Tactics Archives - Page 3 of 4

Dayana Yastremska Hits Harder Than You

At the 2019 Australian Open, tennis balls have more to fear than ever before. Serena Williams is back and appears to be in top form, Maria Sharapova is playing well enough to oust defending champion Caroline Wozniacki, and Petra Kvitova has followed up her Sydney title with a stress-free jaunt through the first three rounds.

And then there are the youngsters. Hyper-aggressive 20-year-old Aryna Sabalenka crashed out in the third round against an even younger threat, Amanda Anisimova. But still in the draw, facing Serena on Saturday, is the hardest hitter of all, 18-year-old Ukrainian Dayana Yastremska. Watch a couple of Sabalenka matches, and you might wonder if we’ve reached the apex of aggression on the tennis court. Nope: Yastremska turns it up to 11.

When Lowell first introduced his aggression score metric a few years ago, Kvitova was the clear leader of the pack, the player who ended points–for good or ill–most frequently with the ball on her racket. Madison Keys wasn’t far behind, with Serena coming in third among the small group of players for which we had sufficient data. Since then, two things have changed: The Match Charting Project now has a lot more data on many more players, and a new generation of ball-bashers has threatened to make the rest of the tour look like weaklings in comparison.

The aggression score metric packs a lot of explanatory power in a simple calculation: It’s the number of point-ending shots (winners, unforced errors, or shots that induce a forced error from the opponent) divided by the number of shot opportunities. The resulting statistic ranges from about 10% at the lower extreme–Sara Errani’s career average is 11.6%–to 30%* at the top end. Individual matches can be even higher or lower, but no player with at least five charted matches sits outside of that range.

* Readers with a keen memory or a penchant for following links will notice that in Lowell’s orignial post, Kvitova’s aggregate score was 33% and Keys was also a tick above 30%. I’m not sure whether those were flukes that have since come back down with larger samples, or whether I’m using a slightly different formula. Either way, the ordering of players has remained consistent, and that’s the important thing.

Here are the top ten most aggressive WTA tour regulars of the 2010s before Sabalenka and Yastremska came along:

Rank  Player                      Agg 
1     Petra Kvitova             27.1%  
2     Julia Goerges             26.8%  
3     Serena Williams           26.8%  
4     Jelena Ostapenko          26.5%  
5     Camila Giorgi             26.0%  
6     Madison Keys              25.9%  
7     Coco Vandeweghe           25.9%  
8     Sabine Lisicki            25.6%  
9     Anastasia Pavlyuchenkova  24.0%  
10    Maria Sharapova           23.2%

All of these women rank among the top 15% of most aggressive players. They end points more frequently on their own racket than plenty of competitors we also consider aggressive, like Venus Williams (21.9%), Karolina Pliskova (21.6%), and Johanna Konta (22.3%). Ostapenko bridges the gap between the two generations; she wasn’t part of the discussion when aggression score was first introduced, though once she started winning matches, it was immediately clear that she’d challenge Kvitova at the top of this list.

Here’s the current top ten:

Rank  Player               Agg  
1     Dayana Yastremska  28.6%  
2     Aryna Sabalenka    27.6%  
3     Petra Kvitova      27.1%  
4     Julia Goerges      26.8%  
5     Serena Williams    26.8%  
6     Jelena Ostapenko   26.5%  
7     Viktoria Kuzmova   26.0%  
8     Camila Giorgi      26.0%  
9     Madison Keys       25.9%  
10    Coco Vandeweghe    25.9%

Yastremska, Sabalenka, and even Viktoria Kuzmova have elbowed their way into the top ten. Yastremska’s and Kuzmova’s places on this list might be a little premature, since their scores are based on only seven and nine matches, respectively. But Sabalenka’s pugnaciousness is well-documented: her Petra-topping score of 27.6% is an average across almost 30 matches.

Tennis tends to swing between extremes, with one generation developing skills to counteract the abilities of the previous one. It’s not yet clear whether the aggression of these young women will catapult them to the top–after all, Sabalenka won only five games today against Anisimova, whose aggression score is a more modestly high 23.0%. Perhaps as they gain experience, they’ll develop more well-rounded games and return Kvitova to her place at the top.

In the meantime, we have the privilege of watching some of the hardest hitters in WTA history battle it out. Tomorrow, Yastremska will contest her first third round at a major in a must-watch match against Serena. There will be fireworks, but it’s safe to say there won’t be much in the way of rallies.

Mackie McDonald’s Secret Weapon

Italian translation at settesei.it

In the first round on Monday, the 23-year-old American Mackenzie McDonald defeated young Russian Andrey Rublev in four sets, 6-4 6-4 2-6 6-4. While Rublev missed part of the 2018 season due to injury and carries a ranking just inside the top 100, the victory still qualifies as a bit of an upset for McDonald, who has never come close to Rublev’s peak of No. 31.

The handful of fans who kept tabs on Court 10 were treated to an unusual display. The American relentlessly attacked Rublev’s second serve, rushing the net behind his return almost two dozen times. Many players don’t hit return approach shots that often in an entire year. What’s more, the tactic worked. Without it, the already close match would have been a coin flip.

By my count, in the log I kept for the Match Charting Project, McDonald came in behind his second serve return 22 times. Approach shot counts are never precise, because when a player hits a winner or an error, he may lean forward as if to continue toward the net, but quickly stop when he realizes it’s unnecessary. To be precise, he came in at least 22 times, and perhaps one more return winner or a couple of return errors should also be added to the total. No matter, the conclusions are similar regardless of whether the number is 22 or 24.

Rublev hit 62 second serves, but 9 of those resulted in double faults, so we’re looking at 53 playable second serves. McDonald netrushed 22 of those, winning 10. Of the other 31, he won only 11. That’s a return winning percentage of 45% on return approaches compared to 35% on other returns. Had he won all of those points at the 35% rate, it would have cost him two, perhaps three points off his overall total. He barely outscored Rublev as it was, 124 points to 118, so every little bit helped.

A rarity in context

The Match Charting Project has shot-by-shot data for nearly 2,000 men’s matches from this decade, and Monday’s four-setter was the first one of those in which a player hit at least 20 second-serve return approaches. (Dustin Brown approached at a higher rate in multiple matches, including his 2015 Wimbledon upset of Rafael Nadal.) There are only ten other matches in the database in which one player hit at least ten such approaches, and Mischa Zverev accounts for three of them. More than three-quarters of the time, the total number of second-serve return approaches is zero.

McDonald is not alone in enjoying some success with the tactic: The 1500 or so second-serve return approaches in the dataset were about 14% more effective than non-approaches in the same matches. However, it’s hard to be sure what that number is telling us, since most players approach so rarely. Some of the attacks are probably on-the-fly decisions against particularly weak serves, not pre-planned plays like many of Mackie’s netrushes on Monday.

Thus, it’s difficult to know how much success most men would have with the tactic, were they to adopt it more often. The fact that they employ it so rarely might tell us all we need to know: If more players thought that attacking the net behind the second serve return would win them more points, they’d do it. But for McDonald, it doesn’t matter what his peers do; it only matters what works for him. These 22 return approaches represented a lot more aggression than he displayed in the four previous matches we’ve charted, and it paid off.

It wasn’t enough to get him a win today against Marin Cilic, but he did outperform expectations, taking a set against the 6th seed and defending finalist. Best of all, he won more than half of Cilic’s second-serve points–a better rate than he managed against Rublev, and several ticks above 46%, the fraction that the average opponent manages against Cilic. In a sport often criticized for its uniformity of tactics, McDonald is an up-and-comer worth watching.

What I Should’ve Known About Playing Styles and Upsets

In the podcast Carl Bialik and I recorded yesterday, I mentioned a pet theory I’ve had for awhile, that upsets are more likely in matches between players with contrasting styles. The logic is fairly simple. If you have two counterpunchers going at it, the better counterpuncher will probably win. If two big servers face off, the better big server should have no problem. But if a big server plays a counterpuncher … then, all bets are off.

