The Likelihood of Live Doubles Rubber in the New Davis Cup

In the new Davis Cup Finals format, each country-versus-country tie consists of three matches: two singles and one doubles. The singles rubbers are played first, so it’s possible that the doubles rubber will be “dead”–irrelevant to the result of the tie.

The Davis Cup Finals organizers aimed to make the doubles matter more, by using tiebreakers (based on sets and games won) to determine which sides advance from the round-robin phase to the knock-out rounds. It may have helped keep dead doubles rubbers interesting at first, but by the final days of the round-robin stage, teams that automatically qualified for the knock-out rounds had no remaining incentive to play doubles. Canada gave the United States a walkover, and Australia retired after one game. This was probably inevitable, but it isn’t ideal. Fans would presumably prefer to watch more tennis, and unfinished matches could wreak havoc with the tiebreaker system.

There are a lot of possible ways to restructure the event–so many that I’m not going to explore that topic today. Since dead doubles rubbers are inevitable, I’d instead like to look at how often we should expect them to occur and, given that they will occur, whether that truly sidelines doubles in comparison with singles.

Live doubles

This topic was prompted by a question ahead of this week’s podcast:

The most extreme way of handling dead doubles rubbers is simply not to play them. If we went that route, how many doubles matches would we see?

At the Davis Cup Finals last week, there were 25 ties: 18 in the round-robin stage, and 7 knock-out ties. 12 of the 25 featured a live doubles rubber: 7 of the 18 round-robin ties, and 5 of the 7 knock-outs. Using Luke’s proposed methodology, that’s roughly what we’d expect. The average tie (across all stages) had a 43% chance of reaching a deciding doubles rubber, suggesting that 11 doubles matches would matter.

Here is a list of the 25 ties, along with the probability that the two sides would split the singles rubbers. I’ve also shown whether the doubles rubber turned out to be necessary. Elo ratings didn’t do a very good job predicting which ties would require a doubles decider, even though they do give us a good estimate of how often the doubles will make the difference.

Tie                  Decider Odds  Decider Actual  
Semi: GBR vs ESP            56.2%             YES  
Quarter: SRB vs RUS         54.3%             YES  
Semi: RUS vs CAN            53.3%             YES  
RR: FRA vs SRB              52.5%              NO  
RR: ARG vs GER              51.6%              NO  
RR: USA vs CAN              51.4%              NO  
RR: ITA vs CAN              50.0%              NO  
Quarter: GBR vs GER         50.0%              NO  
RR: GBR vs KAZ              49.8%             YES  
RR: ESP vs RUS              49.4%             YES  
Quarter: AUS vs CAN         49.4%             YES  
RR: USA vs ITA              48.7%             YES  
RR: BEL vs AUS              46.1%              NO  
RR: KAZ vs NED              46.0%             YES  
RR: CRO vs RUS              45.7%              NO  
RR: GER vs CHI              44.2%             YES  
RR: ARG vs CHI              43.6%              NO  
RR: FRA vs JPN              43.4%             YES  
Final: CAN vs ESP           40.8%              NO  
RR: GBR vs NED              37.5%             YES  
RR: BEL vs COL              36.2%              NO  
Quarter: ARG vs ESP         34.6%             YES  
RR: SRB vs JPN              26.1%              NO  
RR: AUS vs COL              10.4%              NO  
RR: CRO vs ESP               7.3%              NO

Only a few ties were near-guarantees of a singles sweep. Even with a fairly deep 18-team draw, most countries were able to bring two solid singles players, while few sides featured more than one singles elite.

A decade of context

This wasn’t just a fluke. I went through all World Group ties (not including the Playoff round) from 2010-18, and identified the two best singles players who appeared on court for each side. Using their Elo ratings at the time of the contest for the new best-of-three-sets format, I estimated how often we would get a deciding doubles rubber.

