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

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

Thanks for listening!

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

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

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

**Elo to the rescue**

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

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

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

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

**Measuring magnitude**

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

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

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

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

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

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

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

**Steffi, Serena, and the threshold**

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

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

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

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

**Ranking Woz**

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

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

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

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

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

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

**Taylor Fritz: not screwed**

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

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

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

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

**More data**

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

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

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

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

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

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

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

Thanks for listening!

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

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

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

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

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

**Counting stats**

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

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

**Double bagel chances**

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

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

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

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

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

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

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

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

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

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

**Directional decisions**

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

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

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

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

**Point probability**

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

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

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

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

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

**Cautious recommendations**

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

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

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

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

**Player probabilities**

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

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

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

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

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

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

**Next**

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

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

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

**How much?**

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

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

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

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

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

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

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

**Complicating factors**

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

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

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

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

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

]]>Like Richard Gasquet returning a serve, we need to take a step back before we can move forward. Rather than continuing to focus solely on the down-the-line backhand, let’s expand our view to *all shots played from the backhand corner*. The DTL backhand is only one choice among many. A player in position to go down the line has the option of a cross-court shot or a more conservative reply up the middle. She also might run around the backhand entirely, taking aim with a forehand up the line (“inside-in”), down the middle, or cross-court (“inside-out”).

Every shot is a choice, and one of the roles of analytics is to analyze the pros and cons of decisions players make. Ideally, we would even be able to identify cases in which pros make poor choices and recommend better ones. We’re still many steps away from that, at least in any kind of systematic way. But thanks to the thousands of matches with shot-by-shot data logged by the Match Charting Project, we have plenty of raw material to help us get closer.

**The first choice**

In 2,700 charted men’s matches from the last decade (happy new year!), I isolated about 450,000 situations in which one player had a makeable ball in his backhand corner, excluding service returns. The definition of “makeable” is inherently a bit messy. For today’s purposes, a makeable ball is one that the player managed to return or one that turned into an unforced error. With ball-tracking data, we could be more precise, but for now we need to accept this level of imprecision.

Of the 450,000 makeable backhand-corner balls, players hit (non-slice) backhands 63.7% of the time and (non-slice) forehands 14.3% of the time. The remaining 22% were divvied up among slices, dropshots, and lobs, and we’ll set those aside for another day.

Here’s how 2010s men chose to aim their backhands from the backhand corner:

- Down the line: 17.4%
- Down the middle: 29.5%
- Cross-court: 52.9%

And their forehands from the same position:

- Down the line (inside-in): 35.1%
- Down the middle: 12.8%
- Cross-court (inside-out): 51.8%

The inside-in percentage is a bit surprising at first, though we need to keep in mind that it’s 35% of a relatively small number, accounting for only 5% of total shots from the backhand corner. Less surprising is the much higher frequency of shots going cross-court. Not only is that a safer, higher-percentage play, it directs the ball to the opponent’s backhand (unless he’s a lefty), which is typically his weaker side.

**Point probability**

Shot selection is only a means to an end. More important than deploying textbook-perfect strategy is winning the point, and that’s where we’ll turn next.

The average ATPer has a 47.7% chance of winning the point when faced with a makeable ball in his backhand corner. Of course, any particular opportunity could be much better or worse than that. But again, without camera-based ball-tracking data, we can’t make more accurate estimates for specific chances. We can get some clues as to the range of probabilities by looking at how they vary at different stages of the rally. When a player has an opportunity for a “serve-plus-one” shot in the backhand corner–the third shot of the rally–his chances of winning the point are higher, at 51.1%. On the fourth shot of the rally, when pros are often still recovering from the disadvantage of returning, the chances of winning the point from that position are 45.4%. Context matters, in large part because context offers hints as to whether certain shots are better or worse than average.

So far, we have an idea of the probability of winning the point *before* making a choice. There are two ways of looking at the probability *after* choosing and hitting a shot: the odds of winning the point after *hitting* the shot, and the odds of winning the point after *making* the shot. The second number is obviously going to be better, because we simply filter out the errors. By excluding what could go wrong, it doesn’t give us the whole picture, but it does provide some useful information, showing which shots have the capacity to put opponents in the worst positions.

Here are the point probabilities for each of the shots we’re considering. For each choice, I’ve shown the probability of winning the point after hitting the shot (“Post-Shot”) and after *making* the shot (“In-Play”).

