Category: History

Are You There, Margaret? It’s Me, Serena

As I write this, Serena Williams is two matches away from winning her 24th grand slam. She’s been stuck on 23 since early 2017, which must be frustrating, since the all-time record is 24. Serena already holds the open-era record (for titles since 1968), one ahead of Steffi Graf’s 22. But Margaret Court is the leader across all eras, with 24 major championships between 1960 and 1973.

Williams is, of course, one of the greatest players of all time. Maybe the greatest. Court is also in the conversation, along with other luminaries such as Graf, Martina Navratilova, and Chris Evert. Cross-era comparisons in tennis are extremely difficult, because nearly everything about the game has changed. Serena’s technique, training, equipment, and tour schedule–not to mention wealth and celebrity status!–would all be extremely foreign to a 1960s or 70s superstar such as Court.

The challenge of cross-era comparisons hasn’t stopped fans from expressing opinions about where Williams should stand on the all-time leaderboard. Regardless of whose trophy cabinet numbers 23 or 24, Serena supporters tend to rely on three main arguments:

  1. The level of competition is way higher now than it was back then.
  2. Court won the Australian Open 11 times, back when it was the weakest of the four majors.
  3. Court is an obnoxious blowhard whose opinions are unacceptable.

Number one is probably true, but if we’re going to attempt cross-era comparisons, I think the only valid way to do so is to treat all eras as equal. We’ll never know how Williams would have fared with a wooden racket, or how Court’s body would’ve responded to today’s more physical game. You can make a logical case that today’s players are simply better than those of a couple generations ago, who were better than the ones before them, and so on. But the very idea of a “greatest of all time” implies something different than the “greatest of all time measured by today’s standards,” so we’re going to treat all eras as equal.

Number three is also popular, but my database isn’t able to shine much light on that line of argument.

That leaves number two, the relative weakness of the Australian Open.

Aussie ease

Court won the Australian Open 11 times, more than any other woman has claimed a single major title. In itself, that’s not a negative. Nobody counts it against Rafael Nadal that he’s won the French Open 12 times. But in the amateur era–and for some years after tennis went fully professional–the Australian Open wasn’t a mandatory stop for the best players in the world. It was a long trip, and it hadn’t yet gained the prestige that it holds today.

Thus, it’s fair to conclude that Court’s 1963 Wimbledon title was a more noteworthy accomplishment than her trophy 1963 Australian Championships. Most of us would agree that we should discount those Australian Opens. But by how much?

Difficulty-adjusted slam titles

In the past, I’ve compared men’s greatest-of-all-time candidates by major titles, adjusted for the level of competition. In the modern game, the field is almost exactly the same from one major to the next, but the draw can make one tournament considerably more difficult to win than another. The same technique allows us to compare draw difficulty and field quality for tournaments from the 1970s when both varied. For instance, the difficulty of Court’s path to the 1973 US Open title rated as average, in line with many of Williams’s title paths. But her 1973 Australian crown was only two-thirds as difficult–one of the easiest paths to a major title in the open era.

It’s no accident that I’m using Court’s last few major titles as examples. By analyzing performances from the 1970s, we’re pushing up against the edge of the weakness of historical tennis data. It’s well-nigh impossible to estimate the exact difficulty level of most of Court’s titles, because so little data is available from the amateur era. Instead, we’ll need to approximate using the limited information we have.

My difficulty adjustments rely on Elo ratings, which I have calculated as far back as 1972. (We have fairly complete results back to 1970 or so, but it takes a bit of time to amass a decent sample of match results for each player and for ratings to stabilize.) Let’s look at the relative difficulty of the four grand slams in the first five possible years, 1972-76:

Major            Difficulty  
Australian Open        0.60  
French Open            0.54  
Wimbledon              0.99  
US Open                0.85

The average major title, 1972-present, rates 1.0, with more difficult paths earning higher numbers. The fields weren’t as deep in the 1970s as they are now, so the typical path to a slam title then was lower than 1.0. In this first five-year period, we see that Wimbledon was in line with the historical average, the US Open was a bit easier, and the other two quarters of the grand slam were considerably less challenging. If we follow my suggestion above, to treat all eras as equal–except for the weakness of the Australian draws–we need to normalize these difficulties so that the other three slams average 1.0:

Major            Difficulty  
Australian Open        0.76  
French Open            0.68
Wimbledon              1.25  
US Open                1.07

Extrapolating backwards

We don’t know much about the field quality of the Australian majors in Court’s prime. For lack of a better option, then, we’ll use the 1972-76 average, since that’s as close as we can get. These probably overstate the quality of the Australian draws relative to the other slams, but if we’re inching toward calling Serena the all-time leader at Court’s expense, we should make conservative assumptions, to give us more confidence in our end result.

Here’s what happens to Court’s career totals if we apply the normalized adjustments:

Major            Difficulty  Slams  Adj Slams  
Australian Open        0.76     11        8.3  
French Open            0.68      5        3.4  
Wimbledon              1.25      3        3.7  
US Open                1.07      5        5.4  
Total                           24       20.8

The same process–adjusting each slam for difficulty, and normalizing for era–makes milder tweaks to Williams’s and Graf’s totals. Serena ends up with 23.3, and Graf with 21.9. Neither is enough to give us reason to change how we view those players’ accomplishments. And both are better than Court’s modified tally.

The small herd of GOATs

Remember that this is not an era adjustment. To the contrary, this calculation is based on the simplifying assumption that all eras are equal, except for the fact that for many years, some of the best players didn’t travel to Australia, making that major easier to win than the others.

These numbers also–obviously!–don’t tell us that Court wasn’t one of the best ever. Even if she had skipped her home slam, she still would’ve retired with 13 majors, plus a pile of doubles grand slam trophies and a long list of other career accomplishments. If Australia were less geographically remote, she probably wouldn’t have won those eleven titles–but she may well have won eight.

For all of Court’s accomplishments, she loses her top spot on the sport’s most hallowed list once we account for the weakness of the early Australian Open draws. At the very least, she falls behind Williams and Graf. Remember that my adjustments are conservative ones, so if we collect more data and discover that we should more aggressively discount her 1960’s Australian titles, her resulting total might leave her closer to 18, tied with Evert and Navratilova.

