Serve speed – Heavy Topspin

Tomas Machac’s Defiant Angles

*Tomas Machac at the 2023 US Open. Credit: Hameltion*

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

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

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

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

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

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

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

Lean right

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

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

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

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

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

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

The dis-ad-vantage

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

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

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

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

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

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

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

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All Hail the Iga Swiatek … Serve?

*Iga Swiatek at the 2023 US Open. Credit: Hameltion*

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

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

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

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

Here’s the top ten since Miami 2023:

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

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

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

The all-rounder

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

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

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

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

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

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

Here is the relationship in visual form:

Iga clearly occupies a world of her own.

What works

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

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

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

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

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

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

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

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

82%, here we come

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

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

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

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

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

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Alex de Minaur’s Adequate Inaccuracy

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

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

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

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

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

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

Speed first

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

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

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

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

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

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

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

Drowning in caveats

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

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

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

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

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

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

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Serving In an Empty Stadium

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

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

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

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

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

US Open, now and then

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

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

Here are the results:

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

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

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

Improvements in context

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

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

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

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

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

Serving isn’t shooting

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

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

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

The Effect of Serena’s Serve Speed

Italian translation at settesei.it

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:

Quintile     1SP W%  Avg MPH  
Fastest       80.6%    116.9  
2nd fastest   73.7%    112.2  
Middle        79.5%    108.0  
2nd slowest   73.7%    103.7  
Slowest       74.9%     98.1

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 Oddity of Naomi Osaka’s Soft Second Serves

Italian translation at settesei.it

Naomi Osaka has quickly risen to the top of the women’s game on the back of some big hitting, especially a first serve that is one of the fastest in the game. Through Thursday’s semi-final, Osaka’s average first-serve speed in Melbourne was 105 mph, faster than all but two of the other women who reached the third round. Even those two–Aryna Sabalenka and Camila Giorgi–barely edged her out, each with average speeds of 106.

Shift the view to second serves, and Osaka’s place on the list is reversed. While Sabalenka’s typical second offering last week was 90 mph and Giorgi’s was 94, Osaka’s has been a mere 78 mph, the fourth-slowest of the final 32. That mark puts her just ahead of the likes of Angelique Kerber and Sloane Stephens, both whose average first serves are nearly 10 mph slower.

Osaka’s 27 mph gap is the biggest of anyone in this group. The next closest is Caroline Wozniacki’s 23 mph gap, between her 102 mph first serve and 79 mph second serve–both of which are less extreme than the Japanese player’s. Expressed as a ratio, Osaka’s average second serve is only 74% the speed of her typical first. That’s also the widest gap of any third-rounder in Melbourne; Wozniacki is again second-most extreme at 77%.

The following table shows first and second serve speeds, along with the gap and ratio between those two numbers, for a slightly smaller group: women for whom the Australian Open published at least four matches worth of serve-speed data:

Player          Avg 1st  Avg 2nd   Gap  Ratio  
Osaka             105.5     78.5  27.0   0.74  
Keys              105.2     85.4  19.7   0.81  
SWilliams         103.8     88.6  15.2   0.85  
Barty             102.0     88.2  13.7   0.87  
KaPliskova        101.9     80.5  21.4   0.79  
Collins           101.2     82.2  19.1   0.81  
Kvitova            99.6     91.6   8.0   0.92  
Muguruza           98.1     82.5  15.6   0.84  
Pavlyuchenkova     97.9     84.5  13.4   0.86  
Sharapova          97.9     89.6   8.2   0.92  
Svitolina          97.6     78.2  19.4   0.80  
Stephens           96.1     75.1  21.0   0.78  
Halep              95.3     80.9  14.4   0.85  
Kerber             94.0     78.4  15.7   0.83

Oddly enough, having such a slow second serve doesn’t seem to be causing any problems. In today’s semi-final against Karolina Pliskova, Osaka won 81% of first serve points and only 41% of second serve points, but her typical performance behind her second serve is better than that. And in this match, both women feasted on the other’s weaker serves: Pliskova won only 32% of her own second serves. (Though to be fair, Pliskova had the second-largest gap of the players listed above. She tends to rely more on spin than speed when her first serve misses.)

Across her six matches, Osaka has won 73.3% of her first serve points and 49.7% of her second serve points–a bit better than the average quarter-finalist in the former category, a very small amount worse than her peers in the latter. The ratio of those two numbers–68%–is almost identical to those of Danielle Collins, Petra Kvitova, Anastasia Pavlyuchenkova, and Serena Williams, all of whom have smaller gaps between their first and second serve speeds. Of the eight quarter-finalists, Kvitova has the smallest speed gap of all, yet the end result is the same as Osaka’s, she’s just a few percentage points better on both offerings.