Shot Direction Post-Shot In-Play Backhand (all) 48.2% 54.2% Backhand DTL 51.4% 64.6% Backhand Middle 44.2% 48.2% Backhand XC 49.5% 54.6% Forehand (all) 55.1% 63.0% Forehand DTL (I-I) 58.5% 69.0% Forehand Middle 47.3% 52.0% Forehand XC (I-O) 54.9% 61.9%

Forehands tend to do more to improve point-winning probability than backhands, though the down-the-middle forehand is less effective than a backhand to either corner. Again, this is context talking: A player who runs around a backhand just to hit a conservative forehand may have misjudged the angle or spin of the ball and felt forced to make a more defensive play. Still, it’s a relatively common tactic on slower clay courts (on clay, it is almost twice as common than tour average), and it may be used too often.

The most dramatic differences between the two probabilities are on the down-the-line shots. Both forehand and backhand are aggressive, high-risk shots, something reflected in the winner and unforced error rates for each. 9% of all shots from the backhand corner are winners, and another 11% are unforced errors. Of down-the-line shots, 23% are winners and 19% are unforced errors. While the choice to go down the line isn’t superior to other options, both the forehand and backhand are devastating shots when they work.

**Player by player**

Let’s tentatively measure “effectiveness” in terms of increasing point probability. Setting aside the complexity of context, which won’t be the same for every player, the most effective pro is the one who makes the most of a certain class of opportunities.

Here are the 10 best active players (of those with at least 20 charted matches) who do the most when faced with a makeable ball in their own backhand corner. Keep in mind that the average player has a 47.7% chance of winning the point from that position:

Player Post-Shot Rafael Nadal 52.9% Diego Schwartzman 52.4% Novak Djokovic 52.3% Nikoloz Basilashvili 51.9% Andrey Rublev 51.8% Kei Nishikori 51.5% Gilles Simon 51.2% Pablo Cuevas 50.9% Alex De Minaur 50.0% Pablo Carreno Busta 49.6%

The Match Charting Project data might understate just how effective Rafael Nadal, Novak Djokovic, and Kei Nishikori are from their backhand corner, since a disproportionate number of their charted matches are against other top players. In any case, it is no surprise to see them here, along with such backhand warriors as Diego Schwartzman and Gilles Simon.

This list is limited to the tour regulars with at least 20 matches charted. One more name to watch out for is Thomas Fabbiano, with only 12 matches logged so far. In that limited sample, his point probability from the backhand corner is a whopping 59.2%. He isn’t quite that much of an outlier in reality, since his charted matches include contests against Ivo Karlovic, Reilly Opelka, and Sam Querrey, opponents whose ground games leave a bit to be desired. But his overall figure is so far off the charts that, even adjusting downward by a hefty margin, he appears to be one of the more dangerous players on tour from that position.

**Forehands and backhands**

Let’s wrap up by looking at something a bit more specific. For backhands and forehands (without separating by direction), which players are most effective after hitting that shot from the backhand corner? We’re continuing to define effectiveness as winning as many points as possible after hitting the shot. I’ll also show how often each of the players opts for their effective shot, giving us a glimpse at tactical *decisions*, not just tactical success.

Here are the best backhands from the backhand corner. It was supposed to be a top ten list, but I think you’ll understand why I struggled to cut it off before listing the top 16 players, roughly one-fifth of the 75 players with at least 20 charted matches:

Player Post-shot BH Freq Diego Schwartzman 52.8% 74.0% Rafael Nadal 52.7% 64.7% Novak Djokovic 52.7% 76.1% Kei Nishikori 51.7% 74.0% Gilles Simon 51.4% 88.0% Andrey Rublev 51.1% 67.1% Pablo Carreno Busta 51.1% 75.3% Nikoloz Basilashvili 51.0% 75.0% Alexander Zverev 50.8% 75.1% Alex de Minaur 50.6% 74.8% Daniil Medvedev 50.6% 87.2% Juan Martin del Potro 50.3% 49.1% Pablo Cuevas 50.2% 60.6% Andy Murray 50.1% 65.0% Richard Gasquet 49.9% 75.8% Stan Wawrinka 49.8% 63.4%

The “BH Freq” column–for backhand frequency–really demonstrates the range of tactics used by different players. Gilles Simon and Daniil Medvedev opt for the topspin backhand almost every time, rarely slicing or running around the shot. At the opposite extreme, Juan Martin del Potro hits a topspin backhand less the half the time from that position. Perhaps because of his selectiveness–dealing with awkward positions by slicing–he is effective when he makes that choice.

