Elo, Meet COVID-19

Tennis is back, and no one knows quite what to expect. Unpredictability is the new normal at both the macro level–will the US Open be a virus-ridden disaster?–and the micro level–which players will come back stronger or weaker? While I plead ignorance on the macro issues, estimating player abilities is more in my line.

Thanks to global shutdowns, every professional player has spent almost five months away from ATP, WTA, and ITF events–“official” tournaments. Some pros, such as those who didn’t play in the few weeks before the shutdowns began, or who are opting not to compete at the first possible opportunity, will have sat out seven or eight months by the time they return to court. Exhibition matches have filled some of the gap, but not for every player.

Half a year is a long time without any official matches. Or, from the analyst’s perspective: It’s tough to predict a player’s performance without any data from the last six months.

Increased uncertainty

Let’s start with the obvious. All this time off means that we know less about each player’s current ability level than we did before the shutdown, back when most pros were competing every week or two. Back in March, my Elo ratings put Dominic Thiem in 5th place, with a rating of ~2050, and David Goffin in 15th, with a rating of ~1900. Those numbers gave Thiem a 70% chance of winning a head-to-head.

What about now? Both men have played in exhibitions, but can we be confident that their levels are the same as they were in March? Or that they’ve risen or fallen roughly the same amount? To me, it’s obvious that we can’t be as sure. Whenever our confidence drops, our predictions should move toward the “naive” prediction of a 50/50 coin flip. A six-month coronavirus layoff isn’t that severe, so it doesn’t mean that Thiem is no longer the favorite against Goffin, but it does mean our prediction should be closer to 50% than it was before.

So, 60%? Maybe 65%? Or 69%? I can’t answer that–yet, anyway.

The (injury) layoff penalty

My Elo ratings already incorporate a layoff penalty, which I introduced here. The idea is that if a player misses a substantial amount of time (usually due to injury, but possibly because of suspension, pregnancy, or other reasons), they usually play worse when they come back. But it’s tough to predict how much worse, and players regain their form at different rates.

Thus, the tweak to the rating formula has two components:

  • A one-time penalty based on the amount of time missed (more time off = bigger penalty)
  • A temporarily increased k-factor (the part of the formula that determines how much each match increases or decreases a player’s rating) to account for the initial uncertainty. After an injury, the k-factor increases by a bit more than 50%, and steadily declines back to the typical k-factor over the next 20 matches.

Not an injury

A six-month coronavirus layoff is not an injury. (At least, not for players who haven’t lost practice time due to contracting COVID-19 or picking up other maladies.) So the injury-penalty algorithm can’t be applied as-is. But we can take away two ideas from the injury penalty:

  • If we generate those closer-to-50% forecasts by shifting certain players’ ratings downward, the penalty should be less than the injury penalty. (The minimum injury penalty is 100 Elo points for a non-offseason layoff of eight or nine weeks.)
  • The temporarily increased k-factor is a useful tool to handle the type of uncertainty that surrounds a player’s ability level after a layoff.

The injury-penalty framework is useful because it has been validated by data. We can look at hundreds of injury (and other) layoffs in modern tennis history and see how players fared upon return. And the numbers I use in the Elo formula are based on exactly that. We don’t have the same luxury with the last six months, because it is so unprecedented.

Not an offseason, but…

The closest thing we have to a half-year shutdown in existing tennis data is the offseason. The sport’s winter break is much shorter, and it isn’t the same for every player. Yet some of the dynamics are the same: Many players fill their time with exhibitions, others sit on the beach, some let injuries recover, others work particularly hard to improve their games, and so on.

Here’s a theory, then: The first few weeks of each season should be less predictable than average.

Fact check: False! For the years 2010-19, I labeled each match according to how many previous matches the two players had contested that year. If it was both players’ first match, the label was 1. If it was one player’s 15th match and the other’s 21st, the label was the average, 18. Then, I calculated the Brier Score–a measure of prediction accuracy–of the Elo-generated predictions for the matches with each label.

The lower the Brier Score, the better. If my theory were right, we would see the highest Brier Scores for the first few matches of the season, followed by a decrease. Not exactly!

The jagged blue line shows the Brier Scores for each individual label (match 1, match 2, match 23, etc), while the orange line is a 5-match moving average that aims to represent the overall trend.

There’s not a huge difference throughout the season (which is reassuring), but the early-season trend is the opposite of what I predicted. Maybe the women, with their slightly longer offseason, will make me feel better?

No such luck. Again, the match-to-match variation in prediction accuracy is very small, and there’s no sign of early-season uncertainty.

I will not be denied

Despite disproving my own theory, I still expect to see an unpredictable couple of post-pandemic months. The regular offseason is something that players are accustomed to, and there is conventional wisdom in the game surrounding how to best use that time. And it’s two months, not five to seven. In addition, there are many other things that will make tour life more challenging–or different, at the very least–in 2020, such as limited crowds, social distancing protocols, and scheduling uncertainty. Some players will better handle those challenges than others, but it won’t necessarily be the strongest players who respond the best.

So my Elo ratings will, for the time being, incorporate a small penalty and a temporarily increased k-factor. (Something more like 69% for Thiem-Goffin, not 60%.) I haven’t finished the code yet, in large part because handling the two different types of layoffs–coronavirus and the usual injuries, etc–makes things very complicated. If you’re watching closely, you’ll see some minor tweaks to the numbers before the “Cincinnati” tournament in a few weeks.

There is a right answer

It’s clear from what I’ve written so far that any attempt to adjust Elo ratings for the COVID-19 layoff is a bit of a guessing game. But it won’t always be that way!

By the end of the year, we’ll know the right answer: just how unpredictable results turned out to be in the early going. Just as I’ve calculated penalties and k-factor adjustments for injury layoffs based on historical data, we will be able to do the same with match results from the second half of 2020. To be more precise, we’ll be able to work out a class of right answers, because one adjustment to the Elo formula will give us the best Brier Score, while another will best represent the gap between Novak Djokovic and Rafael Nadal, while others could target different goals.

The ultimate after-the-fact COVID-19 Elo-formula adjustment won’t help you win more money betting on tennis, but it will give us more insight into how the coronavirus layoff affected players after so much time off, and how quickly they returned to pre-layoff form. We’ll understand a little bit more about the game, even if we desperately hope never to have reason to apply the newly-won knowledge.

The Rarity of Winning Two Titles at One Tournament

This is a guest post by Peter Wetz.

