In their third round match today at the Australian Open, Sara Errani and Su Wei Hsieh played 232 points. The fastest serve either one hit registered at 93 mph (149 kmh), Hsieh’s first serves averaged 85 mph, and Errani’s mean first serve speed was 75 mph. I use the word “mean” here as more than just a way to avoid saying “average” so many times.
The two veterans are crafty–dare I say tricky–players with an arsenal of weapons once the ball is in play. But the serve is mostly just a stumbling block to make the best of. Hsieh won 62 of her 115 return points, good for 54% of Errani’s serves. This is more impressive than it sounds–the Italian double faulted only four times today. It’s fairly common for a winner on the women’s tour to win more than half of her return points, but what makes this match so weird is that Errani did the same. She won 63 of her 117 return points, also a 54% clip.
About half of WTA losers fail to convert better than 50% of their service points. But only 2.4% of winners miss the mark. And there’s a huge gap between 50%–mediocre and survivable–and Hsieh’s 46%. A 46% rate of service points won translates to a 40% likelihood of holding. Coincidentally, that’s exactly what both players did, each hanging on to their service games in 6 of 15 tries.
I have the relevant stats for just under 25,000 tour-level, main draw women’s matches since 2010, and only about 80 winners–0.3%, or less than once per 300 contests–won service points at a lower clip than Hsieh did today.
** I say “about” because the stats I have from the early 2010s aren’t perfect. A match with 60% of return points won is a prime candidate to be a mistake. I checked these 80 for obvious errors, like matches with a small number of service breaks, but those numbers aren’t perfect either.
There’s no grand analytical insight to be gleaned from a match like this. It’s just a glorious oddity that reminds us how many different ways there are to win matches. (And to be honest, you only need to watch Hsieh for about 90 seconds to recognize that.) In that spirit, here’s some more trivia:
Since 2010, this is only the 12th Australian Open main draw match in which neither player won half of her service points.
The only AO match in which neither player won 46% of their service points was the 2018 third-rounder between Anett Kontaveit and Jelena Ostapenko. They both held about 45.5% of their points, and 68% of total games (17 of 25) were breaks.
There have been about 400 tour-level matches since 2010 in which neither player wins half of their service points. Before today, 21 of those involved Errani, and she won 17 of them.
The other players who have been involved in at least 12 such matches are Monica Niculescu (16), Alize Cornet (14), and Carla Suarez Navarro (13). Today was only Hsieh’s 5th appearance on the list.
Perhaps oddest of all, this the first time in four tries that Hsieh avoiding getting bageled by Errani. Last time they played, in Istanbul in 2017, the Italian won, 6-0 6-1, needing only 55 minutes and a total of 87 points. Errani was so on-form that day that she won a whopping 66% of her service points. Hsieh finally turned the tables, even if she still hasn’t figured out how to stop this dogged opponent from breaking her serve.
An underhand serve functions in two ways–one short term, one long term. The short-term goal is to win a single point. Your opponent is standing way back, and the service equivalent of a drop shot could go for a 50 mile-per-hour ace. The long-term goal is to give your opponent something to worry about, perhaps distracting him or changing his return position for games, or sets to come. It’s not about winning a single point, but about slightly improving your odds in many future points.
In his second-round match yesterday against Ugo Humbert at the Australian Open, Nick Kyrgios opted for both. He unleashed the underhander twice, once at 40-love in his second service game, and again at 5-5, 40-30 in the fourth set.
The first dropper was on as meaningless a point as he could ask for. Kyrgios’s probability of winning a service game from 40-love is about 99.6% (really!), so the risk of losing the game after throwing away a point is essentially nil. He won the point with a backhand winner on his next shot, but the object of the exercise–assuming there was a tactical one, and I’ll give Nick the benefit of the doubt here–was more long-term oriented.
He delivered the second underarm serve on a much higher-pressure point. Kyrgios is still heavily favored to hold serve from 40-30, but he could be forgiven for feeling some nerves and wishing for a free point. This time he netted the underhand attempt and ended up winning the point after a (conventional) second serve.
A drop of data
When the underhand serve first started to go mainstream a couple of years ago, I updated the Match Charting Project spreadsheet to allow us to track these attempts. Counting the Kyrgios-Humbert match, we’ve now gathered the results of 35 drop-serve attempts across 20 different men’s matches. (We’ve recorded many women’s underhand serves as well, but most of those belong to Sara Errani, who has a different set of goals when she goes that route.)
35 points is awfully far from big data, but it is enough to get a taste of how a handful of players are deploying this unorthodox weapon.
The most common point score for an underarm serve is 40-love. Of the 35 attempts, 40-love accounts for 12 of them. Another 4 occured at 40-15, plus two more at 30-love, so roughly half of the recorded drop serves came with a service game more or less secured. A few of the remaining points were also relatively unimportant ones, like Daniil Medvedev’s underhander at love-40 toward the end of a 2019 US Open match against Hugo Dellien, and Alexander Bublik’s back-to-back tries at 0-5 and 1-5 in a tiebreak against John Isner.