Now the best *forehands* from the backhand corner:

Player Post-shot FH Freq Gilles Simon 63.1% 6.7% Rafael Nadal 61.9% 16.6% Benoit Paire 61.9% 1.5% Kei Nishikori 61.2% 10.4% Andrey Rublev 61.0% 20.1% Casper Ruud 60.8% 27.1% Marton Fucsovics 60.5% 16.3% Novak Djokovic 60.0% 9.7% Daniil Medvedev 59.8% 3.3% Pablo Cuevas 58.9% 20.9% Sam Querrey 58.2% 15.6% Felix Auger Aliassime 57.7% 16.0%

This list is more of a mixed bag, in part because there are so many fewer forehands from the backhand corner. Benoit Paire’s numbers are based on a mere 21 shots. I wouldn’t take his effectiveness seriously at all, but it’s always entertaining to see evidence of his uniqueness. At the opposite end of the spectrum is Casper Ruud, who runs around his backhand more than anyone else in the charting dataset except for Jack Sock and Joao Sousa. (Neither one of which is particularly effective, though presumably they do better by avoiding their backhands than they would by hitting it.)

One name you might have expected to see on the last list is Roger Federer. He’s around the 80th percentile in the forehand category, winning 56.9% of points when hitting a forehand from the backhand corner. He’s good, but not off the charts in this category. Like Nadal and Djokovic, he might look better if these numbers were adjusted for opponent, because so many of his charted matches are against fellow elites.

**Next**

There’s clearly a lot more to do here, including looking at probabilities for direction-specific shots, isolating the effect of certain opponents, and trying to control for more of the factors that aren’t explicitly present in the data. Not to mention extending the same framework to other shots from other positions on court. Stay tuned.

]]>Let’s start with the first underlined section. I’ll get to the doubles tweak in a bit.

The ITF is learning that incentives are tricky. In the olden days, back when Adrian Mannarino still had hair, prize money was simple. If you played, you got some. If you didn’t, you got none. Players who get hurt right before one of the four biggest events of the season suffered in silence.

Except it’s never been quite that simple. The slams have spent the last decade taking turns breaking prize-money records, raising in particular the take for first-round losers. A spot in the main draw of the Australian Open is now worth $63,000 USD ($90,000 AUD). Some players in the qualifying draw barely make that much in an entire season. Whatever one’s hangups about honesty or fair play, if you have a chance to grab that check, you take it.

The same logic applies whether you’re healthy or injured. The last decade or so of grand slam tennis has been littered with first-round losers who weren’t really fit to compete. That’s bad for the tournaments, bad for the fans, and probably not that great for the players themselves, even if $63k does buy a lot of physiotherapy.

**Paid withdrawals**

Two years ago, the ITF took aim at the problem. Players with a place in the main draw could choose to withdraw and still collect 50% of first-round loser prize money. The ATP does something similar, giving on-site withdrawals full first-round loser prize money for up to two consecutive tournaments. The ATP’s initiative has been particularly successful, cutting first-round retirements at tour-level events from a 2015 high of 48 to only 20 in 2019. In percentage terms, that’s a decline from 4.4% of first-round matches to only 1.6%.

The results at slams are cloudier. On the men’s side, there were nine first-round retirements in 2010, and nine in 2019. The ITF’s incentives might not be sufficient: 50% of first-round prize money is still a substantial sum to forego. In fairness to the slams, retirements may not tell the whole story. A hobbled player can still complete a match, and perhaps the prize money adjustment has convinced a few more competitors to give up their places in the main draw.

None of this, however, keeps out players who consciously game the system. Both the ATP and WTA allow injured players to use their pre-injury rankings to enter a limited number of events upon their return. Savvy pros maximize those entries (“protected” in ATP parlance, and “special” in WTA lingo) by using them where the prize pots are richest and, if possible, bridging the gap with wild cards into smaller events.

Emblematic of such tactics is Dmitry Tursunov, who played (and lost) his last six matches at majors, all using protected rankings. Two of those, including his final grand slam match at the 2017 US Open against Cameron Norrie, ended in retirement. Three of the others were straight-set losses. In one sense, Tursunov “earned” those paydays. He was ranked 31st going into Wimbledon in 2014, then missed most of the following 18 months. Upon return, he followed ATP tour rules. But with the increasingly disproportionate rewards available at slams, protected rankings seem sporting only when used as part of a concerted comeback effort.