We’ve seen Rafael Nadal struggle against the likes of John Isner and Dustin Brown, and and we’ve seen big servers neutralized by their opposites, as in Marin Cilic’s 1-6 record against Gilles Simon. There are upsets when similar styles clash, as well, but as untested theories go, this one is appealing and not obviously flawed.

Then, to kick off the 2019 Australian Open, Reilly Opelka knocked out Isner. Playing styles don’t come much more evenly matched, and the veteran was the heavy favorite. It was a perfect example of the kind of match I would expect to follow the script, yet the underdog came out on top. They played four tiebreaks and there were only two breaks of serve, but Opelka didn’t even need the Australian Open’s new fifth-set 10-point tiebreak. While it’s just one match, of course, it suggested that I ought to look more closely at my assumptions.

After a couple of hours playing with data this afternoon, my theory is no longer untested … and it turned out to be flawed. Fortunately, it isn’t just another negative result. Playing style is related to upset likelihood, but not in the way I predicted.

Measuring predictability

Let me explain how I tested the idea, and we’ll work our way to the results. First, I used used Match Charting Project data to calculate aggression score for every ATP player with at least 10 charted matches since 2010. Aggression score is, essentially, the percentage of shots that end the point (by winner, unforced error, or inducing a forced error), as will serve as our proxy for playing style. That gives us a group of 106 players, from the conservative Simon and Yoshihito Nishioka with aggression scores around 13%, to the freewheeling Brown and Ivo Karlovic, with scores nearing 30%. I divided those 106 players into quartiles (by number of matches, not number of players, so each quartile contains between 21 and 31 players) so we could see how each general playing style fares against the others. Here are the groups:

Q1: The least aggressive players, with scores from 13% to 16%. Includes Simon, Rafael Nadal, Andy Murray, and David Ferrer.
Q2: Less aggressive than average, but not pure counterpunchers; scores from 16% to 18%. Includes Novak Djokovic (who is just above the border with Q1), Juan Martin del Potro, Kei Nishikori, and David Goffin.
Q3: More aggressive, but not one-dimensional, with scores from 18% to 20.7%. Alexander Zverev is just above the line with Q2, and the group also includes Dominic Thiem, Tomas Berdych, and Stan Wawrinka.
Q4: The biggest servers and otherwise high-risk players, with scores above 20.7%. Roger Federer just barely makes the cut, and he’s joined by players like Jo Wilfried Tsonga, Nick Kyrgios, and Milos Raonic.

(Aggression score conflates two things: big serving/big hitting and tactical aggression. Isner is sometimes not particularly aggressive, but because of his size and serve skill, he is able to end points so frequently that, statistically, he appears to be extremely aggressive. Accordingly, I’ll refer to “big servers” and “aggressive players” interchangeably, even though in reality, there are plenty of differences between the two groups.)

Limiting our view to these 106 men, I found just over 11,000 matches to evaluate and divided them into groups based on which quartiles the two players fell into. Each of the ten possible subsets of matches, like Q1 vs Q2, or Q4 vs Q4, contains at least 400 examples.

For every match, I used surface-adjusted Elo ratings to determine the likelihood that the favorite would win. That gives us pre-match odds that aren’t quite as accurate as what sportsbooks might offer, though they’re close.

Those pre-match odds are key to determining whether certain groups are more predictable than others. If there are 100 matches in which the favorite is given a 60% chance of winning, and the favorites win 70 of them, we’d say that the results were more predictable than expected. If the favorites win only 50, the results were less predictable.

Goodbye, pet theory

For the matches in each of the ten quartile-vs-quartile subsets, I calculated the average favorite’s chance of winning (“Fave Odds”), then compared that to the frequency with which the favorites went on to win (“Fave Win%”). The table below shows the results, along with the relationship between those two numbers (“Ratio”). A ratio of 1.0 means that matches within the subset are exactly as predictable as expected; higher ratios mean that the favorites were even better bets than the odds gave them credit for, and lower ratios indicate more upsets than expected.

Matchup	Matches	Fave Odds	Fave Win%	Ratio
Q1 vs Q1	412	71.1%	75.2%	1.06
Q1 vs Q2	1072	69.5%	70.6%	1.02
Q1 vs Q3	1382	69.7%	68.6%	0.98
Q1 vs Q4	1187	69.7%	70.0%	1.00
Q2 vs Q2	612	70.2%	69.9%	1.00
Q2 vs Q3	1616	68.8%	67.8%	0.99
Q2 vs Q4	1434	68.8%	67.4%	0.98
Q3 vs Q3	886	66.7%	60.3%	0.90
Q3 vs Q4	1685	67.3%	66.8%	0.99
Q4 vs Q4	791	67.1%	61.2%	0.91

There’s a striking finding here: The largest ratio, marking the most predictable bucket of matches, is for the most conservative pairs of players, while the smallest ratio, pointing to the most frequent upsets, is for the most aggressive players.

Before analyzing the relationship, let’s check one more thing. The very best players aren’t evenly divided throughout the quartiles, since Q1 has two of the big four. Elo-based match predictions–one of the building blocks of these results–are tougher to get right for the best players and the most uneven matchups, so we need to be careful whenever the elites might be influencing our findings. Therefore, let’s look at the same numbers, but this time for only those matches in which the favorite has a 50% to 70% chance of winning. This way, we exclude many of the best players’ matchups and all of their more lopsided contests:

Matchup	Matches	Fave Odds	Fave Win%	Ratio
Q1 vs Q1	196	59.5%	62.8%	1.05
Q1 vs Q2	604	59.8%	60.6%	1.01
Q1 vs Q3	731	59.7%	58.1%	0.97
Q1 vs Q4	663	59.9%	60.6%	1.01
Q2 vs Q2	322	59.0%	54.7%	0.93
Q2 vs Q3	931	59.8%	59.8%	1.00
Q2 vs Q4	822	59.7%	57.2%	0.96
Q3 vs Q3	544	59.5%	55.0%	0.92
Q3 vs Q4	1024	59.5%	58.2%	0.98
Q4 vs Q4	493	59.3%	55.0%	0.93

We discard about 40% of our sample, but the predictability trend remains the generally the same. In both the overall sample and the narrower 50%- to 70%-favorite subset, the strongest relationship I could find was between the predictability ratio and the quartile of the less aggressive player. In other words, a counterpuncher is likely to have more predictable results–regardless of whether he faces a big server, a fellow counterpuncher, or anyone in between–than a more aggressive player.

Back to basics

My initial theory is clearly wrong. I expected to find that Q1 vs Q1 matches were more predictable than average, and I was right. But by my logic, I also guessed that Q4 vs Q4 matches went according to script, and that other pairings, like Q1 vs Q4, would be more upset-prone. I would have done better had I let the neighbor’s cat make my predictions for me.

Instead, we find that that matches with more aggressive players are more likely to result in surprises. That doesn’t sound so groundbreaking, and it’s something I should’ve seen coming. Big servers tend to hold serve more often and break serve less frequently, meaning that their matches end with narrower margins, opening the door for luck to play a larger role, especially when sets and matches are determined by tiebreaks.

After all this, you might be thinking that I’ve squandered my afternoon, plus another few minutes of your attention, arriving at something obvious and unremarkable. I agree that it’s not that exciting to proclaim that big servers are more influenced by luck. But there’s still a useful–even surprising–discovery buried here.

Exponential upset potential

We know that the most one-dimensional players are more subject than others to the ups and downs of luck, thanks to the narrow margins of tiebreaks. For a man who rarely breaks serve, no match is a guaranteed win; for a man who rarely gets broken, no opponent is impossible to beat. However, I would have expected that the unpredictability of big servers was already incorporated into our match predictions, via the Elo ratings of the big servers. If a player has unusually random results, we’d expect his rating to drift toward tour average. That’s one reason that it’s very difficult for poor returners to reach the very top of the rankings.