Bublik is the major source of unimportant-point underarm serving. He’s responsible for 19 of the recorded points, 16 of which were at 40-love, 40-15, 30-love, or those two tiebreak points I just mentioned.
Inferring tactics
Since so many underarm serves are deployed at low-pressure moments, it’s tempting to conclude that players are thinking long term.
On the other hand, our handful of recorded underhand deliveries–even the ones on 40-love points–don’t skew toward the beginning of matches. We have two charted matches in which Robin Haase tried an underhander: a 2019 Budapest tilt against Borna Coric in which he made his first attempt in the third game, and a 2020 Davis Cup rubber when he waited until the 32nd game of the match.
Poster boy Bublik is inconsistent on this as well. Twice he has brought out the underhander in his second service game–once in the Newport match versus Isner, and another time the same summer in Washington against Bradley Klahn. Yet at the US Open against Thomas Fabbiano the same year, he didn’t unleash the secret weapon until 40-love in the 32nd game of the match.
I’ll admit, it might be foolish to try to detect the grand plan underlying the behavior of Alexander Bublik.
But it works!
Yeah, our 35 points make up tiny sample, but… the server won 27 of these 35 points! That’s 77%, and it includes underarm first-serve attempts that missed. When players had to hit a conventional second serve, they still won 7 of 10 points–a rate of second serve points won that any player would happily accept.
These numbers–cautiously as we must treat them–suggest that the underarm serve trend has plenty of room to run. The rare players who dare to risk ridicule are still only using the drop serve less than twice per match, and of course the vast majority of men on tour are never hitting them at all. The more common the underhand delivery becomes, the less effective it will be, but there’s a lot of space between the current drop-serve win percentage of 77% and the typical player’s success rate on serve. Tour average is around 65%, and only the most dominant servers exceed 70%.
As Bublik and friends have discovered, there’s little risk in mixing things up. Strong servers like him and Kyrgios have plenty of low-leverage opportunities to remind their opponents that surprises could be in store later in the match, when the stakes are raised. Our very early indicators suggest that where Kyrgios has gone, the rest of the tour could profitably follow.
The pandemic offers a wealth of natural experiments. Ever wondered how the presence of fans affects players? Before last March, we were mostly limited to speculation, because fans were almost always there. The tours have made various compromises to keep the action going, so we have a wealth of data from all sorts of different scenarios–with or without linespeople, with or without towelkids, and of course, with or without fans.
The closest thing we have to a “pure” natural experiment concerning the effect on fans on tennis players is the 2020 US Open. Flushing Meadows is usually packed with spectators on most courts, while in 2020, it was empty save a handful of support staff. There are confounding variables aplenty, such as the aforementioned lack of linespeople (on most courts) and towelkids, and we also must keep in mind that players entered the 2020 US Open with less recent match play than usual. It isn’t a perfect natural experiment–such things are exceedingly rare–but it is better than tennis usually offers.
What should we expect from spectator-free tennis? One suggestion comes from Ben Cohen and Joshua Robinson, who found in August that both basketball and soccer players were shooting more accurately in empty stadiums:
NBA players are making a higher percentage of their free throws and hitting corner 3-pointers at rates the league has never seen. Soccer players are striking dead balls more precisely than they did before the pandemic. Without the distraction of screaming fans, one part of their games seems to have improved: shooting.
We can already speculate that tennis won’t be so clear cut. For one thing, there weren’t screaming fans before the pandemic. For another, everything in tennis is a tradeoff: If you’re serving more accurately, you might be tempted to try for a bit more power or aim closer to the corners. The “accuracy” effect, then, wouldn’t show up as accuracy, but as increased speed, or some mix of several measures. But let’s not rush to throw in the towel (as it were)–let’s look at the numbers.
US Open, now and then
We’ll check four different stats for an empty-stadium effect: first serve in, double faults per second serve (the inverse of second serves made), first serve points won, and average first serve speed.
For each stat, we’ll calculate averages for men and women from 2019 and 2020 US Open single main draw matches, adjusted for player. (I’m using the data available in my slam_pointbypoint GitHub repository.) That is, we’ll limit our focus to those players who appeared in both tournaments and weight each player’s effect by the year they played the least. A player who served 300 points in 2019 and 100 points in 2020 will have a weight of 100 points in both calculations; a player who served 250 points in both years will have a weight of 250 points in both. This corrects for the different mix of players (and the amount that each player competed) in the two adjacent years, which might otherwise affect the numbers in a misleading way.
Here are the results:
WOMEN 2020 2019 Change
First in 61.8% 61.5% 0.5%
DF/second 13.7% 13.4% 2.0%
First won 66.4% 62.2% 6.6%
First KM/H 158.6 155.2 2.1%
MEN 2020 2019 Change
First in 61.7% 59.5% 3.7%
DF/second 10.7% 11.3% -5.4%
First won 72.9% 71.2% 2.3%
First KM/H 186.2 184.8 0.8%
The women didn’t really improve their accuracy: a slight uptick in first serves in, and a bigger decrease in second serves made. On the other hand, they won way more of their first-serve points in 2020 than in 2019, and they served 3.4 KM/h faster. That puts the accuracy figure in perspective–no, they didn’t make more first serves, but it appears that they traded speed for accuracy. They did quite well in the bargain.