Here are the first- and second-serve points won in Melbourne for the eight quarter-finalists, along with the ratio of those two figures and each player’s serve-speed ratio from the previous table:

QFist           1SPW%  2SPW%  W% Ratio  Speed Ratio  
Kvitova         77.9%  52.8%      0.68         0.92  
Williams        74.7%  50.0%      0.67         0.85  
Osaka           73.3%  49.7%      0.68         0.74  
Collins         72.5%  50.0%      0.69         0.81  
Barty           70.8%  55.7%      0.79         0.87  
Pliskova        70.5%  50.0%      0.71         0.79  
Pavlyuchenkova  67.0%  44.9%      0.67         0.86  
Svitolina       66.5%  48.1%      0.72         0.80

Clearly, there’s more than one way to crack the final eight. With Kvitova, we have a server who racks up cheap points with angles instead of speed, rendering the miles-per-hour comparison a bit irrelevant. Serena’s results are close to Osaka’s, though she gets there with bit more bite on her second serves. And then there’s Svitolina, who doesn’t serve very hard or that effectively but can beat you in other ways.

Knowing all this, should Osaka hit harder second serves? In extreme cases, like today’s 81%/41% performance against Pliskova, the answer is yes–had she simply hit nothing but first serves and succeeded at the same rate, she would’ve piled up a lot of double faults but won more total points. But the margins are usually slimmer, and as we’ve seen, her second-serve performance isn’t bad, it just might offer room for improvement. Every player is different, but faster is usually better.

A thorough analysis of that question may be possible with the available data, but it will have to wait for another day. In the meantime, Saturday’s final will offer us a glimpse of contrasting styles: Osaka’s powerful first offering and soft second ball, against Kvitova’s angles and placement on both serves. Both my forecast and the betting market see the title match as a close one–perhaps Osaka’s second serve will be the shot that makes the difference.

How Servers Respond To Double Faults

Italian translation at settesei.it

In the professional game, double faults are quite rare. They sometimes reflect a momentary lapse in concentration, and can negatively impact a server’s confidence. Players are sometimes particularly careful after losing a point to a double fault, taking some speed off their next delivery, or aiming closer to the middle of the box.

Let’s dig into some data from last year’s grand slams to see what players do–and how it affects their results–immediately after double faults. IBM’s Slamtracker provided point-by-point data for most 2017 grand slam singles matches, including serve speed and direction, and the available matches give us about 5,000 double faults to work with. (I’ve organized the data and made it freely available here.)

For each server in each match, I’ve tallied their results on points immediately following double faults. (That means that we exclude after-double-fault points when the double fault ended the game.) Then, for each player, I compared those results with match-long averages. Because double faults are so unusual, and because we only have this data for the majors, the sample isn’t adequate to tell us much about individual players. But for tour-wide analyses, it’s more than enough.

Serve points won: As we’ll see in a moment, men and women have different overall tendencies on the point following a double fault. But by the most important measure of simply winning the next point, gender plays little part. Men, who in this sample win 65.1% of service points, fall just over one percentage point to 64.0% on the point following a double fault. Women, who average 57.8% of service points won, drop even more, to 56.1% after a double.

First serve percentage: I expected that servers become more conservative immediately after a double fault. For women, that hypothesis is correct: In these matches, they land 63.3% of their first serves, while after a double fault, that number jumps to 65.4%. On the other hand, men don’t seem to change their approach very much. On average, they make 62.3% of their first offerings, a number that barely changes, to 62.5%, after double faults.

First serve points won: Here is additional evidence that women become more conservative after double faults, while men do not. In general, women win 63.7% of their first serve points, but just after a double fault, that number drops to 62.9%. For men, there is a decrease in first serve points won, but it is almost as small as their difference in first serve percentage: 72.7% overall, 72.4% after a double fault.

First serve speed: With serve speed, we run into a limitation of the Slamtracker data, which gives us speed only for those serves that go in. So when we look at the average speed of first serves, we’re excluding attempts that miss the box. Even with that caveat, the data keeps pointing in the same direction. Contrary to my “conservative” hypothesis, men serve a bit faster than usual after a double fault–183.3 km/h following doubles, versus 182.8 km/h in general. Women do seem to change their tactics, dropping from an average speed of 155.5 km/h to a post-double-fault pace of 152.2 km/h.

First serve direction: Slamtracker divides serve direction into five categories: wide, body-wide, body, body-center, and center. After a double fault, men are less likely than usual to hit a wide serve (24.1% to 25.8%), and those serves get split roughly evenly between the body and center categories. The difference in body serves is most striking: They account for only 3.5% of first serves overall, but 4.4% of post-double first serves. This may be the one way in which men opt for the conservative path, by maintaining speed but giving themselves a wider margin of error.