But apparently, that isn’t quite right. The randomness-driven Elo ratings of our big servers do a nearly perfect job of predicting match outcomes against counterpunchers, and they’re only a little bit too confident against the more middle-of-the-road players in Q2 and Q3. Against each other, though, upsets run rampant. That extremely volatile fraction of results–the tiebreak-packed outcomes when the biggest servers face off–only accounts for part of these players’ ratings.

We’re accustomed to getting unpredictable results from the most aggressive players, with their big serves, inconsistent returns, and short rallies. Today’s findings give us a better idea of when these do and do not occur. Against counterpunchers, things aren’t so unpredictable after all. But when big servers play each other, we expect the unexpected–and the results are even more unpredictable than that.

Just How Aggressive is Jelena Ostapenko?

Italian translation at settesei.it

If you picked up only two stats about surprise Roland Garros champion Jelena Ostapenko, you probably heard that, first, her average forehand is faster than Andy Murray’s, and second, she hit 299 winners in her seven French Open matches. I’m not yet sure how much emphasis we should put on shot speed, and I instinctively distrust raw totals, but even with those caveats, it’s hard not to be impressed.

Compared to the likes of Simona Halep, Timea Bacsinszky, and Caroline Wozniacki, the last three women she upset en route to her maiden title, Ostapenko was practically playing a different game. Her style is more reminiscent of fellow Slam winners Petra Kvitova and Maria Sharapova, who don’t construct points so much as they destruct them. What I’d like to know, then, is how Ostapenko stacks up against the most aggressive players on the WTA tour.

Thankfully we already have a metric for this: Aggression Score, which I’ll abbreviate as AGG. This stat requires that we know three things about every point: How many shots were hit, who won it, and how. With that data, we figure out what percentage of a player’s shots resulted in winners, unforced errors, or her opponent’s forced errors. (Technically, the denominator is “shot opportunities,” which includes shots a player didn’t manage to hit after her opponent hit a winner. That doesn’t affect the results too much.) For today’s purposes, I’m calculating AGG without a player’s serves–both aces and forced return errors–so we’re capturing only rally aggression.

The typical range of this version AGG is between 0.1–very passive–and 0.3–extremely aggressive. Based on the nearly 1,600 women’s matches in the Match Charting Project dataset, Kvitova and Julia Goerges represent the aggressive end, with average AGGs around .275. We only have four Samantha Crawford matches in the database, but early signs suggest she could outpace even those women, as her average is at .312. At the other end of the spectrum, Madison Brengle is at 0.11, with Wozniacki and Sara Errani at 0.12. In the Match Charting data, there are single-day performances that rise as high as 0.44 (Serena Williams over Errani at the 2013 French Open) and fall as low as 0.06. In the final against Ostapenko, Halep’s aggression score was 0.08, half of her average of 0.16.

Context established, let’s see where Ostapenko fits in, starting with the Roland Garros final. Against Halep, her AGG was a whopping .327. That’s third highest of any player in a major final, behind Kvitova at Wimbledon in 2014 (.344) and Serena at the 2007 Australian Open (.328). (We have data for every Grand Slam final back to 1999, and most of them before that.) Using data from IBM Pointstream, which encompasses almost all matches at Roland Garros this year, Ostapenko’s aggression in the final was 7th-highest of any match in the tournament–out of 188 player-matches with the necessary data–behind two showings from Bethanie Mattek Sands, one each from Goerges, Madison Keys, and Mirjana Lucic … and Ostapenko’s first-round win against Louisa Chirico. It was also the third-highest recorded against Halep out of more than 200 Simona matches in the Match Charting dataset.

You get the picture: The French Open final was a serious display of aggression, at least from one side of the court. That level of ball-bashing was nothing new for the Latvian, either. We have charting data for her last three matches at Roland Garros, along with two matches from Charleston and one from Prague this clay season. Of those six performances, Ostapenko’s lowest AGG was .275, against Wozniacki in the Paris quarters. Her average across the six was .303.

If those recent matches indicate what we’ll see from her in the future, she will likely score as the most aggressive rallying player on the WTA tour. Because she played less aggressively in her earlier matches on tour, her career average still trails those of Kvitova and Goerges, but not by much–and probably not for long. It’s scary to consider what might happen as she gets stronger; we’ll have to wait and see how her tactics evolve, as well.

—

The Match Charting Project contains at least 15 matches on 62 different players–here is the rally-only aggression score for all of them:

PLAYER                    MATCHES  RALLY AGG  
Julia Goerges                  15      0.277  
Petra Kvitova                  57      0.277  
Jelena Ostapenko               17      0.271  
Madison Keys                   35      0.261  
Camila Giorgi                  17      0.257  
Sabine Lisicki                 19      0.246  
Caroline Garcia                15      0.242  
Coco Vandeweghe                17      0.238  
Serena Williams               108      0.237  
Laura Siegemund                19      0.235  
Anastasia Pavlyuchenkova       17      0.230  
Danka Kovinic                  15      0.223  
Kristina Mladenovic            28      0.222  
Na Li                          15      0.218  
Maria Sharapova                73      0.217  
                                              
PLAYER                    MATCHES  RALLY AGG  
Eugenie Bouchard               52      0.214  
Ana Ivanovic                   46      0.211  
Garbine Muguruza               57      0.210  
Lucie Safarova                 29      0.209  
Karolina Pliskova              42      0.207  
Elena Vesnina                  20      0.207  
Venus Williams                 46      0.205  
Johanna Konta                  31      0.205  
Monica Puig                    15      0.203  
Dominika Cibulkova             38      0.198  
Martina Navratilova            25      0.197  
Steffi Graf                    39      0.196  
Anastasija Sevastova           17      0.194  
Samantha Stosur                19      0.193  
Sloane Stephens                15      0.190  
                                              
PLAYER                    MATCHES  RALLY AGG  
Ekaterina Makarova             23      0.189  
Lauren Davis                   16      0.186  
Heather Watson                 16      0.185  
Daria Gavrilova                20      0.183  
Justine Henin                  28      0.183  
Kiki Bertens                   15      0.181  
Monica Seles                   18      0.179  
Svetlana Kuznetsova            28      0.174  
Timea Bacsinszky               28      0.174  
Victoria Azarenka              55      0.170  
Andrea Petkovic                24      0.166  
Roberta Vinci                  23      0.164  
Barbora Strycova               16      0.163  
Belinda Bencic                 31      0.163  
Jelena Jankovic                24      0.162  
                                              
PLAYER                    MATCHES  RALLY AGG  
Alison Riske                   15      0.161  
Angelique Kerber               83      0.161  
Flavia Pennetta                23      0.160  
Simona Halep                  218      0.160  
Carla Suarez Navarro           31      0.159  
Martina Hingis                 15      0.157  
Chris Evert                    20      0.152  
Darya Kasatkina                18      0.148  
Elina Svitolina                46      0.141  
Yulia Putintseva               15      0.137  
Alize Cornet                   18      0.136  
Agnieszka Radwanska            90      0.130  
Annika Beck                    16      0.126  
Monica Niculescu               25      0.124  
Caroline Wozniacki             62      0.122  
Sara Errani                    23      0.121

(A few of the match counts differ slightly from what you’ll find on the MCP home page. I’ve thrown out a few matches with too much missing data or in formats that didn’t play nice with the script I wrote to calculate aggression score.)

Little Data, Big Potential

This is a guest post by Carl Bialik.

I had more data on my last 30 minutes of playing tennis than I’d gotten in my first 10 years of playing tennis — and it just made me want so much more.

Ben Rothenberg and I had just played four supertiebreakers, after 10 minutes of warmup and before a forehand drill. And for most of that time — all but a brief break while PlaySight staff showed the WTA’s Micky Lawler the system — 10 PlaySight cameras were recording our every move and every shot: speed, spin, trajectory and whether it landed in or out. Immediately after every point, we could walk over to the kiosk right next to the net to watch video replays and get our stats. The tennis sure didn’t look professional-grade, but the stats did: spin rate, net clearance, winners, unforced errors, net points won.