With all the drama in the tennis world right now–paradoxically despite the lack of official match results–a dry analytical article might be just what you need. And what better opportunity than quarantine to work through my long list of articles to write?

In June 2019, Feliciano Lopez had to complete five matches in two days. Not because he had to hop between tournaments as a 22-year-old Jo-Wilfried Tsonga did in 2007, but because Lopez went deep into both the singles and doubles draws on the grass courts at Queen’s Club, ultimately winning both titles.

Lopez won all four of his singles matches in the deciding set, and there was not much time to celebrate and recover after the final, because the doubles title match awaited. Partnering a rehabilitating Andy Murray seems to have been a sensible decision based on the fact that Murray’s most lopsided head-to-head of 11-0 is against Lopez. By doing so, Lopez could be guaranteed to avoid facing Murray in the doubles draw. An unusual strategy–and probably not his top consideration in choosing a partner–but it worked.

Lifting two trophies on finals day happens quite often at the Challenger tour, but is unusual on the main tour, where the best singles players often skip the doubles draw entirely. But how rare is it? And has it changed over the years? Longtime fans will immediately think of John McEnroe and his nearly equal tally of doubles titles (78) and singles titles (77). The modest title counts of Roger Federer (6) and Rafael Nadal (11) pale in comparison, even though the Spaniard is an exceptional doubles player.

Let’s take a look at the instances when a player won both trophies at the same tournament since 2005.

Year	Tournament	Player (Partner)
2005	Dusseldorf	Tommy Haas (Alexander Waske)
2005	Halle		Roger Federer (Yves Allegro)
2005	Basel		Fernando Gonzalez (Agustin Calleri)
2006	Vina del Mar	Jose Acasuso (Sebastian Prieto)
2007	Chennai		Xavier Malisse (Dick Norman)
2007	Delray Beach	Xavier Malisse (Hugo Armando)
2007	Munich		Philipp Kohlschreiber (Mikhail Youzhny)
2007	Dusseldorf	Agustin Calleri (Juan Ignacio Chela)
2008	Monte Carlo	Rafael Nadal (Tommy Robredo)
2008	Dusseldorf	Robin Soderling (Robert Lindstedt)
2009	Costa Do Sauipe	Tommy Robredo (Marcel Granollers)
2009	San Jose	Radek Stepanek (Tommy Haas)
2009	Newport		Rajeev Ram (Jordan Kerr)
2010	Memphis		Sam Querrey (John Isner)
2010	Marseille	Michael Llodra (Julien Benneteau)
2010	Bucharest	Juan Ignacio Chela (Lukasz Kubot)
2011	Tokyo		Andy Murray (Jamie Murray)
2012	Zagreb		Mikhail Youzhny (Marcos Baghdatis)
2013	Newport		Nicolas Mahut (Edouard Roger Vasselin)
2014	Newport		Lleyton Hewitt (Chris Guccione)
2017	Montpellier	Alexander Zverev (Mischa Zverev)
2018	Gstaad		Matteo Berrettini (Daniele Bracciali)
2019	London		Feliciano Lopez (Andy Murray)

Two things may catch one’s eye when looking at the list: First, since 2011 the double-title feat occurred slightly less than once per year. But before that it happened several times a year with the sole exception of 2006. Second, the only player who managed to win both titles at a Masters event is Nadal at Monte Carlo in 2008.

It is obvious, and a frequent topic of tennis hipster talk, that top singles players do not care as much about doubles anymore, certainly not as much as McEnroe and his peers did. One line of argument is that the way that modern doubles tennis has evolved to become more and more different from the singles game. In order to keep up with that, singles players would need to adapt their practice routine, which might detract from potential singles success. Long story short, the argument is that doubles became too “difficult” for singles players.

But let’s look at the numbers. The following graphs show the composition of draws since the year 2000. We see the percentage of players in singles draws, who also entered the doubles draw of the same tournament for three different categories (A = All, M = Masters, G = Grand Slams). The first graph shows the numbers for top 50 singles players and the second graph for top 10 singles players.

Percentage of top 50 players entering doubles draws per 5 years
Percentage of top 10 players entering doubles draws per 5 years

The first graph is not very dramatic, but it establishes that the habits of top 50 singles players have been quite steady over the past 20 years among all tournament categories. Since the year 2000, irrespective of event categories, between 41 and 47 percent of top 50 players entering a singles draw also entered the doubles draw of the same tournament.*

The second graph shows us that the numbers for top 10 players are a different story entirely. Ignoring tournament categories, the number of top 10 players participating in doubles draws has plummeted from 35 to 22 percent. While the numbers also decreased if we only look at Masters tournaments, it is interesting that it remains higher than the overall number. This can likely be explained by the fact that the prize money for doubles at Masters events is significantly higher than at regular tour events. Often the organizers of these tournaments also have the financial power to persuade top players to play doubles in order to–I am hypothesizing here–increase ticket sales or attendance in the early days of a tournament. See the Indian Wells Masters for instance, which is known for its stellar doubles draw every year.

The most drastic decline in doubles attendance by top 10 singles players can be seen at the Grand Slams, however. While in the period between the years 2000 and 2004 every fifth singles player took part in the doubles, in the past five years only one out of 183 singles entries also appeared in the doubles draw. The sole exception (of course!) was Dominic Thiem, who entered the 2016 US Open doubles competition ranked number 10 in singles with his countryman Tristan Samuel Weissborn.

As with many analyses it is difficult to provide a definitive answer to the question at hand. But the numbers help us to see the size of the effects and theorize about its causes. That doubles competition has become more and more specialized certainly has its validity. At the same time, the numbers also suggest that top singles players simply optimize for prize money, which means focusing on singles, not doubles. If there was a McEnroe-esque player on tour today (as Rafa might be), he just wouldn’t play enough doubles to win nearly 80 titles.

However, it is hard to tell which was first: The decline of singles players playing doubles due to reasons such as financial motivation (among possibly many others), or the players’ realization that they simply cannot keep up with the elite doubles competition? One thing may be for sure though: Had TennisTV already existed a few decades ago, it would have shown a lot more doubles than it does now.

* Note that there is the possibility that a few singles players might have been willing to enter the doubles draw of a tournament, but couldn’t, because their ranking was too low among other reasons. However, I think this affects the analysis only marginally, if at all.

Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.

Tanking: A Model

The logic behind tanking a part of a tennis match–deliberately playing with less than maximum effort–is simple. If you have fallen behind early in the first set, you could choose to take it easy for the rest of the set. You probably would’ve lost the set anyway, and having semi-rested for several games, you’ll have more mental and physical energy to draw upon for the rest of the match.