The men, on average, took a different approach. They made more first serves and committed fewer double faults (Alexander Zverevnotwithstanding), but they didn’t increase their first serve speed as much. Men also won more first serve points, though their gain was not the enormous boost seen by the women.
Improvements in context
Based on these year-to-year comparisons, it looks like both men and women served better without spectators. The women’s giant boost in first serve points won suggests that there are other factors beyond those we can easily measure–perhaps players were missing first serves at a typical rate not only because they were hitting harder, but also because they were aiming for the corners. It’s also possible that post-restart rustiness affected returns more than serves–in lockdown, it’s easier to drill your own serves than to keep in practice against elite-level first serves.
Another consideration is the usual year-to-year fluctuations. For women, the small changes in first serves in and second serves missed are less than half the magnitude of the year-to-year changes at the US Open between 2015 and 2019. These numbers will always drift up and down for a variety of reasons, sheer randomness not least among them.
The 6.6% jump in the women’s rate of first serve points won, on the other hand, is quite unusual. The average fluctuation in the previous four pairs of years is 1.7%. The serve speed increase is also unusually large. It’s a 2.1% jump, compared to a typical movement of about 0.7%.
The 2019-to-2020 changes in men’s rates are less noteworthy in context, even if they do tell a suggestive story. The rate of first serves made is surprisingly noisy, fluctuating an average of 2.7% in each pair of years between 2015 and 2019, so the fans-to-no-fans shift of 3.7% doesn’t prove much of anything. The double fault and serve speed changes are no greater than previous fluctuations.
The only slightly convincing “pandemic effect” on the men’s side is the percentage of first serve points won. As we’ve seen, men won 2.3% more such points in 2020 than in 2019, adjusted for the mix of players–an increase half-again as large as the typical fluctuation of 1.5%. That’s hardly a slam-dunk case for better post-restart serving. It could be pure luck, or it could be attributed to a mix of the many confounding variables I’ve already mentioned.
Serving isn’t shooting
This stuff is complicated. Penalty kickers in soccer have an objective that is clear to all–to score a goal. While tennis servers have a similarly simple aim–to win the point–the only part of the point they can completely control is the serve, and given the tradeoffs between speed, precision, and keeping the ball in the box, there’s no single variable that tells us whether a player is serving better.
Things get even hairier when we look for data beyond the US Open. We could do the same exercise for the last few years of French Opens, but remember that the post-restart Roland Garros had a sprinkling of paying fans. Is that halfway between an empty stadium and normalcy? Is it worse than a full stadium, because individual voices are easier to discern? Is it a mix, because the French fans filled up the stands for their native players and left other courts empty? I have no idea.
It is clear that women served harder than usual at the 2020 US Open, and they won way more first serve points than in recent years. Men served more accurately, even if their success rate didn’t translate into the same whopping success than the women’s adjustments did. What we can’t say for sure is how much of those shifts can be attributed to the empty stands in Flushing last year. Even the purest natural experiments don’t always return bulletproof findings.
Aryna Sabalenka has won 3 titles and 14 matches in a row. Let’s dig into the data and see if we can identify any improvements that would account for her success.
For the Match Charting Project, I’ve logged every shot of each of the Belarussian’s tour-level matches. (There are a few exceptions where I haven’t found video.) We’ll look at hard-court matches only today. With that constraint, we have 140 Sabalenka matches, dating back to early 2017 (including the current streak), and another 1,121 women’s tour-level contests over the same time period for reference.
Big serving?
Aryna always brings a powerful serve, but it remains a work in progress, at least tactically. The key metric for pure serve dominance is unreturned serves–quite simply, serves that don’t come back. While some are aces, they don’t have to be, and the distinction doesn’t really matter.
This first graph has a lot going on, but as I’ll use the same basic template for several more figures, it’s worth taking a moment to understand what we’re looking at. The two dotted lines show tour average rates of unreturned serves (the lower average is for all players; the higher one is for match winners), the thin jagged line shows Sabalenka’s rate of unreturned serves for each individual match, and the thicker red line shows her five-match rolling average.
Her five-match rolling average has been above 30% for the entire win streak. It’s not an unprecedented level for her, though–she sustained similarly high levels at various points over the last three years. (We should also be a bit cautious ascribing serve effectiveness to a player when the Ostrava, Linz, and Abu Dhabi courts might have been faster than average.) Consistently powerful serving has certainly helped Sabalenka’s cause, but it probably isn’t the whole story.
We might gain from breaking down Aryna’s serve effectiveness into first and second serves. First, let’s look at something else:
Serve plus one
There are two ways we could look at “serve plus one” effectiveness, and we’ll do both. First, let’s count Sabalenka’s opportunities to hit a second shot behind her serve, and see what percentage she puts away. (As with aces and other unreturned serves, the “winner” concept is a distraction: I’m counting second-shot winners together with shots that force errors. If you end the point, it doesn’t matter much whether your opponent touches the ball.)