Across those 135 ties, the average likelihood of a doubles decider was 41%, only a bit lower than the observed rate this year. Barring some radical shift in the geography of global tennis, that gives us a pretty good idea of how frequently we should expect to see a two-match singles sweep in the new Davis Cup format.

How much does doubles matter?

When doubles matches are live, they are particularly important. Each singles rubber has a great deal of influence on each side’s chances of winning the three-match tie, but once the doubles rubber is in play, it has all the influence.

Think of this in terms of leverage, the concept I usually use for in-match shifts from one point or game to the next. Imagine two identical sides, and consider their chances of winning at each step of the process. Each side has a 50% chance of winning each rubber, which means:

  • Each side has a 50% chance of winning the tie.
  • Whichever side wins the first rubber will have a 75% chance of winning the tie.
  • If the two sides split the singles rubbers, each side will once again have a 50% chance of winning the tie.

Now consider the leverage of each match from the perspective of the first side:

  • If they win the first singles rubber, their chances of winning the tie improve to 75%. Otherwise, they fall to 25%. That’s a leverage value of 75% – 25% = 50%.
  • Assume they win the first singles rubber. If they win the second, they win the tie–a probability of 100%. If they lose, it falls to 50%. Again, that’s a leverage value of 100% – 50% = 50%. (If they lose the first rubber, the math is the same, just with probabilities of 50% and 0% instead of 100% and 50%.)
  • If there is a deciding doubles rubber, the pre-match probability of winning the tie is 50%. Win the doubles, and the likelihood increases to 100%; lose it, and the probability is 0%. That’s a leverage value of 100% – 0% = 100%.

Maybe you think this is excessively formal and long-winded, and you might be right. The point is, given two equal sides, the doubles is twice as important. Plenty of other sports have similar features in which certain players appear infrequently, but at key moments. Consider baseball closers, who don’t pitch in every game, only appearing late in tight games. Or NFL kickers, who only take part in a handful of plays each game, but have the potential to score on many of them.

Theory and reality

In the sample framework I’ve just laid out, the doubles rubber will be live exactly 50% of the time, and it is twice as important as each singles rubber. That isn’t exactly how it works out in real life, since the doubles rubber is only decisive a little more than 40% of the time.

Still, when the doubles rubber matters, it is always make-or-break–or, in my terms above, it has a leverage value of 100%.

I’m happy to leave dead doubles rubbers unplayed. Doubles specialists might be unhappy with such a decision, and I fear the wrath of Davis Cup traditionalists. However, this way of thinking about what’s at stake might soften the blow. In a 16- to 18-team Davis Cup structure, the teams are typically balanced enough that the doubles rubber is necessary almost half the time. And when it is, the oft-unsung doubles specialists get to play a match that is–literally!–twice as important as each ratings-grabbing singles rubber.

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.

Forecasting Andy Murray, Doubles Specialist

We are three weeks into the mostly-triumphant doubles comeback of Andy Murray. In his first week back, he raced to the Queen’s Club title with Feliciano Lopez. A week later, he paired Marcelo Melo and lost in the first round. At Wimbledon, he is partnering Pierre-Hugues Herbert, with whom he has already defeated the only-at-a-slam duo of Marius Copil and Ugo Humbert.

Today in the second round, Herbert/Murray face a sterner test: sixth-seeded team Nikola Mektic and Franco Skugor. The betting markets heavily favored Herbert/Murray going into the contest, but we have to assume that punters (including an unusually high number of casual ones) are probably overrating the familiar name on his home turf.

D-Lo to the rescue

Let’s see what D-Lo (Elo for doubles!) says about today’s match. D-Lo treats each team as a 50/50 mix of the two players, and adjusts each player’s rating after every match, depending on the quality of the opponent. It also very slightly regresses both partners to the team average after each match, because it’s impossible to know how much each player contributed to the result.