By the end of this post, we’ll have some idea how useful that extra energy must be to make tanking worthwhile. It will take a few steps to get there.

The scenario

Consider some sample numbers to make this more concrete. Take two evenly matched men, each of whom win 70% of their service points. Maybe they are powerful–though not one-dimensional–servers on a reasonably fast surface. Winning seven out of ten service points means that nine out of ten games are holds of serve, so in our hypothetical match, breaks are at a premium.

Imagine that the match opens with one of those rare breaks. Given the 90% hold rate for both players, the man who got his nose in front has improved to an 83% chance of winning the set. In the simplest formulation, the player who has fallen behind faces two options for the balance of the set:

  • Continue playing at his usual level despite the low chance of winning, or
  • Take it easy, as the set is probably lost.

The tank

In the continue-as-usual scenario, our early front-runner has an 83% chance of winning the set. If both players continue playing at the same level for the duration of a best-of-five-sets match, that translates to a 62% chance of winning the match, leaving our player who decided not to tank with a 38% chance. (I’m using best-of-five because in a longer match, it’s more likely that a player can recover from losing the first set. That makes tanking a more plausible strategy.)

To evaluate the take-it-easy scenario, we need to pile on more assumptions. How much worse does a tanking player play? You will probably disagree with my estimates of the point-level costs and benefits of tanking, which is fine. I don’t have strong opinions about them, and they don’t matter much to the conclusions below. Consider these numbers just one illustration of the model. As soon as the trailing player decides to take it easy, let’s say his numbers fall to the following:

  • 20% return points won (instead of 30%)
  • 65% serve points won (instead of 70%)

That’s not a very good player–picture an unmotivated Nick Kyrgios. Down a break after the first game and playing a newly lackadaisical brand of tennis, he has a mere 1.3% chance of coming back to win the set. We’re simplifying quite a bit here, in large part because a player could always decide midway through the set to pause the tank, perhaps raising his game if he reaches 15-30 or better on his opponent’s serve. But again, this is just a model, and one I’m trying to keep from getting too complex.

The trade-off

The tanking player has, according to these assumptions, chosen to decrease his chance of winning the first set from 17% to a tick above 1%. If he received no benefit from conserving energy and both players returned to their 90% hold rate at the beginning of the next set, the tanking player’s chances of winning the match have fallen from 38% to 32%.

Clearly that’s not the whole story. A player who chooses to conserve energy at the expense of their immediate fortunes must assume that there are benefits coming later.

To further simplify, let’s assume that the tanking player loses the first set. Here are his chances of winning the match based on a few possible post-tank levels he could sustain:

  • 70% serve points won (SPW), 30% return points won (RPW): 31.3% (no benefit from tanking)
  • 71% SPW, 32% RPW: 46.3%
  • 72% SPW, 34% RPW: 61.9%
  • 73% SPW, 36% RPW: 75.8%
  • 74% SPW, 38% RPW: 93.3%

Remember that our tanking player has only a 38% chance of winning the match after sustaining the opening-game break, so the second scenario, in which his level improves to 71% SPW and 32% RPW, represents an improvement. That would be hardly noticeable over the course of three or four more sets. If the remainder of the match spanned 200 more points, it would mean winning 103 of them, instead of 100. If conserving energy early on confers even bigger benefits, it starts to look like a no-brainer.


Of course, it’s never this simple. The leading player might realize that his opponent was tanking and conserve some energy himself. The tanking player could have a hard time resuming his usual level (or better) at the right moment. Some points are more important than others, so the difference between 100 and 103 might not matter. Most matches are best-of-three, and giving up on the opening set in a shorter match is much more dangerous.

Those qualifications shouldn’t stop us from considering what tanking has to offer. While players don’t tank sets as often as they used to, there’s surely some energy-conservation benefit, and extra energy must have some value for the remainder of the match, right? I have no idea whether that value is equivalent to one point per hundred or something much higher or lower, but surely it’s possible that in some situations, it’s worth it.

The illustration I’ve used shows that the value of the extra energy doesn’t have to be that substantial to make tanking a plausible tactic. The small margins that determine the outcome of tennis matches mean that we’ll rarely recognize when a player is taking advantage of a tank, but those margins also mean that a small edge could be enough to make it worthwhile.

All calculations of game, set, and match probabilities are based on my publicly-available code.

Podcast Episode 83: Is the Practice Court Broken?

Episode 83 of the Tennis Abstract Podcast features co-host Carl Bialik, of the Thirty Love podcast, and guest Jeff McFarland of Hidden Game of Tennis. This week we dip our collective toe into a debate in the tennis coaching world.

With rallies short and aggressive, should players be using practice time differently? What types of skills can still be improved, once a player has reached the top? What tactics can a coach teach their charges, and which ones are too deeply ingrained in the physical nature of hitting the shots? The line between technique and tactics may not be a clear-cut as we think.

Is a 3- or 4-shot rally qualitatively different from a 5- or more-shot rally? How would you teach Madison Keys to retain the positives of her aggressive style while dialing back the aggression a bit? We offer more questions than answers, which seems appropriate for a topic that is far from settled, and is likely to remain controversial for years to come.

Thanks for listening!

(Note: this week’s episode is about 67 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

Who’s the GOAT? Balancing Career and Peak Greatness With Elo Ratings

On this week’s podcast, Carl, Jeff and I briefly discussed where Caroline Wozniacki ranks among Open-era greats. She’s among the top ten measured by weeks at the top of the rankings, but she has won only a single major. By Jeff’s Championship Shares metric, she’s barely in the top 30.

I posed the same question on Twitter, and the hive mind cautiously placed her outside the top 20:

It’s difficult to compare different sorts of accomplishments–such as weeks at number one, majors won, and other titles–even without trying to adjust for different eras. It’s also challenging to measure different types of careers against each other. For more than a decade, Wozniacki has been a consistent threat near the top of the game, while other players who won more slams did so in a much shorter burst of elite-level play.

Elo to the rescue

How good must a player be before she is considered “great?” I don’t expect everyone to agree on this question, and as we’ll see, a precise consensus isn’t necessary. If we take a look at the current Elo ratings, a very convenient round number presents itself. Seven players rate higher than 2000: Ashleigh Barty, Naomi Osaka, Bianca Andreescu, Simona Halep, Karolina Pliskova, Elina Svitolina, and Petra Kvitova. Aryna Sabalenka just misses.