The second figure shows us that, on hard courts, when women are faced with a second shot behind their serve, they finish the point about 20% of the time. Sabalenka’s career average is 28%. She far exceeded that over a string of four matches to finish Ostrava and start Linz, maxing out at 42% against Jennifer Brady in the Ostrava semi-final. Since then, her rate returned to roughly her (impressive) career average.
This measure is something of a “key to the match” for Sabalenka. When she converts at least 30% of second-shot opportunities behind her serve, she wins 91% of her matches. When she doesn’t, she wins 62%. Of course, 62% is nothing to be ashamed of, and the dip visible in early 2020 coincides with her Doha title, the one time in her career that the five-match rolling average fell below 20%.
Serve plus serve plus one
These first two measures are related, of course. A big server should post good numbers in both. But a great “pure” serving day might mean a worse-looking serve-plus-one day, because fewer weak returns are coming back at all. The reverse holds as well: A strong server might not hit as many unreturned serves as usual because her opponent is managing to just barely put them back in play–easy sitters for second shots.
To identify the combined benefits of good serving and efficient serve-plus-one’ing, we simply count how often Sabalenka wins service points in two shots or less.
We’ve already seen the two components of this, so there are no surprises here. The typical player wins about 40% of her service points this way, and Aryna has historically averaged 46% on hard courts. This number looks as good for her recent winning streak as we’d expect. But as with the previous graph, it suggests weakness during her 2020 Doha title, so the predictive power here is limited.
First and second serves
The combined metric of unreturned serves plus second-shot putaways gives us a good snapshot of when the offensive game is working. Let’s break down the previous graph into first- and second-serve specific numbers:
These track the overall numbers. Aryna has generally been good lately on both first and second serves, but with neither one has she been more successful or consistent than in previous hot streaks. Second serves are particularly hard to rate because the per-match sample size is so small–fewer than 30 second serve points per player per match, and some of those end up as double faults.
Before moving on to the return game, let’s look at one more indicator of service-point success:
Longer points on serve
As I said at the outset, Sabalenka has always been a good server. While her current momentum might owe a bit to fewer mental lapses on serve, it would be logical to look elsewhere for an explanation, simply because there was more room to improve in other areas.
We’ve seen how her serve and second shot rate. What about serve points that go deeper? This metric considers all points where the returner’s second shot comes back, and then counts how often the server goes on to win the point.
The average hard-court WTA match winner claims almost exactly half of her service points when the rally reaches five shots. Over her career, Sabalenka has won 48%, worse than the typical match winner but better than the overall tour average.
Aryna has done better lately. To cherry-pick a starting point, she has won 51% of these points in her last 24 matches, dating back to the Doha second round. Her average over the first five matches in Abu Dhabi was 55%, the best she has managed since her breakout run in late 2018, when she pushed Naomi Osaka to three sets at the US Open and hoisted the Wuhan trophy a few weeks later.
Return winners
We’ll walk through the dimensions of her return performance in a similar manner, starting with return winners (and point-ending non-winners), then on to “return-plus-one” putaways, followed by the combination of the two.
First, return winners. I use the number of point-ending return winners divided by in-play serves–that is, excluding double faults.
Veronika Kudermetova had a rough day last Wednesday, so Sabalenka’s current five-match rolling average is as high as it’s been since early 2018. Apart from that last-minute burst of return dominance, her recent return winner rates look a bit like the serve stats: consistently solid, if not spectacular.
Return plus one
How about when the serve return doesn’t finish the job? This “return plus one” metric counts opportunities when the server puts her second shot in play and measures how often the returner hits a winner or forces an error with her own second shot. The sample sizes are a getting a bit small here (each player has 43 such opportunities in an average hard-court match), so the per-match rates are rather spiky:
The small single-match samples, combined with the relationship between return-plus-one and return winners–almost interchangeable ways to respond successfully to a mediocre serve–render conclusions a bit tough to come by. Sabalenka was average by this measure in Ostrava, great in Linz, and all over the place in Abu Dhabi.
Short return points won
Will things be clearer when we combine both methods of quickly winning a return point?
Aside from a weak return performance against Elena Rybakina in Abu Dhabi, Sabalenka has been comfortably above average in this metric in every match since she faced Victoria Azarenka in the Ostrava final.
Like “serve plus one,” this is a good indicator of overall success for the Belarussian. If we use this metric to split her 140 charted hard-court matches in half, the dividing line is 27.5% of return points won with a return winner or a return-plus-one putaway. Above that mark, she has won 62 matches, or 88.6%. Below it, she has won only 41, or 58.6%. She was above the line in nearly all of her matches in Linz and Abu Dhabi, and she sat at 25% or higher in every round of her 2020 Doha triumph, clearing 30% in three of five matches there.
