between approach and non-approach winners.) Thus, we’re looking at about 1,250 net approaches in which the other player got his racket on the ball.

The ball came back almost 73% of the time, and on slightly more than half the points, the approaching player put his first volley (or smash, or whatever shot he needed to hit) in play. 19% of the points saw a second passing shot attempt put in play, and nearly 12% had a second net shot keep the point going. About 1 in 30 approach-shot points continued even longer, forcing the the netman to contend with a third pass attempt.

The following visualization is a Sankey diagram showing how these net points developed. “App” stands for approach, “Unret” for “unreturned,” “Pass1” for “first passing shot,” “V1” for “first volley,” and so on. Mouse over any region of the diagram for a brief summary of what it represents.

There’s a lot of information in the graphic, and it may not be entirely intuitive, especially hindered by my clunky design. Each region is sized based on what fraction of points developed in a certain way. As the regions move toward the right side of the diagram, they as classified by whether the approaching player won the point. As we can see, in the 2010s sample, these approach shots resulted in points won about 69% of the time.

The golden era

To compare eras, we need more than just one decade’s worth of data. I separated the approach shots by decade (grouping together the 70s and 80s), and the most distinctive era turned out to be the 1990s, when Pete Sampras ruled the roost and many of his challengers were equally aggressive.

Far more points were opened with a serve-and-volley: almost 81% in the 1990s compared to 7% in this decade. Even with the server claiming the net so early and so often, there were still many more non-serve-and-volley net approaches two decades ago. Then, there were about 85 “other” net approaches per match; this decade, there have been about 27. Thus, it is reasonable to assume that the typical net approach started from a less favorable position. These days, players only approach when the point has developed in a particularly inviting way.

Here is another diagram, this one showing what happened following 1990s net approaches:

It’s striking to see that, back when net play was much more common, with a master such as Sampras dominating our sample, net approaches were less successful than they are today, resulting in a 67% win rate instead of 69%. However, it’s tough to know how today’s players–even a confident aggressor like Roger Federer or a volleying wizard like Rafael Nadal–would fare if they came forward four times as much. Assuming they pick their spots wisely, their success rate would be lower than 69%. The only question is how much lower.

Contrary to my inital hypothesis, passing shots seemed to be higher-risk and higher-reward in the 1990s than in the 2010s. Two decades ago, only 65.5% of initial passing shot attempts were put in play (compared to 72.6% today), though nearly as many of those attempts resulted in winners (21.1% to 21.4%). It was the volleyers who were either more conservative or less powerful in the 1990s. Then, barely half of first volleys ended the point in the netman’s favor; now, the number is closer to 60%. Again, this could be because today’s players pick their spots more carefully, allowing them to hit easier first volleys.

The early days

We’ve seen how net approaches developed in the 1990s and the 2010s. It would be reasonable to assume that the 1980s (with several late ’70s matches thrown in) were like the 1990s, but more so. Instead, the results are more of a mixed bag, with some characteristics that look like the ’90s, and others that are closer to today’s numbers.

Here is the diagram:

In the 1980s, nearly as many passing shot attempts were put in play as they are today, in contrast to the lower rate during the 1990s. First volleys are a similar story. When passing shot attempts came back, approaching players put a volley (or other net shot) back in the court about 70% of the time–similar numbers in the 1980s and 2010s, but a couple percentage points higher than in the 1990s.

What is different is what happened next. In the 1980s, if the approaching player put his first volley back in play, it came back again 53% of the time. That rate is one of the few clear trends over time: It fell to 46% in the 1990s, 45% in the 2000s, and 37% in the 2010s. As a result, the ’80s saw far more second volleys and points that extended even further, compared to more recent eras. The lack of first-volley putaways meant that net approaches only converted into points won about 65% of the time.

A cautious narrative

There is no simple explanation that accounts for all of these numbers, because we are not seeing the direct result of a single factor, like the shift from wooden rackets or to more topspin-friendly string. Technological changes certainly have an impact, but as soon as the balance between approacher and opponent shifts, players adjust their strategy accordingly.