Herbert is D-Lo’s top doubles player in the world on hard and clay courts, though he falls to 6th in the 50/50 blend of overall and grass-specific ratings used for forecasting. Murray, thanks to his run at Queen’s, is up to 54th in the blend, though that’s really more like 40th among players in the draw, since several injured and recently-retired players are clinging to high D-Lo ratings.

Mektic and Skugor are credible specialists, as indicated by their ATP ranking. They are 24th and 26th in the D-Lo, respectively. Combined, the two teams’ ratings are quite close: 1773 for Herbert/Murray to 1763 for Mektic/Skugor. In a best-of-three match, a difference of 10 points translates to a 51.4% edge for the favorites. In best-of-five, the better team is always more likely to come out on top, though with such a small margin it barely matters. Here, the best-of-five number is 51.6%.

Versus the pack

How does a team rating of 1773 compare to the rest of the remaining field? Entering Saturday’s play, 22 men’s doubles pairs were still in the draw. As I write this, Lopez and Pablo Carreno Busta are the only additional team to have been eliminated, reducing the field to 21.

Here are the combined D-Lo ratings of these teams. The rank shown for each player is based on the 50/50 blend of overall and grass rating used for forecasting.

Team D-Lo  Rank  Player             Rank  Player             
1873       2     Mike Bryan         3     Bob Bryan          
1858       4     Lukasz Kubot       7     Marcelo Melo       
1836       9     Raven Klaasen      10    Michael Venus      
1817       8     John Peers         17    Henri Kontinen     
1802       12    Nicolas Mahut      22    E Roger-Vasselin   
1788       18    J S Cabal          19    Robert Farah       
1773       6     P H Herbert        54    Andy Murray        
1764       15    Oliver Marach      36    Jurgen Melzer      
1763       24    Nikola Mektic      26    Franco Skugor      
1757       20    Rajeev Ram         33    Joe Salisbury      
1747       23    Horia Tecau        41    Jean Julien Rojer  
1709       42    Maximo Gonzalez    46    Horacio Zeballos   
1695       29    Ivan Dodig         88    Filip Polasek      
1681       58    Marcus Daniell     62    Wesley Koolhof     
1677       50    Frederik Nielsen   77    Robin Haase        
1644       81    Marcelo Demoliner  90    Divij Sharan       
1637       84    A Ul Haq Qureshi   99    Santiago Gonzalez  
1596       106   Philipp Oswald     123   Roman Jebavy       
1575       101   Mischa Zverev      184   Nicholas Monroe    
1533             Jaume Munar        216   Cameron Norrie     
1517       177   Marcelo Arevalo    214   M Reyes Varela

Herbert/Murray rank 7th among the surviving pairs. The combined rating of 1773 makes them competitive against anyone. The 100-point difference separating them and the Bryans gives them a 33% chance of pulling off a best-of-five upset, while the 29-point gap between them and Nicolas Mahut/Edouard Roger Vasselin translates to a 45/55 proposition.

Fortunately for the French-British pair, they won’t have to play a higher-rated team for some time. If they win today, they’ll face the winner of Dodig/Polasek vs Zverev/Monroe. The first of those teams is rated 80 points lower than Herbert/Murray (64% odds for the favorites), and the second is 200 points lower (81% for the faves). The three teams that could advance to become the quarter-final opponent for Herbert/Murray are all rated lower than Dodig/Polasek.

The draw certainly favored Sir Andrew. Yes, the 1859-rated Pavic/Soares duo crashed out in their section, but even before that, three of the best teams–Bryan/Bryan, Kubot/Melo, and Mahut/Roger-Vasselin–were stuck together in another quarter. While no men’s doubles match is a sure thing, the path is clear for Herbert/Murray to reach the final four.

Beyond Wimbledon

Does Murray have what it takes to become a full-time doubles specialist? Taking his Queen’s Club title into account, his overall D-Lo is already up to 36th best on tour, just ahead of Skugor, and several places better than Roland Garros co-champ Kevin Krawietz. Jurgen Melzer, another excellent singles player making of a go of it on the doubles circuit, is ranked 20 places lower, with a D-Lo 40 points less than Murray’s.