First and second serve returns
Has she been particularly devastating against first or second serves? Let’s see:
Few women feast on second serves the way Sabalenka does, and she’s been particularly relentless of late. The typical tour player wins about 30% of second-serve return points with a first- or second-shot putaway, and over her last 15 matches, Aryna has won 41% that way. 41% is a respectable total percentage of return points won against many servers, and Sablaenka would be winning that many even if she refused to hit more than two shots per rally.
Granted, Sabalenka doesn’t hit that many fifth or sixth shots. How does she fare when her return points extend that far?
Long return points
You’ll be glad to know that the code for this final* graph didn’t throw any divide-by-zero errors–Aryna has played at least one “long” return point in each of her hard-court matches. This metric tallies up all return points in which the server puts her third shot in play, then calculates how often the returner won the point.
** Yes! It’ll be over soon!
This is another spiky mess, with an average of only 20 points per match. Still, if we’re looking for a category in which Sabalenka is newly excelling–not just thriving as usual–this could be our smoking gun.
Tour average for match winners on this stat is 46.7%. The server has an advantage by definition, because she has just put the ball back in play. The Belarussian’s career mark is 44.4%, only a bit better than the overall average. Yet in her last 15 matches, she has won 48.0% of these long return points, her best 15-match span since early in her career, when she faced a weaker mix of opponents.
I don’t want to overemphasize this: When there are only 20 points of this type per match, an improvement of 3.6 percentage points translates to a gain of less than one point per match. That doesn’t explain the magnitude of Sabalenka’s recent gains. But it does indicate that she is shoring up one of her few weaknesses, and in combination with her solid play on long serve points, it suggests that she no longer needs to rely on a one-two punch, even if her one-two punch is as dizzying as anyone’s.
Don’t make me say consistency
Tennis matches are decided by a handful of points: While Sabalenka has been dominant lately, she lost more points than she won against Coco Gauff in the Ostrava opening round. As such, improvements always look minor when we try to quantify them, if we can quantify them at all.
I’ve pointed out some areas where Sabalenka may be improving, others where a good statistical showing usually coincides with a W, and still others where an excellent performance doesn’t seem to matter much. All of these categories have one thing in common: She is putting up stellar numbers right now.
Remember, in the twelve graphs above (yes, twelve, sheesh), the dotted yellow lines indicate the average performance of match winners. In every single one of the categories, Aryna’s five-match rolling average is above that line. Every single one! In most cases, it has been above the line for some time.
It doesn’t take any statistical savvy to see that if a player is better than the average match winner in every category, she’ll be awfully tough to beat. The rest of the Australian Open field can only cross their fingers that Sabalenka’s current form won’t survive two weeks of quarantine.
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:
🤣🤣🤣 Safin to Khachanov on typical US player's approach to the game:
They employ shock-and-awe tactics and want to scare you with one-two shots. Once you drag them into the rally they are screwed.
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.
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.
The ATP Atlanta event is typically packed with big servers. John Isner won five titles in six years between 2013 and 2018, during which time the only man to stop him was Nick Kyrgios–in two tiebreaks, naturally. The last champion before Isner took over was Andy Roddick. It’s a fast hard court and the weather is often scorching, so the tournament tends to be a week-long ace festival.
The 2019 titlist posted another wave of eye-popping service numbers, winning four matches without facing a single break point, and winning more than 90% of his first serve points in each match. Those positively Isnerian numbers didn’t belong to the big man himself, nor were they posted by heir apparent Reilly Opelka. The serve king in Atlanta this year was the “six-feet tall” (sure, buddy) Australian grinder, Alex de Minaur.
Unlike many of his peers, de Minaur doesn’t make his money with a big serve. In the last 52 weeks, both Isner and Opelka have hit aces on one-quarter of their serve points. The Aussie’s 52-week rate is a mere 4.5%. He posted a tour-level career best of 14.8% against Taylor Fritz in the Atlanta final (excluding a Bernard Tomic retirement), but failed to reach double digits in second round against Bradley Klahn, or in the semi-final against Opelka. Last week, de Minaur proved that there are a lot of ways to win serve points without necessarily piling up the aces.
Strike one
The easiest non-ace route to victory is the unreturned serve. Players don’t have the same level of control over the rate of unreturned serves that they do with aces. But many great serves are reachable–if not effectively returnable–so they don’t go down in the ace column. The unreturned-but-not-ace category was de Minaur’s bread and butter in Atlanta.
According to the point-by-point log of the final in the Match Charting Project dataset, Fritz put only 57% of the Aussie’s serves back in play. Across over 1,300 MCP-charted hard court matches from the 2010s, the ATP tour average is 70% returned serves, and de Minaur’s opponents have traditionally done even better than that. De Minaur’s unreturned-serve rate of 43% is exceptionally good, ranking in the 90th percentile of service performances. He was even better against Opelka. Only 5 of his 93 service points went for aces, but 38 moredidn’t come back. That’s an unreturned-serve rate of 46%, a 94th-percentile-level showing.
Strike two
De Minaur was even better when the serve wasn’t quite as good. Coaches and commentators like to talk about the “plus one” tactic: Hit a strong serve and get in position to make an aggressive play on whatever comes back. This is where the Aussie truly excelled in the title match.