Serena may never equal or beat Court’s 24 titles. But even if she retires with 23, the modern level of competition–which showed up at every major, every year–means that she already deserves her place atop the leaderboard.

Podcast Episode 71: An Analytical Approach to the Tennis Hall of Fame

Episode 71 of the Tennis Abstract Podcast, features guest co-host Jeff McFarland, the man behind Hidden Game of Tennis. You may remember Jeff from his previous appearance on episode 52. Following this year’s Hall of Fame induction ceremony in Newport, we take an deep dive into the tennis institution, looking at who deserves to be there, who doesn’t, and how we ought to decide.

Much of our conversation stems from Jeff’s attempts to quantify career accomplishment, including Transformed Wins, men’s Championship Shares, and women’s Championship Shares. We discuss whether the Hall should be big or small, whether the grand slams should be as important as they seem to be, and how to handle greatness on the doubles court.

Thanks for listening!

(Note: this week’s episode is about 68 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.

Introducing Elo Ratings for Mixed Doubles

Scroll down for Wimbledon updates, including a forecast for the title match.

With Andy Murray and Serena Williams pairing up in this year’s Wimbledon mixed doubles event, more eyes than ever are on tournament’s only mixed-gender draw. Mixed doubles is played just four times a year (plus the Olympics, the occasional exhibition, and the late Hopman Cup), so most partnerships are temporary, and it’s tough to get a sense of who is particularly good in the dual-gender format.

That’s where math comes into play. Over the last few years, I’ve deployed a variation of the Elo rating algorithm for men’s doubles. It treats each team as the average of the two members, and after every match, it adjusts each player’s rating based on the result and the quality of the opponent. Doubles Elo–D-Lo–is even better suited for mixed than for single-gender formats, because players rarely stick with the same partner. The main drawback of D-Lo for men’s or women’s doubles is that it doesn’t help us tease out the individual contributions of long-time teams such as Bob and Mike Bryan. By contrast, mixed doubles draws often look like a game of musical chairs from one major to the next.

The rating game

Let’s jump right in. The Wimbledon mixed doubles draw consists of 56 teams. Here are the 10 highest-rated of those 112 players, as of the start of the fortnight:

Rank  Player                 XD-Lo  
1     Venus Williams          1855  
2     Serena Williams         1847  
3     Bethanie Mattek-Sands   1834  
4     Jamie Murray            1809  
5     Ivan Dodig              1793  
6     Latisha Chan            1785  
7     Bruno Soares            1776  
8     Leander Paes            1771  
9     Heather Watson          1770  
10    Gabriela Dabrowski      1760

Serena and Venus Williams require a bit of an asterisk, since both are playing mixed for the first time after a long break. Venus last played at the 2016 Olympics, and Serena last competed in mixed at the 2012 French Open. Maybe they’re rusty. My XD-Lo algorithm doesn’t include any kind of adjustment for injuries or other layoffs, so it’s possible that we should expect them to perform at a lower level. On the other hand, they are among the greatest doubles players of all time, and players tend to age gracefully in doubles. Venus lost her opening match, but perhaps we should blame that on Francis Tiafoe (XD-Lo: 1,494). The sisters will probably trade places at the top of the list once Wimbledon results are incorporated.

Murray’s rating is a decent but more pedestrian 1,648, so Murray/Williams is not the best team in the field. But they’re close. The strongest pair is Jamie Murray and Bethanie Mattek Sands–3rd and 4th on the list above–followed by Ivan Dodig and Latisha Chan, 5th and 6th on the individual list. Due to the vagaries of ATP and WTA doubles rankings and the resulting seedings, Dodig/Chan entered the event as the narrow favorites, because they got a first-round bye and Murray/Mattek-Sands did not.

Here are the top ten teams in the draw:

Rank  Team                                XD-Lo  
1     Bethanie Mattek-Sands/Jamie Murray   1822  
2     Ivan Dodig/Latisha Chan              1789  
3     Bruno Soares/Nicole Melichar         1762  
4     Serena Williams/Andy Murray          1748  
5     Gabriela Dabrowski/Mate Pavic        1734  
6     Leander Paes/Samantha Stosur         1731  
7     Heather Watson/Henri Kontinen        1708  
8     Venus Williams/Frances Tiafoe        1674  
9     Abigail Spears/Marcelo Demoliner     1653  
10    Neal Skupski/Chan Hao-ching          1634

The top five have survived (though Murray/Mattek-Sands and Pavic/Dabrowski will complete their second-round match this afternoon, leaving only four), and of the last 18 teams standing, only one other one–John Peers and Shuai Zhang–is rated above 1,600.

Forecasting SerAndy

Using my ratings, Murray/Williams entered the tournament with a 9.8% chance of winning. That made them fourth favorite, behind Dodig/Chan (17.1%), Murray/Mattek-Sands (16.3%), and the big-serving duo of Bruno Soares and Nicole Melichar (14.5%). I’ll update the forecast this evening, when the second round is finally complete.

Murray/Williams’s second-round match is against Fabrice Martin and Racquel Atawo. They are both excellent doubles players, though neither has excelled in mixed. Atawo, especially, has struggled. Her XD-Lo is 1,304, the third-lowest of anyone who has entered a mixed draw since 2012. (Shuai Peng is rated 1,268, and Marc Lopez owns last place with 1,252.) A player with no results at all enters the system with 1,500 points, so falling to 1,300 requires a lot of losing. The combined ratings translate into a 89% chance of a Murray/Williams victory.

The challenge comes in the third round. Soares/Melichar are the top seed, and they have already advanced to the round of 16, awaiting the winner of Murray/Williams and Martin/Atawo. Thus two of of the top four teams will likely play for a place in the quarter-finals, with Soares/Melichar holding a narrow, 52% edge.