Another 25 active players have reached an Elo rating of at least 2000 at their peak, from all-time greats such as Serena Williams and Venus Williams down to others who had brief, great-ish spells, such as Alize Cornet and Anastasia Pavlyuchenkova. Since 1977, 88 women finished at least one season with an Elo rating of 2000 or higher, and 60 of them did so at least twice.

(I’m using 1977 because of limitations in the data. I don’t have complete match results–or anything close!–for the early and mid 1970s. Unfortunately, that means we’ll underrate some players who began their careers before 1977, such as Chris Evert, and we’ll severely undervalue the greats of the prior decade, such as Billie Jean King and Margaret Court.)

The resulting list of 60 includes anyone you might consider an elite player from the last 45 years, along with the usual dose of surprises. (Remember Irina Spirlea?) I’ll trot out the full list in a bit.

Measuring magnitude

A year-end Elo rating of 2000 is an impressive achievement. But among greats, that number is a mere qualifying standard. Serena has had years above 2400, and Steffi Graf once cleared the 2500 mark. For each season, we’ll convert the year-end Elo into a “greatness quotient” that is simply the difference between the year-end Elo and our threshold of 2000. Barty finished her 2019 season with a rating of 2123, so her greatness quotient (GQ) is 123.

(Yes, I know it isn’t a quotient. “Greatness difference” doesn’t quite have the same ring.)

To measure a player’s greatness over the course of her career, we simply find the greatness quotient for each season which she finished above 2000, and add them together. For Serena, that means a whopping 20 single-season quotients. Wozniacki had nine such seasons, and so far, Barty has two. I’ll have more to say shortly about why I like this approach and what the numbers are telling us.

First, let’s look at the rankings. I’ve shown every player with at least two qualifying seasons. “Seasons” is the number of years with year-end Elos of 2000 or better, and “Peak” is the highest year-end Elo the player achieved:

Rank  Player                     Seasons  Peak    GQ  
1     Steffi Graf                     14  2505  4784  
2     Serena Williams                 20  2448  4569  
3     Martina Navratilova             17  2442  4285  
4     Venus Williams                  14  2394  2888  
5     Chris Evert                     14  2293  2878  
6     Lindsay Davenport               12  2353  2744  
7     Monica Seles                    11  2462  2396  
8     Maria Sharapova                 13  2287  2280  
9     Justine Henin                    9  2411  2237  
10    Martina Hingis                   8  2366  1932  
11    Kim Clijsters                    9  2366  1754  
12    Gabriela Sabatini                9  2271  1560  
13    Arantxa Sanchez Vicario         12  2314  1556  
14    Amelie Mauresmo                  6  2279  1113  
15    Victoria Azarenka                9  2261  1082  
16    Jennifer Capriati                8  2214   929  
17    Jana Novotna                     9  2189   848  
18    Conchita Martinez               11  2191   836  
19    Caroline Wozniacki               9  2189   674  
20    Tracy Austin                     5  2214   647  
Rank  Player                     Seasons  Peak    GQ  
21    Mary Pierce                      8  2161   637  
22    Elena Dementieva                 9  2140   629  
23    Simona Halep                     7  2108   562  
24    Svetlana Kuznetsova              6  2136   543  
25    Hana Mandlikova                  6  2160   516  
26    Jelena Jankovic                  4  2178   450  
27    Pam Shriver                      5  2160   431  
28    Vera Zvonareva                   5  2117   414  
29    Agnieszka Radwanska              8  2106   399  
30    Ana Ivanovic                     5  2133   393  
31    Petra Kvitova                    6  2132   346  
32    Na Li                            4  2095   310  
33    Anastasia Myskina                4  2164   290  
34    Anke Huber                       6  2072   277  
35    Mary Joe Fernandez               4  2110   274  
36    Nadia Petrova                    6  2094   265  
37    Dinara Safina                    3  2132   240  
38    Andrea Jaeger                    4  2087   237  
39    Angelique Kerber                 4  2109   224  
40    Nicole Vaidisova                 3  2121   222  
Rank  Player                     Seasons  Peak    GQ  
41    Manuela Maleeva Fragniere        6  2059   194  
42    Anna Chakvetadze                 2  2107   174  
43    Ashleigh Barty                   2  2123   162  
44    Helena Sukova                    3  2078   150  
45    Jelena Dokic                     2  2110   142  
46    Iva Majoli                       2  2067   119  
47    Elina Svitolina                  3  2052   108  
48    Garbine Muguruza                 2  2061    98  
49    Zina Garrison                    2  2065    96  
50    Samantha Stosur                  3  2061    92  
51    Daniela Hantuchova               2  2050    80  
52    Irina Spirlea                    2  2064    76  
53    Nathalie Tauziat                 3  2041    73  
54    Patty Schnyder                   2  2057    70  
55    Chanda Rubin                     3  2034    68  
56    Marion Bartoli                   2  2033    66  
57    Sandrine Testud                  2  2041    62  
58    Magdalena Maleeva                2  2024    41  
59    Karolina Pliskova                2  2028    37  
60    Dominika Cibulkova               2  2007     7

You’ll probably find fault with some of the ordering here. While it isn’t the exact list I’d construct, either, my first reaction is that this is an extremely solid result for such a simple algorithm. In general, the players with long peaks are near the top–but only because they were so good for much of that time. A long peak, like that of Conchita Martinez, isn’t an automatic ticket into the top ten.

From the opposite perspective, this method gives plenty of respect to women who were extremely good for shorter periods of time. Both Amelie Mauresmo and Tracy Austin crack the top 20 with six or fewer qualifying seasons, while others with as many years with an Elo of 2000 or higher, such as Manuela Maleeva Fragniere, find themselves much lower on the list.

Steffi, Serena, and the threshold

It’s worth thinking about what exactly the Elo rating threshold of 2000 means. At the simplest level, we’re drawing a line, below which we don’t consider a player at all. (Sorry, Aryna, your time will come!) Less obviously, we’re defining how great seasons compare to one another.

For instance, we’ve seen that Barty’s 2019 GQ was 123. Graf’s 1989 season, with a year-end Elo rating of 2505, gave her a GQ of 505. Our threshold choice of 2000 implies that Graf’s peak season has approximately four times the value of Barty’s. That’s not a natural law. If we changed the threshold to 1900, Barty’s GQ would be 223, compared to Graf’s best of 605. As a result, Steffi’s season is only worth about three times as much.