Later that night, we could go online and watch and laugh with friends and family. If you’re as good as Ben and I are, laugh you will: As bad as we knew the tennis was by glancing over to Dominic Thiem and Jordan Thompson on the next practice court, it was so much worse when viewed on video, from the kind of camera angle that usually yields footage of uberfit tennis-playing pros, not uberslow tennis-writing bros.

This wasn’t the first time I’d seen video evidence of my take on tennis, an affront to aesthetes everyone. Though my first decade and a half of awkward swings and shoddy footwork went thankfully unrecorded, in the last five years I’d started to quantify my tennis self. First there was the time my friend Alex, a techie, mounted a camera on a smartphone during our match in a London park. Then in Paris a few years later, I roped him into joining me for a test of Mojjo, a PlaySight competitor that used just one camera — enough to record video later published online, with our consent and to our shame. Last year, Tennis Abstract proprietor Jeff Sackmann and I demo-ed a PlaySight court with Gordon Uehling, founder of the company.

With PlaySight and Mojjo still only in a handful of courts available to civilians, that probably puts me — and Alex, Jeff and Ben — in the top 5 or 10 percent of players at our level for access to advanced data on our games. (Jeff may object to being included in this playing level, but our USPS Tennis Abstract Head2Head suggests he belongs.) So as a member of the upper echelon of stats-aware casual players, what’s left once I’m done geeking out on the video replays and RPM stats? What actionable information is there about how I should change my game?

Little data, modest lessons

After reviewing my footage and data, I’m still looking for answers. Just a little bit of tennis data isn’t much more useful than none.

Take the serve, the most common shot in tennis. In any one set, I might hit a few dozen. But what can I learn from them? Half are to the deuce court, and half are to the ad court. And almost half of the ones that land in are second serves. Even with my limited repertoire, some are flat while others have slice. Some are out wide, some down the T and some to the body — usually, for me, a euphemism for, I missed my target.

If I hit only five slice first serves out wide to the deuce court, three went in, one was unreturned and I won one of the two ensuing rallies, what the hell does that mean? It doesn’t tell me a whole lot about what would’ve happened if I’d gotten a chance to I try that serve once more that day against Ben — let alone what would happen the next time we played, when he had his own racquet, when we weren’t hitting alongside pros and in front of confused fans, with different balls on a different surface without the desert sun above us, at a different time of day when we’re in different frames of mind. And the data says even less about how that serve would have done against a different opponent.

That’s the serve, a shot I’ll hit at least once on about half of points in any match. The story’s even tougher for rarer shots, like a backhand drop half volley or a forehand crosscourt defensive lob, shots so rare they might come up once or twice every 10 matches.

More eyes on the court

It’s cool to know that my spinniest forehand had 1,010 RPM (I hit pretty flat compared to Jack Sock’s 3,337 rpm), but the real value I see is in the kind of data collected on that London court: the video. PlaySight doesn’t yet know enough about me to know that my footwork was sloppier than usual on that forehand, but I do, and it’s a good reminder to get moving quickly and take small steps. And if I were focusing on the ball and my own feet, I might have missed that Ben leans to his backhand side instead of truly split-stepping, but if I catch him on video I can use that tendency to attack his forehand side next time.

Video is especially useful for players who are most focused on technique. As you might have gathered, I’m not, but I can still get tactical edge from studying patterns that PlaySight doesn’t yet identify.

Where PlaySight and its ilk could really drive breakthroughs is by combining all of the data at its disposal. The company’s software knows about only one of the thousands of hours I’ve spent playing tennis in the last five years. But it has tens of thousands of hours of tennis in its database. Even a player as idiosyncratic as me should have a doppelganger or two in a data set that big. And some of them must’ve faced an opponent like Ben. Then there are partial doppelgangers: women who serve like me even though all of our other shots are different; or juniors whose backhands resemble mine (and hopefully are being coached into a new one). Start grouping those videos together — I’m thinking of machine learning, clustering and classifying — and you can start building a sample of some meaningful size. PlaySight is already thinking this way, looking to add features that can tell a player, say, “Your backhand percentage in matches is 11 percent below other PlaySight users of a similar age/ability,” according to Jeff Angus, marketing manager for the company, who ran the demo for Ben and me.

The hardware side of PlaySight is tricky. It needs to install cameras and kiosks, weatherproofing them when the court is outdoors, and protect them from human error and carelessness. It’s in a handful of clubs, and the number probably won’t expand much: The company is focusing more on the college game. Even when Alex and I, two players at the very center of PlaySight’s target audience among casual players, happened to book a PlaySight court recently in San Francisco, we decided it wasn’t worth the few minutes it would have taken at the kiosk to register — or, in my case, remember my password. The cameras stood watch, but the footage was forever lost.

Bigger data, big questions

I’m more excited by PlaySight’s software side. I probably will never play enough points on PlaySight courts for the company to tell me how to play better or smarter — unless I pay to install the system at my home courts. But if it gets cheaper and easier to collect decent video of my own matches — really a matter of a decent mount and protector for a smartphone and enough storage space — why couldn’t I upload my video to the company? And why couldn’t it find video of enough Bizarro Carls and Bizarro Carl opponents around the world to make a decent guess about where I should be hitting forehands?

There are bigger, deeper tennis mysteries waiting to be solved. As memorably argued by John McPhee in Levels of the Game, tennis isn’t so much as one sport as dozens of different ones, each a different level of play united only by common rules and equipment. And a match between two players even from adjacent levels in his hierarchy typically is a rout. Yet tactically my matches aren’t so different from the ones I see on TV, or even from the practice set played by Thiem and Thompson a few feet from us. Hit to the backhand, disguise your shots, attack short balls and approach the net, hit drop shots if your opponent is playing too far back. And always, make your first serve and get your returns in.

So can a tactic from one level of the game even to one much lower? I’m no Radwanska and Ben is no Cibulkova, but could our class of play share enough similarity — mathematically, is Carl : Ben :: Aga : Pome — that what works for the pros works for me? If so, then medium-sized data on my style is just a subset of big data from analogous styles at every level of the game, and I might even find out if that backhand drop half volley is a good idea. (Probably not.)

PlaySight was the prompt, but it’s not the company’s job to fulfill product features only I care about. It doesn’t have to be PlaySight. Maybe it’s Mojjo, maybe Cizr. Or maybe it’s some college student who likes tennis and is looking for a machine-learning class. Hawk-Eye, the higher-tech, higher-priced, older competitor to PlaySight, has been slow to share its data with researchers and journalists. If PlaySight has figured out that most coaches value the video and don’t care much for stats, why not release the raw footage and stats to researchers, anonymized, who might get cracking on the tennis classification question or any of a dozen other tennis analysis questions I’ve never thought to ask? (Here’s a list of some Jeff and I have brainstormed, and here are his six big ones.) I hear all the time from people who like tennis and data and want to marry the two, not for money but to practice, to learn, to discover, and to share their findings. And other than what Jeff’s made available on GitHub, there’s not much data to share. (Just the other week, an MIT grad asked for tennis data to start analyzing.)

Sharing data with outside researchers “isn’t currently in the road map for our product team, but that could change,” Angus said, if sharing data can help the company make its data “actionable” for users to improve to their games.

Maybe there aren’t enough rec players who’d want the data with enough cash to make such ventures worthwhile. But college teams could use every edge. Rising juniors have the most plastic games and the biggest upside. And where a few inches can change a pro career, surely some of the top women and men could also benefit from PlaySight-driven insights.

Yet even the multimillionaire ruling class of the sport is subject to the same limitations driven by the fractured nature of the sport: Each event has its own data and own systems. Even at Indian Wells, where Hawk-Eye exists on every match court, just two practice courts have PlaySight; the company was hoping to install four more for this year’s tournament and is still aiming to install them soon. Realistically, unless pros pay to install PlaySight on their own practice courts and play lots of practice matches there, few will get enough data to be actionable. But if PlaySight, Hawk-Eye or a rival can make sense of all the collective video out there, maybe the most tactical players can turn smarts and stats into competitive advantages on par with big serves and wicked topspin forehands.