While the ITF’s late-withdrawal policy wasn’t in place for Tursunov, it’s easy to imagine a player in a similar situation taking advantage. And that’s the gap that the latest tweak aims to plug. The new rule is not limited to players on protected or special rankings, which typically require absences of six months, not just one. Yet the idea is similar. You can no longer enter, turn up on site, plead injury, and take home tens of thousands of dollars … unless you’ve competed recently. It’s a low bar, but it raises the standard a bit for players who want to take home a $30,000 check.

**One of two prongs**

The rule adjustment wouldn’t have affected Tursunov’s lucrative protected-ranking tour of 2016-17. However, had the Russian come back from injury a couple of years later, his income might not have gone uncontested.

In 2019, both Roland Garros and Wimbledon invoked another rarely-used clause in the rulebook. It requires that players “perform to a professional standard,” and a failure to do so can result in fines up to the amount of first-round prize money. Anna Tatishvili–using a special ranking–was docked her full paycheck at the French Open, and Bernard Tomic–a convenient whipping boy whenever this sort of thing comes up–lost his take-home from the All England Club. Both fines were appealed, and Tatishvili’s was overturned. (Tomic’s should have been, too.)

What matters for the purposes of today’s discussion isn’t the size of Tatishvili’s bank account, but the fact that the majors have dug the “professional standard” clause out of cold storage. It’s worth quoting the various factors that the rulebook spells out as possibly contributing to a violation of the standard:

*the player did not complete the match**the player did not compete in the 2-3 week period preceding the Grand Slam**the player retired from the last tournament he/she played before the Grand Slam**the player was using a Protected or Special Ranking for entry**the player received a Code Violation for failure to use Best Efforts*

Every major has a few players who are skirting the line, perhaps returning to action a bit sooner than they would have if the grand slam schedule were different. With the fines in 2019, the ITF has made clear that they expect to see credible performances from all 256 main draw players. And with the prize money adjustment for 2020, the governing body has closed the door on five-figure paydays for players who shouldn’t have been on the entry list, even if they never take the court.

**I promised to talk about doubles**

The second section of the rulebook quoted above is a bit problematic, because I believe it is missing a key “not” in the opening sentence. Unless the ITF has some bizarre and unprecedented goals, the intention of the doubles regulations is to discourage singles players from retiring in doubles unless they are truly injured, and to prevent singles players from even *entering* doubles unless they plan to take it seriously.

Doubles prize money pales next to the singles pot, but even first-round losers in men’s and women’s doubles will take home $17,500 USD per team, or $8,750 per player. That’s enough to convince most singles players to enter if their ranking makes the cut, no matter how little they care about doubles during the 44 non-slam weeks of the year.

The majors determine which teams make the doubles cut the same way that ATP and WTA tour events do. Teams are ordered by their combined *singles or doubles* ranking. Each player can use whichever is better. The tours allow pros to use their singles rankings to encourage superstars to play doubles, and at events like Indian Wells, many big names do take part. At the slams, the bigger effect is on the next rung of singles players, giving us oddball doubles teams such as Mackenzie McDonald/Yoshihito Nishioka and Lukas Lacko/John Millman at the 2018 US Open.

As with other details of the entry process, most fans couldn’t care less. But they should. Whenever the rules let one team *in*, they leave another team *out*. By including more singles players in the doubles draw, the standard for full-time doubles players is made almost impossibly strict. An up-and-coming men’s singles player can crack the top 100–and gain admission to grand slam main draws–with a solid season on the challenger tour, but even the best challenger-level doubles teams are often left scrambling for partners whose singles rankings are sufficient to gain entry.

This year’s rulebook edit should help matters, at least a bit. (As long as someone inserts the missing “not,” anyway.) Grand slam doubles is not an exhibition, and it shouldn’t be contested by players who treat it that way. The ATP and WTA should follow suit, penalizing players who withdraw from doubles only to prove their health by continuing to play singles.

**Incentives and intentions**

These rule changes, while technical, are aimed at something rather simple: to ensure that the players who enter slam main draws–both singles are doubles–are healthy and motivated to play. The latest tweaks won’t close every loophole, and we can expect more disputes over issues like the Tatishvili and Tomic fines.

The bigger issue, complicated by the on-site withdrawal adjustment, is the underlying purpose of the rise in first-round loser prize money. The slams represent a huge proportion of the season-long prize pool, especially for players between approximately 50th and 110th in the ATP and WTA rankings. These competitors miss the cut for many of the most prestigious Masters and Premier tournaments. Even in later rounds, they are usually playing for four-figure stakes–if that. Four times a year, pros with double-digit rankings get a guaranteed cash infusion, and the potential for much more.