The lower the threshold, the more value we give to longevity and the less value we give to truly outstanding seasons. If we lower the threshold to 1950, Steffi and Serena swap places at the top of the list. (Either way, it’s close.) Even though Williams had one of the highest peaks in tennis history, it’s her longevity that truly sets her apart.

I don’t want to get hung up on whether Serena or Steffi should be at the top of this list–it’s not a precise measurement, so as far as I’m concerned, it’s basically a tie. (And that’s without even raising the issue of era differences.) I also don’t want to tweak the parameters just to get a result or two to look different.

Ranking Woz

I began this post with a question about Caroline Wozniacki. As we’ve seen, greatness quotient places her 19th among players since 1977–almost exactly halfway between her position on the weeks-at-number-one list and her standing on the title-oriented Championship Shares table.

If we had better data for the first decade of the Open era, Wozniacki and many others would see their rankings fall by at least a few spots. King, Court, and Evonne Goolagong Cawley would knock her into the 20s. Virginia Wade might claim a slot in the top 20 as well. We can quibble about the exact result, but we’ve nailed down a plausible range for the 2018 Australian Open champion.

One-number solutions like this aren’t perfect, in part because they depend on assumptions like the Elo threshold discussed above. Just because they give us authoritative-looking lists doesn’t mean they are the final word.

On the other hand, they offer an enormous benefit, allowing us to get around the unresolvable minor debates about the level of competition when she reached number one, the luck of the draw at grand slams she won and lost, the impact of her scheduling on ranking, and so on. By building a rating based on every opponent and match result, Elo incorporates all this data. When ranking all-time greats, many fans already rely too much on one single number: the career slam count. Greatness quotient is a whole lot better than that.

Are American Players Screwed Once You Drag Them Into a Rally?

Long after retiring from tennis, Marat Safin remains quotable. The Russian captain at the ATP Cup had this to say to his charge, Karen Khachanov, during a match against Taylor Fritz:


This isn’t exactly testable. I don’t know you’d quantify “shock-and-awe,” or how to identify–let alone measure–attempts to scare one’s opponent. Or screwed-ness, for that matter. But if we take “screwed” to mean the same as “not very likely to win,” we’ve got something we can check.

Many fans would agree with the general claim that American men tend to have big serves, aggressive game styles, and not a whole lot of subtlety. Certainly John Isner fits that mold, and Sam Querrey doesn’t deviate much from it. While Fritz is a big hitter who racks up his share of aces and second-shot putaways, his style isn’t so one-dimensional.

Taylor Fritz: not screwed

Using data from the Match Charting Project, I calculated some rally-length stats for the 70 men with at least 20 charted matches in the last decade. That includes five Americans (Fritz, Isner, Querrey, Steve Johnson, and Jack Sock) and most of the other guys we think of as ATP tour regulars.

Safin’s implied definition is that rallies of four shots or fewer are “shock-and-awe” territory, points that are won or lost within either player’s first two shots. Longer rallies are, supposedly, the points where the Americans lose the edge.

That is certainly the case for Isner. He wins only 40% of points when the rally reaches a fifth shot, by far the worst of these tour regulars. Compared to Isner, even Nick Kyrgios (44%) and Ivo Karlovic (45%) look respectable. The range of winning percentages extends as high as 56%, the mark held by Nikoloz Basilashvili. Rafael Nadal is, unsurprisingly, right behind him in second place at 54%, a whisker ahead of Novak Djokovic.

Fritz, at 50.2%, ranks 28th out of 70, roughly equal to the likes of Gael Monfils, Roberto Bautista Agut, and Dominic Thiem. Best of all–if you’re a contrarian like me, anyway–is that Fritz is almost 20 places higher on the list than Khachanov, who wins 48.5% of points that last five shots or more.

More data

Here are 20 of the 70 players, including some from the top and bottom of the list, along with all the Americans and some other characters of interest. I’ve calculated each player’s percentage of points won for 1- or 2-shot rallies (serve and return winners), 3- or 4-shot rallies (serve- and return-plus-one points), and 5- or more-shot rallies. They are ranked by the 5- or more-shot column:

Rank  Player                 1-2 W%  3-4 W%  5+ W%  
1     Nikoloz Basilashvili    43.7%   54.1%  55.8%  
2     Rafael Nadal            52.7%   51.6%  54.3%  
3     Novak Djokovic          51.8%   54.6%  54.0%  
4     Kei Nishikori           45.5%   51.2%  53.9%  
11    Roger Federer           52.9%   54.9%  52.1%  
22    Philipp Kohlschreiber   50.1%   50.1%  50.7%  
28    Taylor Fritz            51.1%   47.2%  50.2%  
30    Jack Sock               49.0%   46.5%  50.2%  
31    Alexander Zverev        52.8%   50.3%  50.0%  
32    Juan Martin del Potro   53.8%   49.1%  50.0%  
34    Andy Murray             54.3%   49.5%  49.4%  
39    Daniil Medvedev         53.9%   50.4%  49.0%  
43    Stefanos Tsitsipas      51.4%   50.5%  48.6%  
44    Karen Khachanov         53.7%   48.1%  48.5%  
48    Steve Johnson           49.2%   48.8%  48.3%  
61    Sam Querrey             53.5%   48.0%  46.2%  
62    Matteo Berrettini       53.6%   49.3%  46.1%  
66    Ivo Karlovic            51.8%   43.9%  44.9%  
68    Nick Kyrgios            54.6%   47.4%  44.2%  
70    John Isner              52.3%   48.3%  40.2%

Fritz is one of the few players who win more than half of the shortest rallies and more than half of the longest ones. The first category can be the result of a strong serve, as is probably the case with Fritz, and is definitely the case with Isner. But you don’t have to have a big serve to win more than half of the 1- or 2-shot points. Nadal and Djokovic do well in that category (like they do in virtually all categories) in large part because they negate the advantage of their opponents’ serves.

Shifting focus from the Americans for a moment, you might be surprised by the players with positive winning percentages in all three categories. Nadal, Djokovic, and Roger Federer all make the cut, each with plenty of room to spare. The remaining two are the unexpected ones. Philipp Kohlschreiber is just barely better than neutral in both classes of short points, and a bit better than that (50.7%) on long ones. And Alexander Zverev qualifies by the skin of his teeth, winning very slightly more than half of his long rallies. (Yes, that 50.0% is rounded down, not up.) Match Charting Project data is far from complete, so it’s possible that with a different sample, one or both of the Germans would fall below the 50% mark, but the numbers for both are based on sizable datasets.