PlaySight has already done lots of cool stuff with its tennis data, but the real analytics breakthroughs in the sport are ahead of us.

Carl Bialik has written about tennis for fivethirtyeight.com and The Wall Street Journal. He lives and plays tennis in New York City and has a Tennis Abstract page.

How Much Is a Challenge Worth?

Italian translation at settesei.it

When the Hawkeye line-calling system is available, tennis players are given the right to make three incorrect challenges per set. As with any situation involving scarcity, there’s a choice to make: Take the chance of getting a call overturned, or make sure to keep your options open for later?

We’ve learned over the last several years that human line-calling is pretty darn good, so players don’t turn to Hawkeye that often. At the Australian Open this year, men challenged fewer than nine calls per match–well under three per set or, put another way, less than 1.5 challenges per player per set. Even at that low rate of fewer than once per thirty points, players are usually wrong. Only about one in three calls are overturned.

So while challenges are technically scarce, they aren’t that scarce. It’s a rare match in which a player challenges so often and is so frequently incorrect that he runs out. That said, it does happen, and while running out of challenges is low-probability, it’s very high risk. Getting a call overturned at a crucial moment could be the difference between winning and losing a tight match. Most of the time, challenges seem worthless, but in certain circumstances, they can be very valuable indeed.

Just how valuable? That’s what I hope to figure out. To do so, we’ll need to estimate the frequency with which players miss opportunities to overturn line calls because they’ve exhausted their challenges, and we’ll need to calculate the potential impact of failing to overturn those calls.

A few notes before we get any further. The extra challenge awarded to each player at the beginning of a tiebreak would make the analysis much more daunting, so I’ve ignored both that extra challenge and points played in tiebreaks. I suspect it has little effect on the results. I’ve limited this analysis to the ATP, since men challenge more frequently and get calls overturned more often. And finally, this is a very complex, sprawling subject, so we often have to make simplifying assumptions or plug in educated guesses where data isn’t available.

Running out of challenges

The Australian Open data mentioned above is typical for ATP challenges. It is very similar to a subset of Match Charting Project data, suggesting that both challenge frequency and accuracy are about the same across the tour as they are in Melbourne.

Let’s assume that each player challenges a call roughly once every sixty points, or 1.7%. Given an approximate success rate of 30%, each player makes an incorrect challenge on about 1.2% of points and a correct challenge on 0.5% of points. Later on, I’ll introduce a different set of assumptions so we can see what different parameters do to the results.

Running out of challenges isn’t in itself a problem. We’re interested in scenarios when a player not only exhausts his challenges, but when he also misses an opportunity to overturn a call later in the set. These situations are much less common than all of those in which a player might want to contest a call, but we don’t care about the 70% of those challenges that would be wrong, as they wouldn’t have any effect on the outcome of the match.

For each possible set length, from 24-point golden sets up to 93-point marathons, I ran a Monte Carlo simulation, using the assumptions given above, to determine the probability that, in a set of that length, a player would miss a chance to overturn a later call. As noted above, I’ve excluded tiebreaks from this analysis, so I counted only the number of points up to 6-6. I also excluded all “advantage” fifth sets.

For example, the most common set length in the data set is 57 points, which occured 647 times. In 10,000 simulations, a player missed a chance to overturn a call 0.27% of the time. The longer the set, the more likely that challenge scarcity would become an issue. In 10,000 simulations of 85-point sets, players ran out of challenges more than three times as often. In 0.92% of the simulations, a player was unable to challenge a call that would have been overturned.

These simulations are simple, assuming that each point is identical. Of course, players are aware of the cap on challenges, so with only one challenge remaining, they may be less likely to contest a “probably correct” call, and they would be very unlikely to use a challenge to earn a few extra seconds of rest. Further, the fact that players sometimes use Hawkeye for a bit of a break suggests that what we might call “true” challenges–instances in which the player believes the original call was wrong–are a bit less frequent that the numbers we’re using. Ultimately, we can’t address these concerns without a more complex model and quite a bit of data we don’t have.

Back to the results. Taking every possible set length and the results of the simulation for each one, we find the average player is likely to run out of challenges and miss a chance to overturn a call roughly once every 320 sets, or 0.31% of the time. That’s not very often–for almost all players, it’s less than once per season.

The impact of (not) overturning a call

Just because such an outcome is infrequent doesn’t necessarily mean it isn’t important. If a low-probability event has a high enough impact when it does occur, it’s still worth planning for.

Toward the end of a set, when most of these missed chances would occur, points can be very important, like break point at 5-6. But other points are almost meaningless, like 40-0 in just about any game.

To estimate the impact of these missed opportunities, I ran another set of Monte Carlo simulations. (This gets a bit hairy–bear with me.) For each set length, for those cases when a player ran out of challenges, I found the average number of points at which he used his last challenge. Then, for each run of the simulation, I took a random set from the last few years of ATP data with the corresponding number of points, chose a random point between the average time that the challenges ran out and the end of the set, and measured the importance of that point.

To quantify the importance of the point, I calculated three probabilities from the perspective of the player who lost the point and, had he conserved his challenges, could have overturned it:

his odds of winning the set before that point was played
his odds of winning the set after that point was played (and not overturned)
his odds of winning the set had the call been overturned and the point awarded to him.

(To generate these probabilities, I used my win probability code posted here with the assumption that each player wins 65% of his service points. The model treats points as independent–that is, the outcome of one point does not depend on the outcomes of previous points–which is not precisely true, but it’s close, and it makes things immensely more straightforward. Alert readers will also note that I’ve ignored the possibility of yet another call that could be overturned. However, the extremely low probability of that event convinced me to avoid the additional complexity required to model it.)

Given these numbers, we can calculate the possible effects of the challenge he couldn’t make. The difference between (2) and (3) is the effect if the call would’ve been overturned and awarded to him. The difference between (1) and (2) is the effect if the point would have been replayed. This is essentially the same concept as “leverage index” in baseball analytics.

Again, we’re missing some data–I have no idea what percentage of overturned calls result in each of those two outcomes. For today, we’ll say it’s half and half, so to boil down the effect of the missed challenge to a single number, we’ll average those two differences.

For example, let’s say we’re at five games all, and the returner wins the first point of the 11th game. The server’s odds of winning the set have decreased from 50% (at 5-all, love-all) to 43.0%. If the server got the call overturned and was awarded the point, his odds would increase to 53.8%. Thus, the win probability impact of overturning the call and taking the point is 10.8%, while the effect of forcing a replay is 7.0%. For the purposes of this simulation, we’re averaging these two numbers and using 8.9% as the win probability impact of this missed opportunity to challenge.

Back to the big picture. For each set length, I ran 1,000 simulations like what I’ve described above and averaged the results. In short sets under 40 points, the win probability impact of the missed challenge is less than five percentage points. The longer the set, the bigger the effect: Long sets are typically closer and the points tend to be higher-leverage. In 85-point sets, for instance, the average effect of the missed challenge is a whopping 20 percentage points–meaning that if a player more skillfully conserved his challenges in five such sets, he’d be able to reverse the outcome of one of them.

On average, the win probability effect of the missed challenge is 12.4 percentage points. In other words, better challenge management would win a player one more set for every eight times he didn’t lose such an opportunity by squandering his challenges.

The (small) big picture

Let’s put together the two findings. Based on our assumptions, players run out of challenges and forgo a chance to overturn a later call about once every 320 matches. We now know that the cost of such a mistake is, on average, a 12.4 percentage point win probability hit.

Thus, challenge management costs an average player one set out of every 2600. Given that many matches are played on clay or on courts without Hawkeye, that’s maybe once in a career. As long as the assumptions I’ve used are in the right ballpark, the effect isn’t even worth talking about. The mental cost of a player thinking more carefully before challenging might be greater than this exceedingly unlikely benefit.