Historical peaks

Generating these current ratings required amassing a lot of data, so it would be a waste to ignore the history of the mixed doubles format. Here are the top 25 female mixed doubles players, ranked by their peak XD-Lo ratings:

Rank  Player                   Peak  
1     Billie Jean King         2043  
2     Greer Stevens            2035  
3     Margaret Court           2015  
4     Rosie Casals             2000  
5     Martina Navratilova      1998  
6     Helena Sukova            1991  
7     Anne Smith               1989  
8     Betty Stove              1985  
9     Jana Novotna             1977  
10    Martina Hingis           1964  
11    Wendy Turnbull           1956  
12    Kathy Jordan             1948  
13    Elizabeth Smylie         1947  
14    Arantxa Sanchez Vicario  1946  
15    Serena Williams          1942  
16    Venus Williams           1937  
17    Francoise Durr           1934  
18    Jo Durie                 1929  
19    Kristina Mladenovic      1922  
20    Zina Garrison            1901  
21    Samantha Stosur          1898  
22    Larisa Neiland           1891  
23    Lindsay Davenport        1888  
24    Victoria Azarenka        1887  
25    Natasha Zvereva          1886

Venus really can’t catch a break. She’s one of the best players of all time, and Serena is always just a little bit better.

And the top 25 men:

Rank  Player               Peak XD-Lo  
1     Owen Davidson              2043  
2     Bob Hewitt                 2042  
3     Marty Riessen              2016  
4     Todd Woodbridge            2000  
5     Frew McMillan              1999  
6     Kevin Curren               1997  
7     Jim Pugh                   1995  
8     Ilie Nastase               1975  
9     Tony Roche                 1962  
10    Bob Bryan                  1949  
11    Rick Leach                 1938  
12    Mahesh Bhupathi            1933  
13    Mark Woodforde             1929  
14    Justin Gimelstob           1929  
15    Max Mirnyi                 1926  
16    John Lloyd                 1922  
17    Emilio Sanchez             1918  
18    Ken Flach                  1909  
19    Jeremy Bates               1908  
20    John Fitzgerald            1906  
21    Cyril Suk                  1902  
22    Wayne Black                1889  
23    Dick Stockton              1881  
24    Jean-Claude Barclay        1879  
25    Mike Bryan                 1875

Owen Davidson won eight mixed slams with Billie Jean King, plus three more with other partners. Bob Hewitt won six, spanning 18 years from 1961 to 1979. (We can’t erase his accomplishments from the history books, but any mention of Hewitt comes with the caveat that he is a convicted rapist who has since been expelled from the International Tennis Hall of Fame.)

It is interesting to see two famous pairs represented on the men’s list. Bob Bryan ranks 10th to Mike’s 25th, and Todd Woodbridge comes in 4th to Mark Woodforde’s 13th. We probably can’t conclude from mixed doubles results that one member of the team was a superior men’s doubles player, but it is one of the few data points that allows us to compare these partners.

The ignominious Spaniards

Finally, I can’t spend this much time with mixed doubles ratings without revisiting the case of David Marrero. You may recall the 2016 Australian Open, when Marrero’s first-round match with Lara Arruabarrena triggered “suspicious betting patterns.” As I wrote at the time, the most suspicious thing about it was that Marrero–who was terrible at mixed doubles and admitted that he played differently with a woman across the net–could still find a partner.

He entered that match with an XD-Lo rating of 1,349–the worst of any man in the draw, though Anastasia Pavlyuchenkova was a few points lower–and left it at 1,342. He played his last mixed doubles match at Wimbledon that year, and–surprise!–he lost. One hopes he’ll stick to men’s doubles for the remainder of his career, sticking with an XD-Lo rating of 1,326.

Marrero’s only saving grace is that he’s better than his compatriot Marc Lopez. Lopez has been active in mixed doubles more recently, entering the US Open last year with Arruabarrena. After that loss, he fell to his current rating of 1,252, the lowest mark recorded in the Open Era.

Fortunately for us, this year’s Wimbledon draw includes both Williams sisters, both Murray brothers, a healthy Mattek-Sands … and very few players as helpless in the mixed doubles format as Marrero or Lopez.

—

Update: Murray/Williams won their second-rounder, setting up the final 16. Mixed doubles isn’t the top scheduling priority, so it didn’t exactly work that way–by the time Muzzerena advanced, two other teams had already secured places in the quarter-finals. Ignoring those for the moment, here is the last-16 forecast:

Team                      QF     SF      F      W  
Soares/Melichar        52.5%  44.5%  33.2%  18.8%  
Murray/Williams        47.5%  39.7%  29.0%  15.8%  
Middelkoop/Yang        55.5%   9.5%   3.6%   0.8%  
Daniell/Brady          44.5%   6.3%   2.1%   0.4%  
Peers/Zhang            61.6%  36.9%  13.8%   5.2%  
Lindstedt/Ostapenko    38.4%  18.7%   5.2%   1.5%  
Skugor/Olaru           56.2%  26.3%   8.3%   2.6%  
Mektic/Rosolska        43.8%  18.0%   4.8%   1.3%  
                                                   
Player                    QF     SF      F      W  
Koolhof/Peschke        42.6%  10.1%   2.4%   0.6%  
Qureshi/Kichenok       57.4%  16.7%   4.9%   1.5%  
Sitak/Siegemund        27.4%  16.0%   5.3%   1.8%  
Pavic/Dabrowski        72.6%  57.2%  30.8%  17.5%  
Dodig/Chan             75.9%  64.6%  44.1%  28.1%  
Roger-Vasselin/Klepac  24.1%  15.5%   6.6%   2.5%  
Hoyt/Silva             54.1%  11.3%   3.5%   1.0%  
Vliegen/Zheng          45.9%   8.6%   2.5%   0.6%

The two teams already in the quarters are Skugor/Olaru and Hoyt/Silva. Since both of their matches were close to 50/50, you can roughly double their odds, and the odds of the other teams are only a tiny bit less. The remaining six third-round matches are scheduled for Wednesday, and I’ll try to update again when those are in the books.

Update 2: Murray/Williams are out, so the number of people interested in mixed doubles has fallen from double digits back to the typical level of single digits. The departure of the singles stars also leaves one clear favorite in each half. Here is the updated forecast:

Team                    SF      F      W  
Soares/Melichar      83.4%  64.3%  36.4%  
Middelkoop/Yang      16.6%   6.7%   1.5%  
Lindstedt/Ostapenko  46.0%  12.6%   3.7%  
Skugor/Olaru         54.0%  16.4%   5.2%  
Koolhof/Peschke      37.5%   7.3%   1.8%  
Sitak/Siegemund      62.5%  17.2%   6.0%  
Dodig/Chan           84.4%  68.3%  43.3%  
Hoyt/Silva           15.6%   7.2%   2.0%

All four quarter-finals are scheduled for Thursday, so I’ll post another update tomorrow evening.