Back to Fritz, Isner, and company. Safin may be right that the Americans want to scare you with a couple of big shots. Isner has certainly intimidated his share of opponents with the serve alone. Yet Fritz, the player who prompted the comment, is more well-rounded than the Russian captain gave him credit for. Khachanov won the match on Sunday, and at least at this stage in their careers, the Russian is the better player. But not on longer rallies. Based on our broader look at the data, it’s Khachanov who should try to avoid getting dragged into long exchanges, not Fritz.

Podcast Episode 82: ATP Cup and WTA Season Preview

Episode 82 of the Tennis Abstract Podcast tests out a new format for the new year, featuring co-host Carl Bialik, of the Thirty Love podcast, and guest Jeff McFarland of Hidden Game of Tennis.

The three of us dig into the new ATP Cup, considering whether the format is appealing to players and fans, how we should feel about odd matchups between players hundreds of ranking places apart, and–most importantly–what captains should be doing with the stats available to them.

We also look at the top of the WTA ranking table, considering whether Ashleigh Barty will continue her reign for another twelve months, or if Bianca Andreescu–or Karolina Pliskova–will topple her. We also debate where Caroline Wozniacki stands among Open-era greats, as one of the few women to hang on to the number one ranking for more than a full year.

Thanks for listening!

(Note: this week’s episode is about 66 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

Aleksandre Metreveli’s Bad Day Wasn’t Double-Bagel Bad

Roberto Bautista Agut got his 2020 season off to a roaring start on Saturday at the ATP Cup, knocking out the No. 2 Georgian player, Aleksandre Metreveli, by the embarrassing score of 6-0 6-0. Double bagels are extremely rare on the men’s tour, with fewer than 100 recorded in the last three decades.

About one-quarter of those 6-0 6-0 results have come in Davis Cup, the most likely venue for such an uneven matchup. Davis Cup’s reverse singles, the (largely defunct) part of the competition that pits each side’s top player against the other’s second-best, generates particularly lopsided outcomes. The ATP Cup doesn’t have that, but Bautista Agut is better than many national number ones, and Metreveli is one of the handful of competitors in Australia this week who would never otherwise feature in a tour-level event.

Still, it wasn’t quite as lopsided as all that.

The match lasted 72 minutes, longer than any of the 59 ATP double bagels for which I have match stats. It was only the fourth 6-0 6-0 result to reach the one-hour mark. The previous longest double bagel was a 65-minute contest at the 2005 Rome Masters in which Guillermo Canas battered Juan Monaco. Of the 120 women’s tour-level double bagels for which I have stats, none exceeded 67 minutes.

Counting stats

Match times can be affected by player tics and crowd conditions, but the number of points played cannot. By that measure as well, Metreveli was better than his scoreline. He kept the Spaniard on court for 97 points, longer than all but three of the previous ATP double bagels. The average 6-0 6-0 men’s match lasts only 74 points. Over 150 tour-level matches last year required 97 or fewer points, including several finals and a couple of contests that included a 7-5 set.

Another way to look at the closeness of the match is to consider break points saved. The score requires that Metreveli didn’t break serve, and that Bautista Agut did so six times. But the Georgian fought hard against the Spaniard’s return assault, saving eight break points. Only four of the 59 previous double-bagel losers withstood so many break attempts.

Double bagel chances

Bautista Agut won 83% of his service points, and Metreveli won only 40%. If those rates continued without any unusual streaks of points won or lost, that would translate to a 98.9% hold percentage for the Spaniard and a 26.4% hold percentage for the Georgian. To win all twelve games, RBA needed to hold six times and break six times. Based on these hold rates, his chances of doing so were 14.8%.

Put another way, if these two players kept playing at the same levels for a large number of matches (sorry, Aleksandre!), the score would be 6-0 6-0 only about one match out of six.

Once again, Metreveli’s performance stands out as one of the strongest to result in a double bagel. Only five of the previous 59 drubbings had such a low probability of turning out 6-0 6-0. Measured by double-bagel probability, eight matches from the 2019 season were more lopsided than this one, and only one of them ended in twelve straight games. Three of the losers managed to avoid any bagels at all:

Event          Winner       Loser         Score        DB Prob  
Winston Salem  Fratangelo   Weintraub     6-0 6-0        63.5%  
Los Cabos      Granollers   Gomez         6-0 6-1        24.6%  
Us Open        Federer      Goffin        6-2 6-2 6-0    19.9%  
Estoril        Dav. Fokina  Chardy        6-1 6-2        18.5%  
Acapulco       Millman      Gojowczyk     6-0 6-2        17.2%  
Rome           Nadal        Basilashvili  6-1 6-0        16.6%  
Miami          Car. Baena   Kudla         6-1 6-2        16.6%  
Tokyo          Djokovic     Pouille       6-1 6-2        15.5% 

(Yes, Metreveli fared better against RBA than Basilashvili did against Nadal last May! The Basilashvili-Nadal rematch on Saturday was a bit closer, though.)

None of this is to say that Metreveli had a good day in his ATP Cup debut. However, double bagels are so rare that they tend to grab the headlines, pushing the details to the side. Given how the Georgian played in his ATP Cup debut, he deserved a more pedestrian loss with at least a game or two in the win column.

WTA Decisions From the Backhand Corner

Earlier this week I presented a lot of data about what happens when men face a makeable ball hit to their backhand corner. That post was itself a follow-up on a previous look at what happened when players of both genders attempted down-the-line backhands. You don’t need to read those two articles to know what’s going on in this one, but if you’re interested in the topic, you’ll probably find them worthwhile.

Decision-making in the backhand corner is one of the biggest differences between pro men and women. Let me illustrate in the nerdiest way possible, with bug reports from the code I wrote to assemble these numbers. My first stab at the code to aggregate player-by-player numbers for men failed because some men never hit a topspin backhand from the backhand corner. At least, not in any match recorded by the Match Charting Project. The offending player who generated those divide-by-zero errors was Sam Groth. In his handful of charted matches, he relied entirely on the slice, at least in those rare cases where rallies extended beyond the return of serve.

Compare with the bug that slowed me down in preparing this post. The problematic player this time was Evgeniya Rodina. In nine charted matches, she has yet to hit a forehand from the backhand corner. If your backhand is the better shot, why would you run around it? Of the nearly 200 players with five charted matches from the 2010s, Rodina is the only one with zero forehands. But she isn’t really an outlier. 23 other women hit fewer than 10 forehands in all of their charted matches, including Timea Bacsinszky, who opted for the forehand only four times in 32 matches.