What if some of the assumptions are wrong? Anecdotally, it seems like challenges cluster in certain matches, because of poor officiating, bad lighting, extreme spin, precise hitting, or some combination of these. It seems possible that certain scenarios would arise in which a player would want to challenge much more frequently, and even though he might gain some accuracy, he would still increase the risk.

I ran the same algorithms for what seems to me to be an extreme case, almost doubling the frequency with which each player challenges, to 3.0%, and somewhat increasing the accuracy rate, to 40%.

With these parameters, a player would run out of challenges and miss an opportunity to overturn a call about six times more often–once every 54 sets, or 1.8% of the time. The impact of each of these missed opportunities doesn’t change, so the overall result also increases by a factor of six. In these extreme case, poor challenge management would cost a player the set 0.28% of the time, or once every 356 sets. That’s a less outrageous number, representing perhaps one set every second year, but it also applies to unusual sets of circumstances which are very unlikely to follow a player to every match.

It seems clear that three challenges is enough. Even in long sets, players usually don’t run out, and when they do, it’s rare that they miss an opportunity that a fourth challenge would have afforded them. The effect of a missed chance can be enormous, but they are so infrequent that players would see little or no benefit from tactically conserving challenges.

Winners, Errors, and Misinformation

Italian translation at settesei.it

Of the general ways in which points end–winners, unforced errors, and forced errors, which is the most common? It’s so basic a question that I’d never thought to investigate it. As it turns out, other people have, and they’re making tenuous claims based on their results.

A friend sent me a link to this advertisement for an instructional course, which–eventually, far into a painfully slow video–explains that more points on the pro tour end in forced errors than in winners or unforced errors. And because of this, the video argues, you can use some of the same patterns the pros use with the goal of generating forced errors. Apparently, aiming for winners is too risky, as is waiting for unforced errors.

Pedagogically, it seems reasonable enough to encourage patience and tactical conservatism. I don’t know the first thing about helping amateurs improve their tennis game, and I’ll happily defer to the experts.

However, the use of pro tennis data sparked my interest. I was immediately skeptical of these claims, which were apparently based on Grand Slam matches from 2012.

Using my datasets extracted from IBM Pointstream’s records of the last several slams, I tested the 2015 French Open and the 2015 US Open, tallying winners, unforced errors, and forced errors for men and women at both events. Here’s how they break down:

Dataset    Winners  Unforced  Forced  
FO Men       33.8%     32.9%   33.3%  
FO Women     32.7%     37.8%   29.5%  
                                      
USO Men      34.3%     31.6%   34.1%  
USO Women    31.0%     38.0%   30.9%

On both surfaces, men’s points split fairly evenly among the three categories. For women, winners are roughly even with forced errors (though there are more winners on clay) and unforced errors are the most common type of point-ending shot.

The Pointstream-based dataset has limitations, though, and you might have already guessed what it is. A sizable percentage of forced errors are serve returns, which don’t really seem pertinent to a discussion of tactics. We can separate aces from winners and double faults from unforced errors, but not forced error returns from forced errors.

For that, we need the resources of the Match Charting Project. That data gives us almost 1500 matches (evenly split between men and women) once we limit our view to tour-level contests. The MCP dataset contains everything Pointstream does–winners, unforced and forced errors–and much, much more. For our purposes, the key addition is rally length, which allows to differentiate between forced error returns and forced errors that came later in rallies.

With the MCP data, we can remove serve statistics from this discussion altogether, excluding aces, double faults, and forced error returns, none of which are tactics in the sense we usually use the word.

Here’s the frequency of each type of point-ender:

Dataset  Winners  Unforced  Forced  
Men        32.5%     45.8%   21.7%  
Women      32.4%     49.4%   18.2%

When serves are no longer cluttering the picture, winners retain their relative importance, but the distribution of errors changes enormously. Now, we see that once the returner gets the ball back in play (or receives a serve he or she should be able to put back in play), unforced errors outnumber forced errors by more than two to one.

(I also calculated clay-specific numbers, and all the rates were within one percentage point of the overall averages.)

Forced errors are the most common type of point-ender in only 14 of 728 charted men’s matches and 4 of 751 charted women’s matches. Even if you’re concerned about the representativeness of the MCP sample or the error-labeling tendencies of the charters and add make substantial adjustments to allow for them, these results overwhelming establish that unforced errors are the most common way in which rallies end.

I’m not sure how applicable the tactics and tendencies of pro players are to amateur coaching, so it’s possible that these numbers are irrelevant to a great deal of coaching pedagogy. But if you’re going to base your instructional technique on pro tennis stats, it seems reasonable to start by getting the numbers right.

—

The Match Charting Project is making it possible to answer questions about tennis that were previously unanswerable. Project data is open to all researchers. Please help us grow the project by watching tennis and charting matches!

The Difficulty (and Importance) of Finding the Backhand

Italian translation at settesei.it

One disadvantage of some one-handed backhands is that they tend to sit up a little more when they’re hit crosscourt. That gives an opponent more time to prepare and, often, enough time to run around a crosscourt shot and hit a forehand, which opens up more tactical possibilities.

With the 700 men’s matches in the Match Charting Project database (please contribute!), we can start to quantify this disadvantage–if indeed it has a negative effect on one-handers. Once we’ve determined whether one-handers can find their opponents’ backhands, we can try to answer the more important question of how much it matters.

The scenario

Let’s take all baseline rallies between right-handers. Your opponent hits a shot to your backhand side, and you have three choices: drive (flat or topspin) backhand, slice backhand, or run around to hit a forehand. You’ll occasionally go for a winner down the line and you’ll sometimes be forced to hit a weak reply down the middle, but usually, your goal is to return the shot crosscourt, ideally finding your opponent’s backhand.

Considering all righty-righty matchups including at least one player among the last week’s ATP top 72 (I wanted to include Nicolas Almagro), here are the frequency and results of each of those choices:

SHOT    FREQ  FH REP  BH REP    UFE  WINNER  PT WON  
ALL             9.9%   68.1%  10.8%    5.8%   43.1%  
SLICE  11.9%   34.1%   49.5%   7.1%    0.6%   40.2%  
FH     44.9%    2.8%   69.0%  13.0%    9.8%   42.1%  
BH     43.3%   10.7%   72.2%   9.5%    3.1%   45.0%  
                                                     
1HBH   42.6%   12.0%   69.5%   9.3%    3.8%   44.2%  
2HBH   43.5%   10.0%   73.4%   9.6%    2.8%   45.4%

“FH REP” and “BH REP” refer to a forehand or backhand reply, and we can see just how much shot selection matters in keeping the ball away from your opponent’s forehand. A slice does a very poor job, while an inside-out forehand almost guarantees a backhand reply, though it comes with an increased risk of error.

The differences between one- and two-handed backhands aren’t as stark. One-handers don’t find the backhand quite as frequently, though they hit a few more winners. They hit drive backhands a bit less often, but that doesn’t necessarily mean they are hitting forehands instead. On average, two-handers hit a few more forehands from the backhand corner, while one-handers are forced to hit more slices.

One hand, many types

Not all one-handed backhands are created equal, and these numbers bear that out. Stanislas Wawrinka‘s backhand is as effective as the best two-handers, while Roger Federer‘s is typically the jumping-off point for discussions of why the one-hander is dying.

Here are the 28 players for whom we have at least 500 instances (excluding service returns) when the player responded to a shot hit to his backhand corner. For each, I’ve shown how often he chose a drive backhand or forehand, and the frequency with which he found the backhand–excluding his own errors and winners.