Update 3: We’re down to four teams. Of the Elo favorites in the quarter-finals, only Dodig/Chan survived, leaving them as the overwhelming pick to take the title. Here’s the full forecast:

Team                     F      W  
Middelkoop/Yang      42.3%   8.2%  
Lindstedt/Ostapenko  57.7%  14.1%  
Koolhof/Peschke      14.1%   6.3%  
Dodig/Chan           85.9%  71.4%

Update 4: Both favorites won in Friday’s semi-finals, so we’ve got a final between Lindstedt/Ostapenko and Dodig/Chan. The first team didn’t get an opening-round bye, so they won one more match to get here. They also have a better story, since Ostapenko keeps hitting her partner in the head. Dodig/Chan entered as the 8th seeds, despite being the second-best team according to XD-Lo.

Consequently, Dodig/Chan get the edge here, with an 81% of winning the 2019 Wimbledon Mixed Doubles title.

Net Play Has Declined, But This Isn’t Why

Italian translation at settesei.it

Wimbledon is here, so it’s time for another cycle of media commentary about the demise of net play, especially the serve-and-volley. The New York Times published a piece by Joel Drucker last week that covered this familiar territory, cataloguing various reasons why the game has changed. Racket and string technology, along with tweaks to the All England Club playing surface, are rightfully on the list.

But the first reason Drucker gives is the rise of the two-handed backhand and, by extension, the threat posed by players with weapons on both sides:

In May 1999, 43 of the top 100 male players in the world hit their backhands with one hand. As of June 2019, there were 15. According to Mark Kovacs, a sports science consultant and tennis coach, “Most players used to have a weaker side, usually the backhand. And the two-handed backhand changed that completely. It doesn’t give you a spot you can hit to.”

I’m more interested in the “weaker side” argument than the fortunes of the one-handed and two-handed backhands. Many players who still use one-handers, such as Stan Wawrinka, would rightly bristle at a claim that their shots are weak. In terms of effectiveness, the contemporary one-handed shot might have more in common with a two-hander of old than the all-slice, only-defensive backhand favored by many pros in the 1970s and 1980s.

Both sides, now

The “weaker side” argument can be slightly rephrased into a research question: For contemporary players, is there a smaller gap between forehand effectiveness and backhand effectiveness than there used to be?

To answer that, we need a working definition of “effectiveness.” Long-time readers may recall a stat of mine called “potency,” as in “backhand potency” (BHP) or “forehand potency” (FHP). It’s a simple stat, using data derived from the shot-by-shot records of the Match Charting Project, calculated as follows:

BHP approximates the number of points whose outcomes were affected by the backhand: add one point for a winner or an opponent’s forced error, subtract one for an unforced error, add a half-point for a backhand that set up a winner or opponent’s error on the following shot, and subtract a half-point for a backhand that set up a winning shot from the opponent.

The same procedure applies to forehand potency and slice potency. The weights–plus one for some shots, plus a half point for others, and so on–are not precise. But the results generally jibe with intuition. Across 3,000 charted ATP matches, an average player’s results from a single match are:

  • Forehand potency (FHP): +6.5
  • Backhand potency (BHP): +0.8
  • Slice potency (SLP): -1.3
  • Backhand side potency (BSP): -0.5

The first three stats isolate single shots, while the final one combines BHP and SLP into a single “backhand side” metric. All of these exclude net shots, and since forehand slices are so rare, I’ve left those out of today’s discussion as well.

The forehand reigns

The numbers above shouldn’t come as a surprise. The average ATP player has a stronger forehand than backhand, regardless of how many hands are on the racket for the latter shot. Novak Djokovic possesses one of the best backhands in the history of sport, but the gap between his FHP and BSP numbers is greater than average: +11.3 per match for the forehand, and +2.5 for the backhand, resulting in a difference of 8.8. Even a backhand master reaps more rewards on his other side.

The Match Charting Project has at least three matches worth of data for 299 different men across several generations, spanning from Vitas Gerulaitis to Jannik Sinner. Only 30 of them–about one in ten–gain more points on their backhand than on their forehands, and for half of that minority, the difference is less than a single point. It’s a diverse group, including Pat Cash, Jimmy Connors, Guillermo Coria, Ernests Gulbis, Daniil Medvedev, and Benoit Paire. This mixed-bag minority doesn’t provide much evidence to settle the question.

Proponents of the “weaker side” argument often point to the arrival of Lleyton Hewitt as a turning point between the net-play-was-feasible era and the approach-at-your-peril era. Others might point to Andre Agassi. As it turns out, both of these figures are surprisingly average.

The Match Charting Project has extensive records on both men. Hewitt’s forehand was worth +10.0 per match, while his backhand and slice combined for +2.9. That’s a difference of 7.1, a bit greater than average, though less than Djokovic’s. Agassi’s FHP was good for +13.0 per match, compared to a BSP of +6.8. That’s a difference of 6.2, even closer to the mean than Hewitt. Ironically, that gap is almost identical to that of Pete Sampras, whose FHP of +6.3 and BSP of -0.1 were equally spaced, even though his groundstrokes were considerably less effective.

Comparing eras

We can’t answer a general question about trends over time simply by calculating shot potencies for individual players, no matter how pivotal. Instead, we need to look at the whole population.

First, a quick note about our data: The Match Charting Project is extremely heavily weighted toward current players. Our sample of 300 players consists of only 40 whose careers were mostly or entirely in the 20th century, and 30 more whose matches mostly took place in the first decade of this century. Thus, the averages mentioned above are skewed toward the 2010s. That said, the 70 “older” players in the sample are the most prominent–the guys who played in major finals and semi-finals, and Masters finals. If there has been a marked trend across decades, those players should help us reveal it.

The earlier players in our sample are, in fact, quite similar to the contemporary ones. I ranked the 299 players by the absolute difference between their FHP and their BSP, with the most balanced player ranked 1, and the least balanced ranked 299. I looked at two subgroups: the 52 oldest players in the sample, most of whose careers were fading out when Hewitt arrived; and the 78 players with the most recent matches in the sample.

  • Oldest — Average rank: 143, Average (FHP – BSP): 5.7
  • Most recent — Average rank: 155, Average (FHP – BSP): 6.5

These numbers do not indicate that players used to have a weak side, and now they don’t. They don’t really reflect any trend at all. The difference between forehand effectiveness and backhand side effectiveness has barely changed over several decades.