Faced with a makeable ball in the backhand corner, men and women both hit a non-slice groundstroke about four-fifths of the time. But of those topspin and flat strokes, women stick with the backhand 94% of the time, compared to 82% for men.

A few WTA players seek out opportunities to run around their backhands, including Sam Stosur and Polona Hercog, both of whom hit the forehand 20% of the time they are pushed into the backhand corner. Ashleigh Barty also displays more Federer-like tactics than most of her peers, using the forehand 13% of the time. Yet most of the women with powerful forehands, like Serena Williams, have equal or better backhands, making it counter-productive to run around the shot. Serena hits a forehand only 1% of the time her opponent sends a makeable ball into her backhand corner.

Directional decisions

Backhand or forehand, let’s start by looking at which specific shot that players chose. The Match Charting Project contains shot-by-shot logs of about 2,900 women’s matches from the 2010s, including 365,000 makeable balls hit to one player’s backhand corner. (“Makeable” is defined as a ball that either came back or resulted in an unforced error.)

Here is the frequency with which players hit backhand and forehands in different directions from their backhand corner. I’ve included the ATP numbers for comparison:

BH Direction               WTA Freq  ATP Freq  
Down the line                 17.4%     17.4%  
Down the middle               35.2%     29.5%  
Cross-court                   47.3%     52.9%  
FH Direction               WTA Freq  ATP Freq  
Down the line (inside-in)     35.2%     35.1%  
Down the middle               16.2%     12.8%  
Cross-court (inside-out)      48.4%     51.8%

Once a forehand or backhand is chosen, there isn’t much difference between men and women. Women go up the middle a bit more often, which may partly be a function of using the topspin or flat backhand in defensive positions slightly more than men do. I’ve also observed that today’s top women are more likely to hit an aggressive shot down the middle than men are. The level of aggression and risk may be similar to that of a bullet aimed at a corner, but when we classify by direction, it looks a bit more conservative. That’s just a theory, however, so we’ll have to test that another day.

Point probability

Things get more interesting when we look at how these choices affect the likelihood of winning the point. On average, a woman faced with a makeable ball in her backhand corner has a 47.2% chance of winning the point. (For men, it’s 47.7%.) The serve has some effect on the potency those shots toward the backhand corner. If the makeable ball was a service return–presumably weaker than the average groundstroke–the probability of winning the point is 48.2%. If the makeable ball is one shot later, an often-aggressive “serve-plus-one” shot, the chances of fighting back and winning the point are only 46.3%. It’s not a huge difference, but it is a reminder that the context of any given shot can affect these probabilities.

The various decisions available to players each have their own effect on the probability of winning the point, at least on average. If a woman chooses to hit a down-the-line backhand, her likelihood of winning the point increases to 53.0%. If she makes that shot, her odds rise to 68.4%.

The following table shows those probabilities for every decision. The first column of percentages, “Post-Shot,” indicates the likelihood of winning after making the decision–the 53.0% I just mentioned. The second column, “In-Play,” is the chance of winning if she makes that shot, like 68.4% for the down-the-line backhand.

Shot      Direction  Post-Shot  In-Play  
Backhand  (all)          48.5%    55.2%  
Backhand  DTL            53.0%    68.4%  
Backhand  Middle         44.6%    48.8%  
Backhand  XC             49.9%    55.8%  
Forehand  (all)          56.3%    56.1%  
Forehand  DTL (I-I)      61.4%    73.7%  
Forehand  Middle         45.7%    50.3%  
Forehand  XC (I-O)       56.2%    64.4%

The down-the-line shots are risky, so the gap between the two probabilities is a big one. There is little difference between Post-Shot and In-Play for down-the-middle shots, because they almost always go in. For the forehand probabilities, keep in mind that they are skewed by the selection of players who choose to use their forehands more often. Your mileage may vary, especially if you play like Rodina does.

Cautious recommendations

Looking at this table, you might wonder why a player would ever make certain shot selections. The likelihood of winning the point before choosing a wing or direction is 47.2%, so why go with a backhand down the middle (44.6%) when you could hit an inside-in forehand (61.4%)? It’s not the risk of missing, because that’s baked into the numbers.

One obvious reason is that it isn’t always possible to hit the most rewarding shot. Even the most aggressive men run around only about one-quarter of their backhands, suggesting that it would be impractical to hit a forehand on the remaining three-quarters of opportunities. That wipes out half of the choices I’ve listed. And even a backhand wizard such as Simona Halep can’t hit lasers down the line at will. The probabilities reflect what happened when players thought the shot was the best option available to them. Even though were occasionally wrong, this is very, very far from a randomized controlled trial in which a scientist told players to hit a down-the-line backhand no matter what the nature of the incoming shot.

Another complication is one that I’ve already mentioned: The success rates for rarer shots, like inside-in forehands, reflect how things turned out for players who chose to hit them. That is, for players who consider them to be weapons. It might be amusing to watch Monica Niculescu hit inside-out topspin forehands at every opportunity, but it almost certainly wouldn’t improve her chances of winning. You only get those rosy forehand numbers if you can hit a forehand like Stosur does.

That said, the table does drive home the point that conservative shot selection has an effect on the probability of winning points. Some women are happy sending backhand after backhand up the middle of the court, and sometimes that’s all you can do. But when more options are available, the riskier choices can be more rewarding.

Player probabilities

Let’s wrap up for today by taking a player-by-player look at these numbers. We established that the average player has a 47.2% chance of winning the point when a makeable shot is arcing toward her backhand corner. Even though Tsvetana Pironkova’s number is also 47.2%, no player is average. Here are the top 14 players–minimum ten charted matches, ranked by the probability of winning a point from that position. I’ve also included the frequency with which they hit non-slice backhands:

Player                     Post-Shot  BH Freq  
Kim Clijsters                  53.4%    77.6%  
Na Li                          53.2%    87.5%  
Camila Giorgi                  52.9%    93.8%  
Patricia Maria Tig             52.1%    66.1%  
Simona Halep                   52.1%    83.6%  
Belinda Bencic                 51.5%    91.7%  
Dominika Cibulkova             51.3%    70.1%  
Veronika Kudermetova           50.9%    73.9%  
Jessica Pegula                 50.7%    73.7%  
Su-Wei Hsieh                   50.6%    81.8%  
Dayana Yastremska              50.6%    87.6%  
Anna Karolina Schmiedlova      50.3%    87.4%  
Serena Williams                49.9%    89.2%  
Sara Errani                    49.8%    70.0%

These numbers are from the 2010s only, so they don’t encompass the entire careers of the top two players on the list, Kim Clijsters and Li Na. It is particularly impressive that they make the cut, because their charted matches are not a random sample–they heavily tilt toward high-profile clashes against top opponents. The remainder of the list is a mixed bag of elites and journeywomen, backhand bashers and crafty strategists.