Women move many of their after-double-fault serves toward the middle of the box. On average, over 44% of serves are classified as either “wide” or “center,” but immediately after a double fault, that number drops below 41%. It’s not a huge difference, but like all of the other tendencies we’ve seen in the women’s game, it suggests that for many players, caution creeps in immediately after missing a second serve.

Tactics

As usual, it’s difficult to move from these sorts of findings to any sort of tactical advice. Even the first data point, that both men and women win fewer service points than usual right after they’ve double faulted, can be interpreted in multiple ways. By one reading, players may be serving too conservatively, missing out of the benefits of big first serves. On the other hand, if confidence is an issue, perhaps serving more aggressively would just result in more misses.

When in doubt, we have to trust that the players and coaches know what they’re doing–they’ve honed these tradeoffs through decades of experience and thousands of hours of match play. For fans, these numbers add to our understanding of the conclusions that players have reached. For the pros, perhaps a more detailed look at what happens after a double fault would help tweak their own strategies, both bouncing back from their own double faults and taking advantage of the lapses in concentration of their opponents.

The Effect of One More MPH

Italian translation at settesei.it

All else equal, increasing your first serve speed is a good thing … so how useful is it? Earlier this week, I published some generic numbers, but those are far too crude to answer this question.

To get a better answer, we need to see what happens when specific players serve a little faster or slower. Sometimes, players dramatically mix up serve speed (as with slice serves wide), but most of the time, each player stays within a fairly limited range defined by his own power and skill.

The algorithm I’ve employed is fairly complicated, so I’ll give you the results first.

It appears that most players, if they increased their average serve speed by one mile per hour, would win 0.2% more first service points. That’s not many–it’s not even one point in every match. But every little bit helps, and according to my win probability models, winning 0.2% more first serve points can increase your chance of winning an even match from 50% to just short of 51%. Except possibly at the extremes, that continues to be the case for 2 MPH, 3 MPH, and greater increases–so a 5 MPH increase takes that 50/50 match and turns it into a 54/46 contest.

(One assumption here is that all players respond to increases in serve speed the same way. I’m sure that’s not true, but at this stage it’s a necessary assumption.)

The effect of a speed increase is even greater on ace and service winner rates. Each additional MPH on a player’s serve increases his ace rate by about 0.4%, and his service winner rate by about 0.5%.

Now for the algorithm and some caveats.

Process

The algorithm was designed to control (to the extent possible) for different types of serving and playing styles, as well as the different average speeds to the deuce and ad court, as well as to different directions (wide, body, and T).

I used only US Open data, to avoid differences between surfaces and between the speed guns used at different events. I used data only from the 18 players who had more than 150 first-serve points tracked by Pointstream. For each of those players, I found their average first-serve speed for each of six directions: wide, body, and T to the deuce and ad courts. Then, I randomly selected 150 of their first-serve points, and for each point, noted the difference between the point’s serve speed and the player’s average in the relevant court/direction.

Thus, every one of 2700 points was labeled 0 (average for that player/court/direction), or +1 (one mph above average), or -4, and so on. That results in large pools of points with each label. Many of the pools were too small for useful analysis, so I grouped them in sets of five: (-2, -1, 0, +1, +2), (-1, 0, +1, +2, +3), and so on. The pools, then, were useful from about -15 to +15.

From there, I looked at each of several stats (points won, aces, service winners) for each pool, and compared the rates from one pool to the next. The results were somewhat erratic–in some instances, an additional mph results in aces or points won going down, but over the set of 31 pools, they generally went up. The numbers presented above are the averages of each one-mph change.

Caveats

It’s not a very big sample, especially when separating serves into pools of 0, +1, +2, and so on.

One issue with the dataset is that the 18 servers were usually winning–that’s how they got enough first serves to merit inclusion. Thus, the average returner in the dataset is below average. That isn’t necessarily a bad thing–perhaps below-average returners respond to changes in serve speed the way above-average returners do–but without more data, it’s tough to know.

Another concern is what the numbers really tell us below about 5 mph slower than average. The algorithm operates on the assumption that a 120 mph serve is the same as a 121 mph serve, only slower. Comparing 120 and 121, that’s probably true. But comparing 120 and 108–for the same player, serving in the same direction–it probably isn’t. The 108 mph isn’t a simulation of what would happen if the player wasn’t as good; it’s probably a strategic choice, likely accompanied by some spin.