As further evidence, here is a selection of players who are both well-represented in the Match Charting Project data and noteworthy representatives of their eras. They’re listed in approximate chronological order. Each of the shot-potency numbers is given on a per-match basis, and the final column (“Diff”) is the difference between FHP and BSP–the gap between each player’s forehand and backhand sides.

Player              FHP    BHP   SLP   BSP  Diff  
Bjorn Borg          12.9  11.5  -0.5  11.0   2.0  
Jimmy Connors       6.5    9.1  -0.3   8.9  -2.4  
John McEnroe        2.0   -0.4  -2.1  -2.4   4.4  
Mats Wilander       7.2    6.8  -0.5   6.3   0.9  
Ivan Lendl          10.3   4.0   0.6   4.6   5.7  
Stefan Edberg       1.9    1.8  -1.1   0.7   1.1  
Boris Becker        5.9    2.1  -1.5   0.7   5.2  
Jim Courier         13.3   4.2  -0.3   3.9   9.4  
Michael Stich       2.0    2.0  -3.4  -1.4   3.4  
Michael Chang       9.7    5.0  -0.6   4.4   5.3  
                                                  
Player              FHP    BHP   SLP   BSP  Diff  
Thomas Muster       18.4   2.2  -1.1   1.1  17.3  
Pete Sampras        6.3    0.7  -0.7  -0.1   6.4  
Andre Agassi        13.0   7.2  -0.5   6.8   6.3  
Patrick Rafter      3.5    0.5  -1.6  -1.1   4.6  
Carlos Moya         9.8   -0.9  -1.4  -2.3  12.1  
Lleyton Hewitt      10.0   3.5  -0.6   2.9   7.1  
Guillermo Coria     4.7    6.3  -1.2   5.2  -0.5  
David Nalbandian    8.8    5.6  -1.7   3.9   4.9  
Nikolay Davydenko   7.2    4.4  -1.2   3.2   4.0  
Roger Federer       10.0   0.2  -0.4  -0.3  10.2  
                                                  
Player              FHP    BHP   SLP   BSP  Diff  
Rafael Nadal        15.3   2.6  -1.0   1.6  13.7  
Andy Murray         7.2    2.9  -1.8   1.1   6.1  
Novak Djokovic      11.3   3.4  -0.8   2.5   8.8  
Richard Gasquet     1.9    1.4  -1.4   0.0   1.9  
Stan Wawrinka       6.2    0.5  -1.7  -1.2   7.3  
Kei Nishikori       5.4    3.8  -1.1   2.7   2.8  
Dominic Thiem       9.3   -0.1  -1.6  -1.7  11.0  
Alexander Zverev    3.6    4.2  -1.1   3.0   0.6  
Stefanos Tsitsipas  8.3   -0.9  -2.2  -3.0  11.4  
Daniil Medvedev     1.6    3.3  -1.4   1.9  -0.3

Not weaker, but weak

These numbers cast a lot of doubt on the “weaker side” hypothesis, that it used to be easier to move forward by approaching an opponent’s less dangerous wing.

Instead, what has probably happened is that for the typical player, both sides got stronger. As a result, the weaker side was no longer flimsy enough to make approaching the net a profitable strategy. Even players with weaker-than-average backhands are now able to hit powerful topspin passing shots. This is essentially the racket-and-string-technology argument, and it seems to me to be the most valid.

There’s no question that tennis has drastically changed in the last few decades. But the conventional explanations for those trends don’t always hold up under scrutiny. In this case, while volleys have been reduced to a vestigial part of the singles game, groundstrokes–on both sides–have only gotten better.

Rafael Nadal and the Greatest Single-Tournament Performances

Italian translation at settesei.it

In the last two weeks, Rafael Nadal recorded his 11th titles in both Monte Carlo and Barcelona. His career records at those two events, along with his ten Roland Garros championships, reflect a level of dominance never before seen on a single surface. They have to be considered among the greatest achievements in tennis history, and perhaps in all of sport.

The tennis fan in me is content to speculate about whether anyone will ever stop him. The analyst wants to dig deeper: Has Nadal’s performance at one of the tournaments been even better than the rest? How do these single-event records compare to other exploits, such as Roger Federer’s trophy haul at Wimbledon, or Bjorn Borg’s nearly-undefeated career at the French Open?

Barcelona by the numbers

Let’s start with Barcelona. Since 2005–we’ll ignore his 2003 appearance as a 16-year-old wild card–he has played the event 13 times, winning 11 of them. That’s a won-loss record of 57-2.

Usually, I would calculate the probability of a player winning so many tournaments in that many chances, then come up with a tiny percentage that would represent his odds of achieving such a feat. That would miss the mark here. Instead, I want to look at the problem from the opposite perspective: In order to win so many titles, how good must Nadal be?

We already know that Rafa is the best of all time on clay, in general. Using the Elo rating system, his peak surface-specific rating–that is, Elo calculated using only results on clay courts–is over 2,500, better than anyone else on clay … or anyone else on any surface. (Nadal’s current clay-specific Elo is around 2,400, and the closest things he has to rivals on the surface right now, Dominic Thiem and Kei Nishikori, sit at about 2,190 and 2,150. Stefanos Tsitsipas’s rating is 1865.) Since Rafa has posted his best results at these three events, it stands to reason that his tournament-specific levels are even higher.

Here, then, is the method we can use to figure that out. First, for each year he entered Barcelona, determine his path to the title. (For the 11 titles, that’s easy; for the other two, we use the players he would have faced had he kept winning.) Using each opponent’s clay court Elo rating at the time of the match, we can determine the odds that various hypothetical (and dominant) players would have progressed through the draw and won the title.

Here is Nadal’s path to the 2018 title, showing each player’s pre-match clay court Elo*, along with the odds that Rafa (given his own current rating) would beat him:

Round  Opponent                 Opp Elo  p(Rafa W)  
R32    Roberto Carballes Baena     1767      97.3%  
R16    Guillermo Garcia Lopez      1769      97.2%  
QF     Martin Klizan               1894      94.5%  
SF     David Goffin                2079      84.5%  
F      Stefanos Tsitsipas          1900      94.3%

* from this point on, the clay court Elos I use are 50/50 blends of clay-specific Elo–that is, a rating calculating only with clay court results–and overall Elo. The blended rating is the one that has proven best at predicting match outcomes. Nadal is the all-time leader in this category as well, with a 50/50 clay Elo that peaked around 2,510.