In addition to the 43% of unreturned serves against Fritz, another 26% of his service points fell into the “plus one” category: second-strike shots that his opponent couldn’t handle. Tour average is 15%, and again, de Minaur hasn’t always been this good. His average over 15 charted hard-court matches in 2018 was only 12.6%. His 26% rate on Sunday ranks in the 98th percentile among charted hard-court matches. Of the 67 single-match performances on record that were better than 26%, 15 were recorded by Roger Federer. Most players never have such a good day in the plus-one category.
Strike three
Even the best servers have to deal with the occasional long rally. In our sample of charted hard-court matches, 40% of points see the returner survive the plus-one shot and put the ball back in play. From that point, the rally is more balanced, and returners win a bit more than half of points. (That’s partly because 4-shot rallies are more common than 5-shot rallies, and so on, and because a 4-shot rally, by definition, is won by the returner. Put another way, once you exclude 3-or-fewer-shot rallies, you bias the sample toward the returner; if you excluded 4-or-fewer-shot rallies, you would bias the sample toward the server, because 5-shot rallies make up a disproportionate amount of the remaining points.)
Serving like de Minaur did, he didn’t see nearly so many “long” rallies. 22% of his service points against Fritz, and 29% against Opelka, reached four shots. Facing the typical one-dimensional big server, this is the returner’s chance to even the score. But de Minaur is known more for his ground game than his service. In the final, he won 58% of these points, good enough for the 83rd percentile in our sample.
De Minaur’s performance on longer rallies didn’t really move the needle on Sunday, mostly because he so effectively prevented points from lasting that long. But the fact that he won more than half of the extended exchanges is a reminder that a great serving performance depends on more than just the serve. On a good day, even a six-footer can post numbers that leave Isner and Opelka in the dust. It isn’t always about the aces.
Yesterday at FiveThirtyEight, Tom Perrotta highlighted the relationship between Serena Williams’s first serve performance and her chances of winning. According to the article, Serena has won only (“only”) 74% of her first serve points over the fortnight, compared to an outlandish 87.5% when she won the title in 2010. She has never won Wimbledon while winning fewer than 75% of her first-serve points, and even the three-quarters mark is no guarantee, as she topped 77% last year en route to a second-place finish.
A lot of factors go into first-serve winning percentage, including serve placement, serve tactics, and all the shots that a player hits when the return comes back. The most obvious, though, is another category in which Serena has often topped the charts: serve speed. When Williams beat Garbine Muguruza to win the Championships in 2015, her average first serve clocked in at 113 miles per hour, the third straight match in which her typical first delivery topped 111 mph. Over her last 13 matches, she has averaged only (“only”) 106.4 mph, never exceeding 109 mph in a single contest.
How much does it matter?
It seems fair to assume that, all else equal, a faster serve is more effective than a slower one. Complicating things is the fact that all else is rarely equal: wide serves are often deadly despite requiring less raw power, more conservative serves can be easier to place, andwe haven’t even scratched the surface of the effect of spin. A faster serve isn’t always better than a slower one. But on average, the basic assumption holds true.
For each of Serena’s 23 matches at Wimbledon 2014, 2015, 2018, and 2019 (she didn’t play in 2017, and I don’t have the relevant data at hand for 2016–don’t ask), I split her first serve points into quintiles, ranked from fastest serves to slowest serves. This is a crude way of controlling for the effects of different opponents and giving us an initial sense of how much Serena’s serve speed influences the outcome of first-serve points:
Clearly, serve speed doesn’t tell the whole story. At the same time, it looks like a 117 mph serve–or even a 108 mph one–is a better bet than a 98 mph offering.
Another way to isolate the effect of serve speed is to ignore the influence of specific opponents and simply sort first serves by miles per hour. From these 23 matches, we have 43 first serves recorded at exactly 100 mph, with a corresponding winning percentage of 72.1%. Serena hit 33 first serves at 101 mph, of which she won 72.7%. While the winning percentages don’t usually move so neatly in lockstep with first serve speed, there is a general trend:
The correlation is a loose one: winning percentages at 99 mph and 103 mph are better than those at 116 mph and 117 mph, for example. We could attribute that to the possibility that the slower serves are tactically savvier, or more approximate placement of the faster deliveries, or just dumb luck, because our sample size at any specific speed isn’t that great. Still, we can draw an approximate conclusion:
Each additional two miles per hour of first-serve speed is worth an additional one percentage point to Serena’s 1st serve winning percentage.
To take it one step further: Serena usually lands about 60% of her first serves, and roughly half of total points will be on her serve, so each additional two miles per hour of first-serve speed is worth an additional 0.6 percentage points of total points won. In a close match, like her 2014 loss to Alize Cornet–in which she averaged only 104 mph on her first serves and won exactly 50% of the points played–that could be the difference.