The presence of the four majors effectively funds the rest of the season for many players. The slams have upped first-round prize money–both nominally and relative to increases in later-round awards–partly in recognition of that fact. It is expensive to be a touring pro, and without paydays from the majors, it can easily be a money-losing endeavor.

**Salary, not prize money**

The majors rely on the less-lucrative tours for year-round publicity and a pool of highly-skilled players to drive fans and media attention to their mega-events. Much of the first-round loser prize money is in recognition of that fact. No one really thinks that the 87th-best player in the world deserves $63k just for showing up and giving Serena Williams a mild 59-minute workout. But does the 87th-best player in the world deserve to collect annual revenue of $250k–a figure that will largely go to cover travel, training, coaching, and equipment expenses? I think so, it appears that the slams think so, and I suspect you do, too.

So, when the ITF closes loopholes like these, keep in mind that they are operating within the silly $63k-per-hour framework, not the more reasonable $250k-per-season model. It is an important goal to ensure the integrity and quality of play at slams, but it ought to be paired with an effort to support tennis’s rank-and-file, even when those journeymen are injured.

A more sensible policy would be to separate much of the first-round loser prize pool from the literal act of playing a first round match. Perhaps the slams could each contribute $7.5 million each year–that’s $30k per singles player–to a general fund that would disburse annual grants to players ranked outside the top fifty, and lower every singles award by the same amount. (The details would be devilish, starting with these few parameters.) Such an approach would come out in the wash for most players, who would simply receive the extra $30k per slam in a different guise. But it would help injured players return to top form, and it would leave plenty of money for high-stakes combat at the sport’s biggest stages. Such a solution, of course, would require a lot more than a few minor edits to the rulebook.

]]>It’s right to look at results like Djokovic-Federer and conclude that many matches are decided by slim margins or that performance on certain points is crucial. Indeed, players occasionally win matches while winning as few as 47% of points.

Still, it’s possible to take the “slim margins” claim too far. 51% sounds like a narrow margin, as does 53%. In many endeavors, sporting and otherwise, 55% represents a near-tie, and even 60% or 65% suggests that there isn’t much to separate the two sides. Not so in tennis, especially in the serve-centered men’s game. However it sounds, 60% represents a one-sided contest, and 65% is a blowout verging on embarrassment. In 2019, only three ATP tour matches saw one player win more than 70% of total points.

**Answer a different question**

For several reasons, total points won is an imperfect measure of one player’s superiority, even in a single match. One flaw is that it is usually stuck in that range between 35% and 65%, incorrectly implying that all tennis matches are relatively close contests. Another drawback is that not all 55% rates (or 51%s, or 62%s) are created equal. The longer the match, the more information we gain about the players. For a specific format, like best-of-three, a longer match usually requires closely-matched players to go to tiebreaks or a third set. But if we want to compare matches across different formats (like best-of-three and best-of-five), the length of the match doesn’t necessarily tell us anything. Best-of-five matches are longer because of the rules, not because of any characteristics of the players.

The solution is to think in terms of probabilities. Given the length of a match, and the percentage of points won by each player, *what is the probability that the winner was the better player?*

To answer that question, we use the binomial distribution, and consider the likelihood that one player would win as many points as he did *if the players were equally matched*. If we flipped a fair coin 100 times, we would expect the number of heads to be around 50, but not that it will always be exactly 50. The binomial distribution tells us how often to expect any particular number of heads: 49, 50, or 51 are common, 53 is a bit less common, 55 even less so, 40 or 60 quite uncommon, as so on. For any number of heads, there’s some probability that it is entirely due to chance, and some probability that it occurs because the coin is biased.

Here’s how that relates to a tennis match. We start the match pretending that we know nothing about the players, assuming that they are equal. The number of points is analogous to the number of coin flips–the more points, the more likely the player who wins the most is really better. The number of points won by the victor corresponds to the number of heads. If the winner claims 60% of points, we can be pretty sure that he really is better, just as a tally of 60% heads in 100 or more flips would indicate that the coin is probably biased.

**More than just 59%**

The binomial distribution helps us convert those intuitions into probabilities. Let’s look at an example. The 2019 Roland Garros final was a fairly one-sided affair. Rafael Nadal took the title, winning 58.6% of total points played (116 of 198) over Dominic Thiem, despite dropping the second set. If Nadal and Thiem were equally matched, the probability that Nadal would win so many points is barely 1%. Thus, we can say that there is a 99% probability that Nadal was–on the day, in those conditions, and so on–the better player.