Given those five single-match probabilities, the odds that Nadal would win the tournament were just over 70%. That’s dominant, but it’s not 11-out-of-13 dominant.

What if Rafa were underrated by Elo, at least in Barcelona? Here is the probability that a player at various Elo ratings would have beaten the five opponents that he faced last week:

Clay Elo  p(2018 Title)  
2200              41.2%  
2250              50.4%  
2300              59.1%  
2350              66.9%  
2400              73.6%  
2450              79.3%  
2500              83.9%  
2550              87.6%  
2600              90.5%

It turns out that this year’s title path was one of the weakest since 2005. It is roughly equivalent to the players Nadal needed to defeat in 2006 (with Nicolas Almagro in the semis and Tommy Robredo in the final), and a bit tougher than last year’s route, which didn’t feature a top-50 player until Thiem in the final. The toughest was his hypothetical path in 2015, when he lost to Fabio Fognini in the second round. Had he progressed, he would have faced David Ferrer in the semis and Nishikori in the final.

Once we figure out the quality of Rafa’s opponents (and would-have-been opponents, for the two years he lost early), we can work out the odds that any player–given those paths–would have won the tournament each year.

If we assume that Rafa’s average level since 2005 is the same as his current level–a clay Elo of around 2,400–the odds that he would have won 11 Barcelona titles in 13 tries is 13.0%. We don’t have the luxury of replaying those 13 tournaments in a few thousand alternate universes, so it’s not entirely clear what to make of that number–was Rafa lucky? would he do it again, given the chance? is he actually way better than an Elo level of 2,400 in Barcelona?

I don’t know the answer to those questions; all we know is what happened. To compare (un)decimas (and related accomplishments by other players), we’re going to look at the Elo level that would have resulted in the achievement at least 50% of the time. In other words, how good would Nadal have to have been to give himself a 50/50 chance at winning 11 Barcelona titles in 13 tries?

At various clay Elo levels, here are the odds that Rafa would have completed the Barcelona undécima:

Clay Elo  p(11 of 13)  
2300             1.0%  
2350             4.6%  
2400            13.0%  
2450            28.0%  
2500            47.2%  
2550            64.2%  
2600            77.7%  
2650            87.3%  
2700            93.1%

Thus, a player with a clay Elo of about 2,505 would have had a 50% chance of matching Nadal’s feat at his home tournament. To put it another way: At this event, over a span of 14 years, he has played at a level roughly equal to his career peak which, incidentally, is the all-time best clay Elo rating ever achieved by an ATP player.

Comparing las (un)decimas

I hope that my method makes sense and seems like a reasonable way of quantifying a rare feat. Algorithm in hand, we can compare Nadal’s Barcelona record with his efforts in Monte Carlo and Paris.

Monte Carlo

Rafa has entered 14 times since 2005 (again, excluding his 2003 appearance) and won 11. That’s a bit less impressive than 11-of-13, but the competition level is much higher. Only last year’s tournament, in which the opposing finalist was Albert Ramos, is in the same league as most of the Barcelona draws.

Sure enough, the Monte Carlo undécima is lot more impressive. To have a 50% chance of winning 11 titles in 14 attempts, a player would need a clay Elo of about 2,595, almost 100 points higher than the comparable number for Barcelona, and well above the level any player has ever achieved, even at their peak.

Roland Garros

At the French Open, Nadal has entered 13 times, winning 10. The field is even more challenging than in Monte Carlo, but on the other hand, the five-set format gives a greater edge to favorites, lessening the chance of an underdog scoring an upset with two magical sets.

The Roland Garros 10-of-13 is not quite as eye-popping as the record at Monte Carlo. The clay Elo required to give a player a 50% chance of matching Nadal’s French Open feat is “only” around 2,570–still better than any player has ever attained, but a bit short of the comparable mark for Monte Carlo.

But wait … what about 2016? Rafa won two rounds and then withdrew from his third-rounder against Marcel Granollers. I don’t know whether that should count, but at least for argument’s sake, we should run the numbers without it, treating Nadal’s French Open record as 10 titles in 12 appearances, not 13. In that case, the clay Elo that would give a player a 50/50 shot at matching the record is 2,595–the same as the Monte Carlo number.

At the moment, Monte Carlo appears to be the tournament where Nadal has played his very best. With another French Open a few weeks away, though, that answer may be temporary.

Rafa vs other record holders

A few other players have racked up impressive totals at single events. Wikipedia has a convenient list, and a few accomplishments stand out: Federer’s tallies at Wimbledon, Basel, and Halle, Guillermo Vilas’s eight titles in Buenos Aires, and Borg’s six French Open titles in only eight appearances.

Let’s have a look at how they compare, ranked by the surface-specific Elo rating that would give a player a 50% chance of equaling the feat:

Player   Tourney          Wins  Apps  50% Elo  
Nadal    Monte Carlo        11    14     2595  
Nadal    French Open*       10    12     2595  
Nadal    French Open        10    13     2570  
Borg     French Open**       6     7     2550  
Nadal    Barcelona          11    13     2505  
Borg     French Open         6     8     2475  
Vilas    Buenos Aires***     8    10     2285  
Federer  Wimbledon           7    18     2285  
Federer  Halle               8    15     2205  
Federer  Basel               8    15     2180

* excluding 2016

** excluding 1973, when Borg was 16 years old, and lost in the fourth round

*** excluding 1969-71, both because Vilas was very young, and due to sketchy data

The only single-event achievement that ranks with Nadal’s is Borg’s record at Roland Garros–and even then, only when we don’t consider Borg’s loss there as a 16-year-old. Federer’s records in Wimbledon, Halle, and Basel are impressive, but fail to rate as highly because he has entered those tournaments so many times. Federer didn’t appear on tour ready to win everything on his chosen surface, the way Rafa did, and those early losses are part of the reason that his records at these tournaments are so low.