That said, the algorithm doesn’t directly compare 120 and 108, it compares 108 and 109, and perhaps in the aggregate, there is something useful to be gleaned from comparing a strategic spin first serve to an identical serve one mph faster. In any event, limiting the range to between -10 and 10, or even -7 and 7, doesn’t change the results much.

Finally, the sample is completely inadequate to tell us what happens at the extremes. The average player appears to improve his chances by adding another bit of speed, but does John Isner? There may be a ‘sweet spot’ where a player can get maximum gains from an additional 1, 5, or 10 mph on his first serves, but beyond which, the gain is more limited.

US Open Serve Speed by Player

It’s time for more serve-speed research notes. Most of the matches at the 2011 U.S. Open were tracked by Pointstream, and serve speed was recorded for the vast majority of those points. The Open website published some serve speed numbers, but not as conveniently as I would like.

Below, find the average first and second serve speeds for every man who played three or more Pointstream-tracked matches. Oddly enough, the top and bottom of the list are held by Americans; John Isner is where you’d expect him, while Donald Young barely kept his first-serve average in the triple digits.

I didn’t expect to see nearly so much variation in the difference between first and second serve averages. Sure, Isner and Young are the endpoints in both lists, but David Nalbandian–below average on firsts–is third of 22 on seconds. To take another angle, both Marin Cilic and Jo-Wilfried Tsonga each have more than double the difference in averages than does either Alex Bogomolov or Fernando Verdasco.

(“M” is the number of matches tracked by Pointstream for each player.)

Player                 M  1sts  1stAvg  2nds  2ndAvg  
John Isner             4   313   124.5   125   106.2  
Andy Roddick           5   249   122.1   118   100.5  
Tomas Berdych          3    85   120.3    71    95.0  
Jo-Wilfried Tsonga     5   289   119.7   206    90.6  
Marin Cilic            3   125   118.7   121    86.3  
Janko Tipsarevic       3   148   116.5    84    90.5  
Roger Federer          6   355   115.6   186    94.6  
Juan Martin Del Potro  3   180   114.5    96    88.2  
Julien Benneteau       3   177   114.0    86    89.9  
Tommy Haas             3   211   113.9   124    94.1  
Novak Djokovic         7   421   113.7   226    91.4  

Player                 M  1sts  1stAvg  2nds  2ndAvg
Andy Murray            6   338   112.6   204    85.2  
Mardy Fish             4   231   112.4   165    88.0  
David Nalbandian       3   165   112.3   125    96.1  
David Ferrer           3   128   112.2    74    88.9  
Rafael Nadal           7   435   110.5   176    84.5  
Juan Monaco            3   167   109.4    70    90.4  
Gilles Simon           3   235   108.3   179    81.6  
Fernando Verdasco      3   175   107.3    72    92.6  
Alex Bogomolov Jr.     3   264   103.1    96    89.1  
Donald Young           4   213   101.9   111    80.6

The Effect of Serve Speed

Italian translation at settesei.it

All else equal, you want to serve harder. But how much does it really matter?

That’s a more difficult question than it sounds, and I don’t yet claim to have an answer. In the meantime, I can share the results of some data crunching.

In 2011 U.S. Open matches covered by Pointstream, there were more than 9,000 first serve points. The server won almost exactly 70% of those points. About 11% of points were aces, and another 24% were service winners.

To see the effect of serve speed, I looked at four outcomes: aces, service winners, short points (three or fewer shots), and points won. It’s no surprise that each type of results happens more on faster serves.

Below, find the full numbers for serves of various speeds. The finding that sticks out to me is the small change in service points won from the 95-99 MPH group to the 115-119 MPH group. It may be that the modest increase–put another way, the surprising success rate at 95-104 MPH–is a result of strategic wide serves, or the better ground games of the players who hit slower serves.

So as I said, there’s much more work to be done, identifying the effects of faster serves for individual players, looking at deuce/ad court differences (for righties and lefties), and the results on different serve directions.

MPH      SrvPts   Ace%  SvcW%  Short%  PtsWon%  
85-89       140   2.1%  17.9%   47.1%    55.0%  
90-94       275   0.7%  21.5%   47.6%    63.6%  
95-99       546   2.2%  18.5%   48.4%    66.1%  
100-104     885   4.2%  24.6%   51.0%    66.0%  
105-109    1400   6.4%  29.3%   56.6%    68.7%  
110-114    1524   8.7%  34.0%   57.3%    69.1%  
115-119    1487  12.2%  35.9%   60.8%    69.4%  
120-124    1553  16.1%  40.1%   65.2%    73.2%  
125-129     941  21.5%  48.1%   72.4%    76.3%  
130-134     353  29.7%  58.4%   77.3%    84.4%  
135-139      66  27.3%  65.2%   80.3%    89.4%