Serena in context
The same general rule cannot be applied to all women. (Several years ago, I took a similar look at ATP serve speeds, and–perhaps foolishly–I didn’t break it down by player.) I ran the same algorithm on the recent Wimbledon records of the nine other women for whom I have at least 15 matches worth of data. The effect of serve speed varies from “quite a bit” for Johanna Konta to “not at all” for Venus Williams and “I don’t understand the question” for Caroline Wozniacki.
The following table shows two numbers for each player. The “Addl MPH =” column shows the effect of one additional mile per hour on first serve winning percentage, and the “_ MPH = 1% SPW” column shows how many additional miles per hour are required to increase first serve winning percentage by one percentage point:
Player Addl MPH = MPH = 1% SPW
Johanna Konta 0.89% 1.1
Angelique Kerber 0.56% 1.8
Serena Williams 0.48% 2.1
Garbine Muguruza 0.47% 2.1
Simona Halep 0.41% 2.5
Petra Kvitova 0.29% 3.5
Agnieszka Radwanska 0.28% 3.6
Victoria Azarenka 0.02% 50.9
Venus Williams 0.00% -
Caroline Wozniacki -0.40% -
Konta’s serve speed is almost twice as important to her first-serve success as Serena’s is. Her average first-serve speed in her quarter-final loss to Barbora Strycova was 99.9 mph, her lowest at Wimbledon since a first-round loss in 2014.
At the opposite extreme, we have Victoria Azarenka and Venus, for whom serve speed doesn’t seem to matter. (Venus, for one, excels at the deadly wide serve, which she converts into aces regardless of speed.) Wozniacki apparently lulls her opponents into confusion and illogic, giving her better results on slower first serves.
Serena vs Simona
These are small effects, so even the range between Serena’s slowest serving performance this fortnight (105 mph first serves against Carla Suarez Navarro) and the 2015 final against Muguruza would only have effect Serena’s total points won by about 2.5 percentage points. Nine out of ten times Williams and Halep have gone head to head, Serena has come out on top, always with more than 52.5% of total points, usually with more than 55%. That’s an ample margin of error–or, more precisely, margin of slow serving.
On the other hand, the most recent Serena-Simona contest, the only time they’ve played since 2016, was the closest of the lot. Halep is a great returner, but she is not immune to powerful serving: her rate of return points won is affected by serve speed just as much as Williams’s serve stats are. The gap between the finalists could be narrow, and Serena’s serve speed is one of the few tools completely in her own power that she could deploy to tilt the scales in her favor.
The players are right. Wimbledon’s surface–or balls, or atmosphere, or aura–has slowed down in comparison with recent years. We’ve heard comments to that effect from Roger Federer, Milos Raonic, Boris Becker, Rafael Nadal, and many others. Raonic attributes the change to the grass, and Nadal to the balls. Regardless of the reason, the numbers back up their perceptions.
Here is an overview of several surface-speed indicators for the first three rounds of singles matches at Wimbledon, 2017-19:
The second set of rows, "Unret," is the percent of unreturned serves. The next set, "<=3 Shots," is the percent of points that ended in three shots or less. For all four of the stats shown, including aces and average rally length, men's numbers point to slower conditions. The women's numbers are less clear, but to the extent that they point in either direction, they concur.
Not just 2019
Aggregate numbers such as these usually give us an idea of what's going on. But we can do better. The numbers above do not control for the mix of players or the length of their matches. For instance, 2019's rates would be different if John Isner, instead of Mikhail Kukushkin, had played a third-round match. The surface speed might have affected that result, but if we're going to compare ace rate from one year to the next, we shouldn't compare Isner's ace rate with Kukushkin's ace rate.
That's where my surface speed metric comes in. For each tournament, I control for the mix of servers and returners (yes, returners affect ace rate, too) to boil down each event to one number, representing how the tournament's ace rate compares to tour average. While there's more to surface speed than ace rate, aces are a good proxy for many of those other indicators, and more importantly, aces are one of the few stats that are available for every match.
The resulting score usually ranges between 0.5--50% fewer aces than average, usually on a slow clay court like Monte Carlo--and 1.5--50% more aces than average, on a fast grass or indoor hard court, like Antalya or Metz. Over the last decade, Wimbledon's conditions have drifted from the high end of that range to the middle:
Year Men Women Average
2011 1.26 1.37 1.31
2012 1.27 1.06 1.17
2013 1.29 1.04 1.17
2014 1.35 1.19 1.27
2015 1.20 1.16 1.18
2016 1.06 1.03 1.04
2017 1.03 1.07 1.05
2018 1.14 0.98 1.06
2019 1.04 0.96 1.00
The men's numbers are usually more reliable measurements, because they are based on many more aces, which means that the ace rate for any given match is less fluky. Ideally, we'd see the men's and women's speed ratings move in lockstep, but there is some noise in the calculation, and the ratings are also relative to that year's tour average, which depends in turn on the changing speeds of dozens of other surfaces.
Caveats aside, the direction of the trend is clear. There isn't a substantial difference between 2019 and the last few years, but the gap between the first and second half of the decade is dramatic.