For instance, the rate of points won on net approaches appears to have steadily increased, from 65% in the 1980s to 67% in the 1990s to 69% today. The first rise could be attributed to racket technology, which gave aggressors more power and control. But the second rise came over a time period in which string technology offered more help to defenders. The higher rate of approach points won isn’t because players are better at it, it’s because they picked their spots more carefully.

What we might focus on instead, then, is how much these diagrams look alike, even though they represent vastly different eras. While there isn’t exactly a net-approach-strategy equilibrium that has held through the decades, player decision-making has kept these rates from varying too wildly. If passing shot winners start going up, we’ll probably see even fewer approaches–with the remaining approaches in still more favorable moments–or a continued increase in the percentage of approaches to the backhand side. That’s another clear trend over the last few decades, but it’s a topic for another day.

Rather than succumbing to nostalgia and bemoaning the decline of net play, it’s better to celebrate the adaptability of tennis players at the highest level. While the game a whole has become more defensive, backcourt denizens from Bjorn Borg (94 approaches per charted grass-court match) to Novak Djokovic (21 approaches per match) have reminded us that adjustments work in both directions. With parameters such as technology, surface, and opponent skills constantly changing, we can’t expect winning strategy to remain the same.

Thanks to SankeyMATIC for making it easy to create the diagrams.

Nick Kyrgios Really Is Different Under Pressure

Italian translation at settesei.it

Earlier this week, we looked at whether Nick Kyrgios is unusually inconsistent. That is, is he more likely to upset higher-ranked players and lose to lower-ranked players than his peers? The numbers say he isn’t.

But that isn’t all we mean when we talk about Kyrgios’s unreliability. He often undergoes dramatic shifts within matches. At times, he is visibly distracted; during his Delray Beach match against Radu Albot, he even shouted that he wanted to get off the court. Other times, he comes up with breathtaking serving and shotmaking at the most crucial moments. He seems motivated by both packed grandstands and on-court pressure. Unfortunately, both of those are missing from a lot of professional tennis.

We already have some evidence for the better-under-pressure hypothesis. In his five matches in Acapulco last week, he won a mere 50.4% of points, one of the lowest totals ever for a title-winner. In three of the five matches, he won return points at a lower rate this opponent, resulting in Dominance Ratios (DRs) below 1.0. Winning a match with a sub-1.0 DR (or fewer than 50% of total points won) isn’t unheard of, but it’s not a reliable way to rise to the top of the sport. Such contests are called “lottery matches” for a reason–there’s a lot of luck involved in winning with such fine margins, and fortune tends to even out.

Yet Kyrgios’s “luck” keeps nudging his results in the same direction. He has played 15 career tour-level matches in which his DR is between 0.9 and 0.99–close matches in which he was slightly outplayed, at least in the points column. With stats like that, players tend to win about one-third of the time. Kyrgios, however, has won eleven of those 15 matches. His good fortune doesn’t cancel out when he narrowly edges out an opponent: In 13 matches with DRs between 1.0 and 1.1, he has lost only two. The Australian is doing something right.

Big points are big

You probably already know what’s going on here, even if you haven’t listened to commentators speculate during Nick’s matches. The key to such narrow victories is converting the “big” points–break points, deuces, tiebreaks, and so on. It doesn’t matter if you throw away a point or two when serving at 40-love. Other situations have considerably more leverage, and that’s when Kyrgios brings his best tennis.

I tallied up Kyrgios’s return points won over the course of his career, based on the point score of each one. (I don’t have the point-by-point sequence of every one of his tour-level matches, but most of them are included, more than enough to constitute a reliable sample.) Here are the five games scores when he wins the most return points, starting with the most effective:

0-40, 40-AD, 15-30, 30-40, 40-40

And the five scores, again in order, starting with least effective:

30-0, 40-0, 40-15, 0-15, 0-0

In other words, when he has a chance to break, he’s great. In my sample of matches, he won 31.5% of return points; when the opposing server is facing him at 0-40, he wins the point 45.0% of the time. At 40-AD, it’s 41.9%. When his opponent serves with a 30-0 advantage, Kyrgios wins a mere 27.3% of return points.