We never needed any numbers to know that Nadal’s accomplishments at his three favorite tournaments are among the best of all time. With these results, though, we can see just how dominant he has been, and how few achievements in tennis history can even compare. The scary thing: A month from now, I may need to come back and update this post with even more eye-popping numbers. The greatest show on clay courts isn’t over yet.

The Case for Novak Djokovic … and Roger Federer … and Rafael Nadal

Italian translation at settesei.it

By winning the US Open last weekend and increasing his career total to ten Grand Slams, Novak Djokovic has pushed himself even further into conversations about the greatest of all time. At the very least, his 2015 season is shaping up to be one of the best in tennis history.

A recent FiveThirtyEight article introduced Elo ratings into the debate, showing that Djokovic’s career peak–achieved earlier this year at the French Open–is the highest of anyone’s, just above 2007 Roger Federer and 1980 Bjorn Borg. In implementing my own Elo ratings, I’ve discovered just how close those peaks are.

Here are my results for the top 15 peaks of all time [1]:

Player                 Year   Elo  
Novak Djokovic         2015  2525  
Roger Federer          2007  2524  
Bjorn Borg             1980  2519  
John McEnroe           1985  2496  
Rafael Nadal           2013  2489  
Ivan Lendl             1986  2458  
Andy Murray            2009  2388  
Jimmy Connors          1979  2384  
Boris Becker           1990  2383  
Pete Sampras           1994  2376  
Andre Agassi           1995  2355  
Mats Wilander          1984  2355  
Juan Martin del Potro  2009  2352  
Stefan Edberg          1988  2346  
Guillermo Vilas        1978  2325

A one-point gap is effectively nothing: It means that peak Djokovic would have a 50.1% chance of beating peak Federer. The 35-point gap separating Novak from peak Rafael Nadal is considerably more meaningful, implying that the better player has a 55% chance of winning.

Surface-specific Elo

If we limit our scope to hard-court matches, Djokovic is still a very strong contender, but Fed’s 2007 peak is clearly the best of all time:

Player          Year  Hard Ct Elo  
Roger Federer   2007         2453  
Novak Djokovic  2014         2418  
Ivan Lendl      1989         2370  
Pete Sampras    1997         2356  
Rafael Nadal    2014         2342  
John McEnroe    1986         2332  
Andy Murray     2009         2330  
Andre Agassi    1995         2326  
Stefan Edberg   1987         2285  
Lleyton Hewitt  2002         2262

Ivan Lendl and Pete Sampras make much better showings on this list than on the overall ranking. Still, they are far behind Fed and Novak–the roughly 100-point difference between peak Fed and peak Pete is equivalent to a 64% probability that the higher-rated player would win.

On clay, I’ll give you three guesses who tops the list–and your first two guesses don’t count. It isn’t even close:

Player           Year  Clay Ct Elo  
Rafael Nadal     2009         2550  
Bjorn Borg       1982         2475  
Novak Djokovic   2015         2421  
Ivan Lendl       1988         2408  
Mats Wilander    1984         2386  
Roger Federer    2009         2343  
Jose Luis Clerc  1981         2318  
Guillermo Vilas  1982         2316  
Thomas Muster    1996         2313  
Jimmy Connors    1980         2307

Borg was great, but Nadal is in another league entirely. Though Djokovic has pushed Nadal out of many greatest-of-all-time debates–at least for the time being–there’s little doubt that Rafa is the greatest clay court player of all time, and likely the most dominant player in tennis history on any single surface.

Djokovic is well back of both Nadal and Borg, but in his favor, he’s the only player ranked in the top three for both major surfaces.

The survivor

As the second graph in the 538 article shows, Federer stands out as the greatest player of all time at his age. Most players have retired long before their 34th birthday, and even those who stick around aren’t usually contesting Grand Slam finals. In fact, Federer’s Elo rating of 2393 after his US Open semifinal win against Stanislas Wawrinka last week would rank as the sixth-highest peak of all time, behind Lendl and just ahead of Andy Murray.

Here are the top ten Elo peaks for players over 34:

Player         Age   34+ Elo  
Roger Federer  34.1     2393  
Jimmy Connors  34.1     2234  
Andre Agassi   35.3     2207  
Rod Laver      36.6     2207  
Ken Rosewall   37.4     2195  
Tommy Haas     35.3     2111  
Arthur Ashe    35.7     2107  
Ivan Lendl     34.1     2054  
Andres Gimeno  35.0     2035  
Mark Cox       34.0     2014

The 160-point gap between Federer and Jimmy Connors implies that 34-year-old Fed would win about 70% of the time against 34-year-old Connors. No one has ever sustained this level of play–or anything close to it–for this long.

At the risk of belaboring the point, similar arguments can be made for 33-year-old Fed, all the way to 30-year-old Fed. At almost any stage in the last four years, Federer has been better than any player in history at that age [2].  Djokovic has matched many of Roger’s career accomplishments so far, especially on clay, but it would be truly remarkable if he maintained a similar level of play through the end of the decade.

Current Elo ratings

While it’s not really germane to today’s subject, I’ve got the numbers, so let’s take a look at the current ATP Elo ratings. Since Elo is new to most tennis fans, I’ve included columns to indicate each player’s chances of beating Djokovic and of beating the current #10, Milos Raonic, based on their rating. As a general rule, a 100-point gap translates to a 64% chance of winning for the favorite, a 200-point gap implies 76%, and a 500-point gap is equivalent to 95%.

Rank  Player                  Elo  Vs #1  Vs #10  
1     Novak Djokovic         2511      -     91%  
2     Roger Federer          2386    33%     84%  
3     Andy Murray            2332    26%     79%  
4     Kei Nishikori          2256    19%     71%  
5     Rafael Nadal           2256    19%     71%  
6     Stan Wawrinka          2186    13%     62%  
7     David Ferrer           2159    12%     58%  
8     Tomas Berdych          2148    11%     56%  
9     Richard Gasquet        2128    10%     54%  
10    Milos Raonic           2103     9%       -  
                                                  
Rank  Player                  Elo  Vs #1  Vs #10  
11    Gael Monfils           2084     8%     47%  
12    Jo-Wilfried Tsonga     2083     8%     47%  
13    Marin Cilic            2081     8%     47%  
14    Kevin Anderson         2074     7%     46%  
15    John Isner             2035     6%     40%  
16    David Goffin           2027     6%     39%  
17    Grigor Dimitrov        2021     6%     38%  
18    Gilles Simon           2005     5%     36%  
19    Jack Sock              1994     5%     35%  
20    Roberto Bautista Agut  1986     5%     34%  
                                                  