What is less clear--and will require considerable further research--is how much it matters. In 2014, Nick Kyrgios upset Nadal in four sets, while last week, the result was reversed. How much of that can we attribute to the surface? Would faster conditions have allowed Isner to outlast Kukushkin? Kevin Anderson to hold off Guido Pella? Jelena Ostapenko to withstand Su Wei Hsieh?
For now, those questions remain in the speculation-only file. Now that we can conclude that the grass really has gotten slower, we can focus that speculation on the fates of several grass court savants, including Federer, Raonic, and Karolina Pliskova. By the end of the fortnight, they--like Kyrgios--might be wishing it was 2014 again.
Yesterday at the New York Open, Paolo Lorenzi battled through three sets to defeat Ryan Harrison. It was a notable result for a number of reasons, starting with the fact that Lorenzi is rarely seen on a hard court when there’s any other option. The 37-year-old Italian is one of the many men defying the aging curve these days, and with the victory, he’ll play at least one tour-level quarter-final for the eighth year in a row, despite not reaching his first until he was 30.
The way in which Lorenzi won the match was almost as unique as his career trajectory. Take a look at the average rally length per set:
Set Avg Rally
1 3.2
2 4.0
3 4.9
You probably don’t need me to tell you which set Harrison won. The opening frame was serve-dominated, typical of American indoor hard court events. As the match progressed, the points increasingly resembled the clay-court sparring that Lorenzi surely would have preferred.
Theorizing
The Lorenzi-Harrison match was extreme, but it tracks with what I believe to be the conventional wisdom. Throughout a match, players get better at reading their opponents’ games, cutting down on unreturned serves and making it more likely that each point will turn into a more protracted exchange. That’s the theory, anyway. There are some countervailing forces, such as fatigue, which work in the other direction, but in general we expect points to get longer.
Yesterday’s contest didn’t exactly follow that script, though. The rallies might have gotten longer because the two men better predicted each other’s shots, but it doesn’t show up so neatly in aces–Harrison hit aces on between 18% of 21% of his points in each set–or the more inclusive category of unreturned serves:
While serve recognition may explain the rally length jump from set 1 to set 2, it goes in the opposite direction from set 2 to set 3. Yes, these are small samples, and yes, unreturned serves don’t tell the whole story. But there are signs that our initial theory is missing something.
More matches
As interesting as Lorenzi is, we’re going to need more players, and more data, to better understand what happens to serve returns and rally length over the course of a match. Let’s start with the main draw singles matches from the 2019 Australian Open. Not only are there are a lot of them, but since they are best of five, we have an opportunity to see how these trends unfold over several sets per match.
For each match, I measured the average rally length and rate of unreturned serves for each set, and then made set-by-set comparisons for the length of the match. For instance, in Lorenzi-Harrison, rally length increased by 25% from set 1 to set 2. Then, for each set, I aggregated all the matches of sufficient length to figure out how much the tour as a whole was changing from one set to the next.
The results are considerably less eye-catching than those of the Lorenzi match. In the following table, the “Avg Rally” and “Unret%” columns show the change in ratio form: If the baseline rate in the first set is 1.0, the rally length in set 2 increases by 0.8% and the number of unreturned serves goes up by 2.4%. I’ve also included example columns, showing realistic rally lengths and unreturned-serve rates for each set based on tournament averages of 3.2 shots by point and 34% of serves unreturned:
The set-to-set differences in rally length are barely enough to qualify for the name. The shift in the rate of unreturned serves, however, is much more striking, all the more so because it moves in the opposite direction that we expected.* Perhaps fatigue–or strategic energy conservation–plays a bigger role than I thought, or servers gain more from familiarity with their opponent than returners do.
* You might wonder if the effect is an artifact of the data, that players who reach 4th and 5th sets are bigger servers. That may be true, but it’s not what we’re seeing here. I’m comparing the stats in each set to the previous set in the match itself, and then averaging the set-to-set changes, weighted by the number of points in the sets. A John Isner 5th set, then, is compared only to an Isner 4th set.
WTA to the rescue
The results are completely different for women. Here is the same data for the 127 main draw women’s singles matches at the Australian Open:
Set Avg Rally Ex Rally Unret% Ex Unret
1 1 3.40 1 27.0%
2 1.035 3.52 0.974 26.3%
3 1.103 3.75 0.915 24.7%
Still not as dramatic as Harrison-Lorenzi, but the trends are more marked than for the men. The number of unreturned serves drops quite a bit, and rally length increases by an amoun that an attentive spectator might notice. Those two are related–if there are fewer unreturned serves, there are more shots per point, even if we only consider the second shot. Beyond that, there are more opportunities for longer exchanges. In any case, the set-by-set trends for women fit closer to the intial theory than the men’s results did.
As with every aggregate stat, I’m guessing that there is a huge amount of variation among players. Perhaps players who are particularly good in third sets really do return more serves or, as Lorenzi did, shift their tactics in the direction of a more favorable style of play. Looking at these types of numbers for individual competitors is a reasonable next step, but it’s one that will need to wait for another day.