Next are the players with the best chances of winning the point after hitting a forehand from the backhand corner. I’ve drawn the line at 100 charted forehands, a minimum that limits our pool to about 50 players:

Player                Post-Shot  FH Freq  
Maria Sharapova           69.0%     4.1%  
Dominika Cibulkova        65.1%    10.5%  
Ana Ivanovic              64.7%    11.1%  
Yafan Wang                64.4%     8.8%  
Rebecca Peterson          63.4%    15.2%  
Simona Halep              63.1%     6.8%  
Carla Suarez Navarro      63.0%     7.7%  
Andrea Petkovic           62.3%     5.3%  
Christina McHale          61.9%    15.2%  
Anastasija Sevastova      61.3%     4.2%  
Petra Kvitova             60.8%     4.6%  
Caroline Garcia           60.7%     7.5%  
Misaki Doi                60.5%    17.0%  
Madison Keys              59.3%     9.3%  
Elina Svitolina           59.1%     3.9%

Maria Sharapova is the Gilles Simon of the WTA. (Now there’s a sentence I never thought I’d write!) Both players usually opt for the backhand, but are extremely effective when they go for the forehand. Kudos to Sharapova for her well-judged attacks, though it could be that she’s leaving some points on the table by not running around her backhand more often.


As I wrote on Thursday, we’re still just scratching the surface of what can be done with Match Charting Project data to analyze tactics such as this one. A particular area of interest is to break down backhand-corner opportunities (or chances anywhere on the court) even further. The average point probability of 47.2% surely does not hold if we look at makeable balls that started life as, say, inside-out forehands. If some players are facing more tough chances, we should view those numbers differently.

If you’ve gotten this far, you must be interested. The Match Charting Project has accumulated shot-by-shot logs of nearly 7,000 matches. It’s a huge number, but we could always use more. Many up and coming players have only a few matches charted, and many interesting matches of the past (like most of those played by Li and Clijsters!) remain unlogged. You can help, and if you like watching and analyzing tennis, you should.

How Much Will the ATP Cup Raise for Australian Bushfire Relief?

Yesterday, the ATP announced that it would make a sizeable donation to the Australian Red Cross:

Several players, including Nick Kyrgios, have made additional pledges of their own that extend across the several tournaments of the Australian summer. (Kyrgios’s pledge started the ball rolling, a rare instance of the tour following the lead of its most controversial star.)

How much?

The ATP offered an estimate of 1,500 aces. This is the first edition of the ATP Cup, not to mention the first men’s tour event in Perth, so we can’t simply check how many aces there were last year. Complicating things even further, we don’t know who will play for each nation in each day of the tournament, or which countries will advance to the knockout stages.

In other words, any ace prediction is going to be approximate.

Start with the basics. The ATP Cup will encompass 129 matches. That’s 43 ties, with two singles rubbers and one doubles rubber each. As in the new Davis Cup finals, many doubles rubbers are likely to be “dead,” so all 43 will probably not be played. In Madrid, 21 of the 25 doubles matches were played*, so let’s say that doubles will be skipped at the same rate in Australia, giving us 36 doubles matches.

* one of the four matches I’ve excluded was a 1-0 retirement, which for the purpose of ace counting–not to mention common sense–is effectively unplayed.

The average ace counts in best-of-three matches across the entire tour last year were 12 per singles match and 7 per doubles match. That gives us 1,284 for the 122 total contests we expect to see over the course of the event.

But we can do better. There are more aces on hard courts by a healthy margin. Over the 2019 season, the average best-of-three hard-court singles match returned 15 aces, while doubles matches featured half as many. That works out to a projected total of 1,542, 20% higher than where we started, and quite close to the ATP’s estimate.

While we don’t have much data on the surface in Perth, we have years worth of results from Brisbane and Sydney. Brisbane was one of the ace-friendliest surfaces on tour, while Sydney was at the other end of the spectrum. The figures have also varied from year to year, even controlling for the changing mix of players. Whether we look at one year or a longer time span, the average ace rates in Brisbane and Sydney combine to something in the neighborhood of the tour-wide rate.

Complicating factors

The record-setting temperatures in Australia are likely to nudge ace rates upwards. But the mix of players makes things considerably more difficult to forecast.

One challenge is the extreme range between the best players in the event (Rafael Nadal and Novak Djokovic) and the weakest, like Moldova’s 818th-ranked Alexander Cozbinov. Not only are underdogs like Cozbinov likely to see their typical ace rates plummet against higher-quality competition, they will probably struggle to keep matches competitive. The shorter the match, the fewer aces. Ironically, Cozbinov fought Steve Darcis for over three hours on the first day of play, but even at that length, only 2 of his 116 service points went for aces. He and Darcis combined for a below-average total of 10.

Another difficulty is one that would arise in predicting the total aces at any tournament. Overall ace counts depend heavily on who advances to the later rounds. The Spanish team of Nadal, Roberto Bautista Agut, and Pablo Carreno Busta is likely to do well despite relatively few first-serve fireworks. But if Canada reprises its Davis Cup Finals success, the top-line combination of Denis Shapovalov and Felix Auger Aliassime could give us six rounds of stratospheric serving stats. The American duo of John Isner and Taylor Fritz could do the same, though their odds of advancing took a dire turn after a day-one loss to Norway. At least Isner has already done his part, tallying 33 aces in a three-set loss to Casper Ruud.

As I write this, day one is not quite in the books. The first ten completed singles matches worked out to 16 aces each, slightly above the hard-court tour average. Thanks to Isner and Kyrgios, the outliers propped up that number, with 37 and 35 aces in the Isner-Ruud and Kyrgios-Struff matches, respectively. The three completed doubles matches have averaged just over 6 aces each, a bit below tour average.

This is all of long way of saying, surprise! The ATP’s estimate isn’t bad at all. A full simulation of each matchup and the event as a whole would give us more precision, but barring that, 1,500 aces and $150,000 looks like a pretty good bet. Philanthropists should line up behind the big hitting teams from Australia, Canada, and the USA, or at least cheer for an above-average number of free points off the serve of Rafael Nadal.