Player                 BH  BH FRQ  FIND BH%  FH FRQ  FIND BH%  
Alexandr Dolgopolov     2   45.7%     94.2%   43.3%     98.7%  
Kei Nishikori           2   51.1%     94.0%   38.9%     98.1%  
Andy Murray             2   41.0%     92.4%   46.5%     98.6%  
Stanislas Wawrinka      1   48.6%     92.1%   37.5%     98.0%  
Bernard Tomic           2   33.8%     91.7%   43.8%     97.9%  
Novak Djokovic          2   47.2%     91.7%   41.4%     98.5%  
Kevin Anderson          2   41.0%     91.5%   45.8%     96.6%  
Borna Coric             2   46.5%     90.7%   44.2%     96.9%  
Pablo Cuevas            1   41.9%     90.6%   54.5%     96.5%  
Marin Cilic             2   45.4%     89.7%   43.3%     97.2%  
                                                               
Player                 BH  BH FRQ  FIND BH%  FH FRQ  FIND BH%  
Tomas Berdych           2   41.6%     89.3%   44.2%     97.5%  
Pablo Carreno Busta     2   55.4%     87.8%   41.1%     93.5%  
Fabio Fognini           2   46.0%     87.4%   47.0%     96.1%  
Richard Gasquet         1   57.2%     87.3%   32.1%     96.8%  
Andreas Seppi           2   40.3%     87.2%   50.0%     93.9%  
Nicolas Almagro         1   53.6%     86.5%   39.3%     98.0%  
Dominic Thiem           1   38.5%     86.2%   50.0%     96.5%  
Gael Monfils            2   48.0%     85.3%   46.3%     85.3%  
David Ferrer            2   48.2%     84.9%   40.4%     97.1%  
Roger Federer           1   42.7%     84.8%   43.6%     94.5%  
                                                               
Player                 BH  BH FRQ  FIND BH%  FH FRQ  FIND BH%  
Gilles Simon            2   46.9%     84.6%   46.5%     94.6%  
David Goffin            2   45.4%     84.6%   45.7%     94.9%  
Roberto Bautista Agut   2   39.6%     83.3%   46.7%     98.4%  
Jo Wilfried Tsonga      2   43.5%     82.0%   44.5%     96.3%  
Grigor Dimitrov         1   41.4%     78.6%   39.4%     92.8%  
Milos Raonic            2   31.5%     63.5%   56.5%     94.3%  
Jack Sock               2   27.0%     62.5%   62.9%     96.3%  
Tommy Robredo           1   26.6%     56.1%   62.3%     88.4%

One-handers Wawrinka, Pablo Cuevas, and Richard Gasquet (barely) are among the top half of these players, in terms of finding the backhand with their own backhand. Federer and his would-be clone Grigor Dimitrov are at the other end of the spectrum.

Taking all 60 righties I included in this analysis (not just those shown above), there is a mild negative correlation (r^2 = -0.16) between a player’s likelihood of finding the opponent’s backhand with his own and the rate at which he chooses to hit a forehand from that corner. In other words, the worse he is at finding the backhand, the more inside-out forehands he hits. Tommy Robredo and Jack Sock are the one- and two-handed poster boys for this, struggling more than any other players to find the backhand, and compensating by hitting as many forehands as possible.

However, Federer–and, to an even greater extent, Dimitrov–don’t fit this mold. The average one-hander runs around balls in their backhand corner 44.6% of the time, while Fed is one percentage point under that and Dimitrov is below 40%. Federer is perceived to be particularly aggressive with his inside-out (and inside-in) forehands, but that may be because he chooses his moments wisely.

Ultimate outcomes

Let’s look at this from one more angle. In the end, what matters is whether you win the point, no matter how you get there. For each of the 28 players listed above, I calculated the rate at which they won points for each shot selection. For instance, when Novak Djokovic hits a drive backhand from his backhand corner, he wins the point 45.4% of the time, compared to 42.3% when he hits a slice and 42.4% when he hits a forehand.

Against his own average, Djokovic is about 3.6% better when he chooses (or to think of it another way, is able to choose) a drive backhand. For all of these players, here’s how each of the three shot choices compare to their average outcome:

Player                 BH   BH W   SL W   FH W  
Dominic Thiem           1  1.209  0.633  0.924  
David Goffin            2  1.111  0.656  0.956  
Grigor Dimitrov         1  1.104  0.730  1.022  
Gilles Simon            2  1.097  0.922  0.913  
Tomas Berdych           2  1.085  0.884  0.957  
Pablo Carreno Busta     2  1.081  0.982  0.892  
Kei Nishikori           2  1.070  0.777  0.965  
Roberto Bautista Agut   2  1.055  0.747  1.027  
Stanislas Wawrinka      1  1.050  0.995  0.936  
Borna Coric             2  1.049  1.033  0.941  
                                                
Player                 BH   BH W   SL W   FH W  
Bernard Tomic           2  1.049  1.037  0.943  
Jack Sock               2  1.049  0.811  1.010  
Gael Monfils            2  1.048  1.100  0.938  
Fabio Fognini           2  1.048  0.775  0.987  
Milos Raonic            2  1.048  0.996  0.974  
Nicolas Almagro         1  1.046  0.848  0.964  
Kevin Anderson          2  1.038  1.056  0.950  
Novak Djokovic          2  1.036  0.966  0.969  
Andy Murray             2  1.031  1.039  0.962  
Roger Federer           1  1.023  1.005  0.976  
                                                
Player                 BH   BH W   SL W   FH W  
Richard Gasquet         1  1.020  0.795  1.033  
Andreas Seppi           2  1.019  0.883  1.008  
David Ferrer            2  1.018  0.853  1.020  
Alexandr Dolgopolov     2  1.010  1.010  0.987  
Marin Cilic             2  1.006  1.009  0.991  
Pablo Cuevas            1  0.987  0.425  1.048  
Jo Wilfried Tsonga      2  0.956  0.805  1.095  
Tommy Robredo           1  0.845  0.930  1.079

In this view, Dimitrov–along with his fellow one-handed flame carrier Dominic Thiem–looks a lot better. His crosscourt backhand doesn’t find many backhands, but it is by far his most effective shot from his own backhand corner. We would expect him to win more points with a drive backhand than with a slice (since he probably opts for slices in more defensive positions), but it’s surprising to me that his backhand is so much better than the inside-out forehand.

While Dimitrov and Thiem are more extreme than most, almost all of these players have better results with crosscourt drive backhands than with inside-out (or inside-in forehands). Only five–including Robredo but, shockingly, not including Sock–win more points after hitting forehands from the backhand corner.

It’s clear that one-handers do, in fact, have a slightly more difficult time forcing their opponents to hit backhands. It’s much less clear how much it matters. Even Federer, with his famously dodgy backhand and even more famously dominant inside-out forehand, is slightly better off hitting a backhand from his backhand corner. We’ll never know what would happen if Fed had Djokovic’s backhand instead, but even though Federer’s one-hander isn’t finding as many backhands as Novak’s two-hander does, it’s getting the job done at a surprisingly high rate.

Are Two First Serves Ever Better Than One?

Italian translation at settesei.it

It’s one of those ideas that never really goes away. Some players have such strong first serves that we often wonder what would happen if they hit only first serves. That is, if a player went all-out on every serve, would his results be any better?

Last year, Carl Bialik answered that question: It’s a reasonably straightforward “no.”

Bialik showed that among ATP tour regulars in 2014, only Ivo Karlovic would benefit from what I’ll call the “double-first” strategy, and his gains would be minimal. When I ran the numbers for 2015–assuming for all players that their rates of making first serves and winning first-serve points would stay the same–I found that Karlovic only breaks even. Going back to 2010, 2014 Ivo was the only player-season with at least 40 matches for whom two first serves would be better than one.

Still, it’s not an open-and-shut case. What struck me is that the disadvantage of a double-first strategy would be so minimal. For Karlovic (and others, mainly big servers, such as Jerzy Janowicz, Milos Raonic,and John Isner), hitting two first serves would only slightly decrease their overall rate of service points won. For Rafael Nadal and Andy Murray, opting for double-first would reduce their rate of service points won by just under two percentage points.

Here’s a visual look at 2015 tour regulars (minimum 30 matches), showing the hypothetical disadvantage of two first serves. The diagonal line is the breakeven level; Ivo, Janowicz, and Isner are the three points nearly on the line.

Since some players are so close to breaking even, I started to wonder if some matchups make the double-first strategy a winning proposition. For example, Novak Djokovic is so dominant against second serves that, perhaps, opponents would be better off letting him see only first serves.