No surprises there, and there shouldn’t be. Things get more interesting when we alter the length of the match. The two other 2019 ATP finals in which one player won about 58.6% of points were both claimed by Djokovic. In Paris, he won 58.7% of points (61 of 104) against Denis Shapovalov, and in Tokyo, he accounted for 58.3% (56 of 96) in his defeat of John Millman. Because they were best-of-three instead of best-of-five, those victories took about half as long as Nadal’s, so our confidence that Djokovic was the better player–while still high!–shouldn’t be quite as close to 100%. The binomial distribution says that those likelihoods are 95% and 94%, respectively.

The winner of the average tour-level ATP match in 2019 won 55% of total points–the sort of number that sounds close, even as attentive fans know it really isn’t. When we convert every match result into a probability, the average likelihood that the winner was the better player is 80%. The latter number not only makes more intuitive sense–fewer results are clustered in the mid 50s, with numbers spread out from 15% to 100%–but it considers the length of the match, something that old-fashioned total-points-won ignores.

**Why does this matter?**

You might reasonably think that anyone who cared about quantifying match results already has these intuitions. You already know that 55% is a tidy win, 60% is an easy one, and that the length of the match means those numbers should be treated differently depending on context. Ranking points and prize money are awarded without consideration of this sort of trivia, so what’s the point of looking for an alternative?

I find this potentially valuable as a way to represent *margin of victory*. It seems logical that any player rating system–such as my Elo ratings–should incorporate margin of victory, because it’s tougher to execute a blowout than it is a narrow win. Put another way, someone who wins 59% of points against Thiem is probably better than someone who wins 51% of points against Thiem, and it would make sense for ratings to reflect that.

Some ratings already incorporate margin of victory, including the one introduced recently by Martin Ingram, which I discussed with him on a recent podcast. But many systems–again, including my Elo ratings–do not. Over the years, I’ve tested all sorts of potential ways to incorporate margin of victory, and have not found any way to consistently improve the predictiveness of the ratings. Maybe this is the one that will work.

**Leverage and lottery matches**

I’ve already hinted at one limitation to this approach, one that affects most other margin-of-victory metrics. Djokovic won only 48.3% of points in the 2019 Wimbledon final, a match he managed to win by coming up big in more important moments than Federer did. Recasting margin of victory in terms of probabilities gives us more 80% results than 55% results, but it also gives us more 25% results than 48% results. According to this approach, there is only a 24% chance that Djokovic was the better player that day. While that’s a defensible position–remember the 218 to 204 point gap–it’s also a bit uncomfortable.

Using the binomial distribution as I’ve described above, we completely ignore leverage, the notion that some points are more valuable than others. While most players aren’t consistently good or bad in high-leverage situations, many matches are decided entirely by performance in those key moments.

One solution would be to incorporate my concept of Leverage Ratio, which compares the importance of the points won by each player. I’ve further combined Leverage Ratio with Dominance Ratio, a metric closely related to total points won, into a single number I call DR+, or adjusted Dominance Ratio. It’s possible to win a match with a DR below 1.0, which means winning fewer return points than your opponent did, an occurrence that often occurs when total points won is below 50%. But when DR is adjusted for leverage, it’s extremely uncommon for a match winner to end up with a DR+ below 1.0. Djokovic’s DR in the Wimbledon final was 0.87, and his DR+ was 0.97, one of the very few instances in which a winner’s adjusted figure stayed below 1.0.

It would be impossible to fix the binomial distribution approach in the same way I’ve “fixed” DR. We can’t simply multiply 65%, or 80%, or whatever, by Leverage Ratio, and expect to get a sensible result. We might not even be interested in such an approach. Calculating Leverage Ratio requires access to a point-by-point log of the match–not to mention a hefty chunk of win-probability code–which makes it extremely time consuming to compute, even when the necessary data is available.

For now, leverage isn’t something we can fix. It is only something that we can be aware of, as we spot confusing margin-of-victory figures like Djokovic’s 24% from the Wimbledon final.

**Rethinking, fast and slow**

As with many of the metrics I devise, I don’t really expect wide adoption. If the best application of this approach is to create a component that improves Elo ratings, then that’s a useful step forward, even if it goes no further.

The broader goal is to create metrics that incorporate more of our intuitions. Just because we’ve grown accustomed to the quirks of the tennis scoring system, a universe in which 52% is close and 54% is not, doesn’t mean we can’t do better. Thinking in terms of probabilities takes more effort, but it almost always nets more insight.

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