Everybody does it (a little)

Astute readers will realize that I haven’t accounted for a key variable. In a data set of dozens of matches, scores that favor the returner will occur more often against weaker servers. Kyrgios didn’t get many 0-40 or even 40-AD chances against John Isner last week, but he can expect to get more against the likes of Albot. So to some extent, we should expect players to win more return points at these moments. In the last 52 weeks, ATPers have won 37.3% of return points, but 40.1% of break points.

Everybody does it, but Nick does it more. The following table shows the ratio of return points won at each game score to average return points won. The middle column shows Kyrgios’s ratios and the right-most column shows the 2018 ATP tour average:

Situation       NK   ATP  
0-40          1.43  1.14  
40-AD         1.33  1.09  
15-30         1.27  1.05  
30-40         1.26  1.06  
40-40         1.16  1.02  
15-40         1.13  1.06  
15-15         1.11  0.99  
15-0          1.11  0.98  
30-15         1.09  1.00

Situation       NK   ATP  
0-30          1.07  1.06 
AD-40         1.06  1.02  
40-30         1.05  1.00  
30-30         1.03  1.01  
0-0           1.02  0.99  
0-15          1.01  1.05  
40-15         0.95  0.92  
40-0          0.91  0.87  
30-0          0.87  0.91

Most players take advantage in 0-40 situations, and to a lesser extent at break points, but Kyrgios is on another planet. The average player wins roughly 10% more return points in break situations; Kyrgios triples the ratio.

Leverage

We’ve taken a big step toward explaining Kyrgios’s pattern-breaking results and his in-match inconsistency. But even game scores don’t tell the whole story. A deuce point at 5-0 usually matters a great deal more than a break point when the returner is already up a set and a break.

To account for those differences, we’ll turn to the leverage metric. (You’ll also see it referred to as “volatility” or “importance.”) Here’s the idea: Given what we know about two players, we can calculate the probability that one of them will win the match, based on the current situation. If the server wins, that probability shifts in his favor. If the returner wins, it shifts in the opposite direction. Leverage is the sum of those two shifts: the amount of win probability that is at stake at any given point.

For today’s purposes, there are no specific numbers; you need only to understand the concept. The higher the leverage, the more the point matters. Players might disagree with some of the details that a purely math-based approach spits out, but for the most part, the equations capture our intuition about which points matter, and how much.

I calculated the leverage for every point of the 2018 ATP season and split the points into ten categories, from least important (1) to most important (10). The following graph shows the tour average rate of return points won (RPW) for each of those ten categories:

If we ignore the leftmost and rightmost data points, there’s something of a trend here. From the second-to-least-important category to the second-to-most-important, players increase their return points won from about 36.0% to 37.5%. Some of that shift can be explained by a phenomenon I’ve already mentioned: returners find themselves in crucial situations (such as break points) more often against weaker servers.

Here’s the same graph, now with a second line showing Kyrgios’s RPW in the ten categories, from least important to most important. I’ve kept the ATP average trendline for comparison:

Remember that 36.0% to 37.5% increase I mentioned a minute ago? For Kyrgios, the same shift is 27.0% to 35.2%–eight percentage points instead of less than two. It appears that the Australian is extremely sensitive to what’s at stake throughout matches, and when the rewards are high enough, he turns into a credible returner.

Some of you are probably thinking, “of course, I knew that all along.” First of all, I hate it when people say that, because what they really mean is, “I suspected that all along,” and they didn’t really know. Some of the other things such people “know” are actually wrong.

Second, I need to underline just how unusual this is. I’ve been playing around with point-by-point data for a few years now, looking for in-match patterns, for specific players and for the sport overall. Such patterns exist: points and games aren’t entirely independent of each other. But usually they are minor–a percentage point or two, not the kind of thing you could spot even in a fortnight’s worth of matches. Kyrgios breaks the mold. When it comes to the mercurial Australian, the assumptions that are adequate to account for most of professional tennis simply fail.