Rank  Player                  Elo  Vs #1  Vs #10  
21    Philipp Kohlschreiber  1982     5%     33%  
22    Tommy Robredo          1963     4%     31%  
23    Feliciano Lopez        1955     4%     30%  
24    Nick Kyrgios           1951     4%     29%  
25    Ivo Karlovic           1949     4%     29%  
26    Jeremy Chardy          1940     4%     28%  
27    Alexandr Dolgopolov    1940     4%     28%  
28    Bernard Tomic          1936     4%     28%  
29    Fernando Verdasco      1932     3%     27%  
30    Fabio Fognini          1925     3%     26%

Continue reading The Case for Novak Djokovic … and Roger Federer … and Rafael Nadal

Event History Pages at Tennis Abstract

If you like tennis records and trivia, you’d better clear your calendar. I knew I was on to something when I kept getting distracted from my own project by all the cool stats it was spitting out.

The project: Event history pages at TennisAbstract.com. Think of them as almanacs for every stop on the ATP tour. For each tournament, you’ll find a chronological list of winners, finalists, and final scores. Then come the leaderboards–132 of them per tournament, at last count. That’s where the fun really begins.

In addition to the basics, like most matches won, most quarterfinal appearances, and the like, you’ll find tiebreak records, bagel records, the youngest titlists (and finalists, and more), the oldest titlists (and finalists, and more), and the lowest ranked titlists, finalists, and semifinalists.

Then come the match-level stats records (all links head to the Washington event’s page as an example). These are broken down into four categories:

  • Single-match records (combined): Longest and shortest matches, most aces, most breaks of serve, longest tiebreaks, and much more.
  • Single-match player records: Most aces by a single player, highest and lowest first-serve percentage, highest and lowest first-serve winning percentage, most break points earned and saved, and lots more.
  • Single-tournament player records: Marks set by players at a single year’s event, including most time spent on court, most points won, highest rate of points won, aces, double faults … you get the idea.
  • Event player records: Best all-time performances at the tournament over multiple years, including most of the same stat categories from the other sections.

Player names are linked to each guy’s own page, and years are linked to a page with each individual tournament’s results.

The links above all go to the Washington tournament’s page. Here are links to this week’s ATP events:

(I’d love to have equivalent WTA pages, and I hope to add them soon. It’ll take quite a bit more work, however, and without the 24-year history of matchstats that is available for ATP events, the resulting pages will be much less thorough.)

While I’ve put a ton of work into these this week, you’ll still probably some bugs. That’s one of the downsides of leaderboards–they have a knack for uncovering mistakes in the database. I’ve been able to add several checks to the process to avoid matches with obviously incorrect stats (e.g. impossibly short match durations), but I’m sure we’ll keep discovering more.

Enjoy!

Lleyton Hewitt and the Elusive Triple-Hundred

Lleyton Hewitt is within a whisker of qualifying for a very elite club–players who have won 100 matches on each of the three major tennis surfaces, hard, clay, and grass. He has 367 on hard, 120 on grass, and 98 on clay. If he manages to reach this milestone, he’ll be the last player to do so for a long time.

Roger Federer, of course, is already a member. Hewitt would become only the seventh, joining Fed, Jimmy Connors, John McEnroe, Boris Becker, John Alexander, and Stan Smith. Arthur Ashe and Stefan Edberg are close: both retired with 99 grass-court wins.

Typically, the grass-court threshold is the most difficult to reach, but that’s not the issue for Hewitt.  In fact, the Aussie is one of only 16 players in ATP history to win 100 or more matches on grass courts.

Federer has 123 career wins on grass, good for second of all time, behind Connors. Hewitt, at 120, is the only other active player even close.  Next on the active list is Andy Murray at 74, followed by Novak Djokovic, Mikhail Youzhny, and Tommy Haas, all tied at 53. Of the 80 players in ATP history who have won at least 50 matches on grass, 73 are retired.

Of the active players with 50 or more grass-court wins, only Hewitt and Murray have won more matches on grass than on clay. That’s all a long-winded way of saying, if someone’s going to reach the 100-win milestone on three surfaces, you wouldn’t expect them to need a few more wins on clay.

No other active players are anywhere near striking distance of the 3×100 mark. While Murray could reach 100 wins on grass with a few more good seasons, his clay win total lags far behind–on that surface, he only recently got to 50.  And as we’ve seen, no other active player has more than 53 career wins on grass. The extended grass-court season, starting next year, will help players like Djokovic, but it’s safe to say that Haas’s window has closed.

In an era that barely rewards grass-court specialists, Hewitt has put himself in position to join this elite group by performing at a very high level on the surface. It’s ironic, then, that he’ll cross into such rarefied territory with a win on red clay.

One Year of Heavy Topspin

A few weeks ago, a glance through my archives revealed that, today, HeavyTopspin.com is one year old!  We’ve come a long way in that time, pushing tennis research in new directions, getting advanced tennis stats in The Wall Street Journal, and more recently, launching TennisAbstract.com.

Thanks to everyone for reading, and thank you especially to those who comment, whether here on the blog, by email, or on Twitter.  Nods are due in particular to Rick Devereaux, Tom Welsh, Carl Bialik, and Eric from stevegtennis.com.  Slowly, analytical tennis research is getting more popular as well as more fruitful.

Here’s to an even better year two!

Bernoulli and Court Tennis

Italian translation at settesei.it

As if you needed more proof that there’s nothing new under the sun.

Most of us are fairly new to the mathematical study of tennis.  It turns out that probabilistic analysis of tennis goes back almost as far as probability theory itself, to Jacob Bernoulli, a Swiss mathematician best known for the Law of Large Numbers.

In the late 17th century, Bernoulli wrote a Letter to a Friend on Sets in Court Tennis.  I haven’t given it a thorough reading yet, but for now, I have to share a line that ought to be the epigram to just about every work of statistical analysis in sport:

You cannot conceive, as you say, that one could measure the strengths of players with numbers, much less that one could draw from these numbers all the conclusions I have drawn.

Bernoulli was born, taught, and died in Basel, which must be why tennis is still so popular there today.