However, it remains a good idea–at least in general–to take the traditional approach against Djokovic. Hypothetically, two first serves would result in Novak raising his rate of return points won by 1.2 percentage points. Gilles Simon and Andy Murray are in similar territory, right around 1 percentage point.

Here’s the same plot, showing the disadvantage of double-first against tour-regular returners this season:

There just aren’t any returners who would cause the strategy to come as close to breaking even as some big servers do.

The match-level tactic

What happens if a nearly-breakeven server, like Karlovic, faces a not-far-from-breakeven returner, like Djokovic? If opting for double-first is almost a good idea for Ivo against the average returner, what happens when he faces someone particularly skilled at attacking second serves?

Sure enough, there are lots of matches in which two first serves would have been better than one. I found about 1300 matches between tour regulars (players with 30+ matches) this season, and for each one, I calculated each player’s actual service points won along with their estimated points won had they hit two first serves. About one-quarter of the time, double-first would have been an improvement.

This finding holds up in longer matches, too, avoiding some of the danger of tiny samples in short matches. In one-quarter of longer-than-average matches, a player would have still benefited from the double-first strategy. Here’s a look at how those matches are distributed:

Finally, some action on the left side of the line! One of those outliers in the far upper right of the graph is, in fact, Ivo’s upset of Djokovic in Doha this year. Karlovic won 85% of first-serve points but only 50% of second-serve points. Had he hit only first serves, he would’ve won about 79% of his service points instead of the 75% that he recorded that day.

Another standout example is Karlovic’s match against Simon in Cincinnati. Ivo won 81% of first-serve points and only 39% of second-serve points. He won the match anyway, but if he had pursued a double-first strategy, Simon could’ve caught an earlier flight home.

Predicting double-first opportunities

Armed with all this data, we would still have a very difficult time identifying opportunities for players to take advantage of the strategy.

For each player in every match, I multiplied his “double-first disadvantage” (the number of percentage points of serve points won he would lose by hitting two first serves) with the returner’s double-first disadvantage. Ranking all matches by the resulting product puts combinations like Karlovic-Djokovic and Murray-Isner together at one extreme. If we are to find instances where we could retroactively predict an advantage from hitting two first serves, they would be here.

When we divide all these matches into quintiles, there is a strong relationship between the double-first results we would predict using season-aggregate numbers and the double-first results we see in individual matches. However, even if the most double-first-friendly quintile–the one filled with Ivo serving and Novak returning–there’s still, on average, a one-percentage-point advantage to the traditional serving tactic.

It is only at the most extreme that we could even consider recommending two first serves. When we take the 2% of matches with the smallest products–that is, the ones we would most expect to benefit from double first–26 of those 50 matches are one in which the server would’ve done better to hit two first serves.

In other words, there’s a ton of variance at the individual match level, and since the margins are so slim, there are almost no situations where it would be sensible for a player to hit two first serves.

A brief coda in the real world

All of this analysis is based on some simplifying assumptions, namely that players would make their first serves at the same rate if they were hitting two instead of one, and that players would win the same number of points behind their first serves even if they were hitting them twice as often.

We can only speculate how much those assumptions mask. I suspect that if a player hit only first serves, he would be more likely to see streaks of both success and failure; without second serves to mix things up, it would be easier to find oneself repeating mechanics, whether perfect or flawed.

The second assumption is probably the more important one. If a server hit only first serves, his ability to mix things up and disguise serving patterns would be hampered. I have no idea how much that would affect the outcome of service points–but it would probably act to the advantage of the returner.

All that said, even if we can’t recommend that players hit two first serves in any but the extreme matchups, it is worth emphasizing that the margins we’re discussing are small. And since they are small, the risk of hitting big second serves isn’t that great. There may be room for players to profitably experiment with more aggressive second serving, especially when a returner starts crushing second serves.

Ceding the advantage on second-serve points to a player like Djokovic must be disheartening. If the risk of a few more double faults is tolerable, we may have stumbled on a way for servers to occasionally stop the bleeding.

Sabr Metrics: The Case For the Hyper-Aggressive Return

Italian translation at settesei.it

Roger Federer has made waves the last few weeks by occasionally moving way up the court to return second serves. While the old-school tactic was nearly extinct in today’s game of baseline attrition, it seems to be working for Fed.

At least in one sense, it’s too early to say whether the kamikaze return is an effective tactic. Federer has used it sparingly for only a handful of matches, and in that tiny sample, he’s missed plenty of returns. But in the view of many pundits, the hyper-aggressive return gets in his opponents’ heads, making the tactic more valuable than simply changing the result of a few points. Presumably Roger agrees, since he keeps using it.

I agree that the tactic is a good one, though for a different reason. By taking greater risks, Fed is generating more unpredictability, or streakiness, on his opponents’ service games, which is valuable even if he doesn’t win any more return points.

Watching and waiting

To win a match, a player usually needs to break serve, and in the contemporary men’s game, that’s not an easy thing to do. On average, servers win about 64% of points and hold about 80% of service games. On hard courts, the equivalent numbers are even higher. Against a good server–let alone John Isner, Fed’s opponent tonight–they are higher still.

Returners who stand well behind the baseline and try only to put the ball back in play are basically crossing their fingers and hoping for the best. Maybe their opponent will miss several first serves, or the server will make a couple of errors against those weak returns. It can work, and for a brilliant returner such as Novak Djokovic, hitting moderately aggressive returns and winning some of the ensuing rallies is usually good enough for several breaks per match.

For most players, however, breaks of serve rely more on the server’s occasional lapses. To put it in numerical terms: A passive returner is playing the lottery in every return game–a lottery with only a 10% to 20% chance of winning.

Generating the coin flip

The best way to earn more breaks of serve, of course, is to win more return points. But unless you’re spending the offseason at Djokovic’s training camp, that’s unlikely.

The alternative is to change the rules of the lottery. Instead of accepting a steady rate of 35% of return points, a hyper-aggressive strategy is more likely to make the point-by-point results more streaky, even if the overall rate doesn’t change.

To see why this is effective, we need to oversimplify a bit. A player who wins 35% of return points will, on average, break in 17% of his return games. If we introduce a slight variation in the rate of return points won, we see a slight improvement in break rate, as well. If that same player wins 30% of return points in half of his games and 40% of return points in the other half, he’ll break serve 18% of the time.

That one percent improvement is barely noticeable. It probably represents what’s already going on in most matches, often because servers are a bit streaky already. The more volatility we introduce, though, the more the odds tilt toward the returner.

Double the variation and say that the returner wins 25% of return points half the time and 45% the other half. Now he’ll break serve in 21% of games, or one extra break per 25 return games. Still not overwhelming, but that’s one extra break in a five-setter.

The real magic happens when we expand the variation to an even split between 20% of return points and 50% of return points. In that scenario–when, remember, our returner is still winning 35% of points–the break rate improves to 26%, almost one more break per ten return games. On average, that’s an extra break per best-of-three match, and closer to two extra breaks in a typical best-of-five match.

Back to reality

A hyper-aggressive return game is going to result in more return errors as well as more return winners. That’s true regardless of return position: Mikhail Kukushkin managed to break Marin Cilic four times on Friday by going for return winners, even if he stayed in the general area of the baseline.

So a new return tactic is unlikely to make a player much better in general. And of course, it’s unlikely to generate anything like the neat, theoretical examples shown above, when one game is better and one game is worse.

However, I suspect that higher-risk shots are more likely to be streaky, which would result in something like those neat examples. And if the pundits are right, that Fed’s kamikaze return unnerves his opponents, that ought to make his return games even streakier still, as his opponents deal with a new challenge mid-match.

Whenever there’s an opportunity to change the nature of the game and make it less predictable, the underdog should take it. Odd as it is to think of Federer as the underdog, he–like everyone else on the men’s tour–is in fact fighting an uphill battle in every return game. Hyper-aggressive tactics are a small step toward leveling the field.