The short answer, then, is yes. It must be noted, though, that he isn’t the best choice among the big four to have a successful post-singles career as part of a team. That honor goes overwhelmingly to Rafael Nadal. Nadal’s career peak D-Lo is 100 points higher than Murray’s, and even his grass-court rating–based, admittedly, on some old results–is 70 points higher. Aside from the injured doubles wizard Jack Sock, Nadal is the best active player absent from the Wimbledon draw.

So, Murray/Nadal, Wimbledon 2021 champions? Sounds good to me–as long as Herbert relinquishes his new partner and finally commits to focusing on singles.

Is Doubles As Entertaining As We Think?

For as long as I’ve been following tennis, there’s been a tension between the amount of doubles available to watch and the amount of doubles that fans say they want to watch. In-person spectators flock to doubles matches at grand slams and aficionados pass around GIFs of the most outrageous, acrobatic doubles points. Yet broadcasters almost always stick with singles, leaving would-be viewers chasing down online streams, often illegal ones.

There are some good reasons for that, foremost among them the marquee drawing power of the best singles players. Broadcasters are convinced that their audiences would rather watch a Fed/Rafa/Serena/Pova blowout than a potentially more entertaining one-on-one contest between unknowns, let alone a doubles match. And they’re probably right–at least, they’ve got ratings numbers to back them up. So we’re left with a small population of hipster doubles fans, confident that two-on-two is the good stuff, even if most of us rarely watch it.

It’s probably impossible to quantify entertainment value, but that doesn’t mean we shouldn’t try. What can the numbers tell us about the watchability of doubles?

Hip to be rectangular

There’s plenty of room for a diversity of preferences–one fan’s Monfils may be another fan’s Isner. But there are some general principles that seem to define entertaining tennis for most spectators. Winners are better than errors, for one. Long rallies are better than short ones, at least within reason. And you can never go wrong with more net play.

If net play were the only criterion, doubles would beat singles easily. But what about other factors? I started wondering about this while researching a recent post on gender differences in mixed doubles, when I came across a match in which every rally was four shots or fewer. For every brilliant reflex half-volley, doubles features a hefty dose of big serving and tactically high-risk returning. Especially in men’s doubles, that translates into a lot of team conferences and not very much shotmaking.

Let’s see some numbers. For each of the five main events at the 2019 Australian Open–men’s and women’s singles, men’s and women’s doubles, and mixed doubles–here is the average rally length, the percentage of points ended in three shots or less, and the percentage of points that required at least ten shots:

Event            Avg Rally  <3 Shots  10+ Shots  
Men's Singles          3.2     72.6%       5.1%  
Women's Singles        3.4     67.9%       5.4%  
Men's Doubles          2.5     81.6%       1.1%  
Women's Doubles        2.9     76.7%       2.4%  
Mixed Doubles          2.8     74.0%       1.8%

There's a family resemblance in these numbers, but it's clear that doubles points are shorter. Men's doubles is the most extreme, at 2.5 shots per point. By comparison, only 8% of the men's singles matches in the Match Charting Project database have an average rally length lower than that. More than four out of every five men's doubles points ends by the third shot, and with barely one in one hundred points lasting to ten shots, you'd be lucky to sit through an entire match and see more than one such exchange.

Quantity and quality

Shorter points are the nature of the format. Even recreational players can find it hard to keep the ball in play when half of each team is patrolling the net, looking for an easy putaway. Short-rally tennis can still be entertaining, as long as the quality of play offsets the unfavorable watching-to-waiting ratio.

I've mentioned my perception that men's doubles features a lot of unreturned serves. The numbers suggest that I spoke too soon. For the five events, here are the percentage of points in which the return doesn't come back in play:

Event            Unret%  
Men's Singles     31.7%  
Women's Singles   24.3%  
Men's Doubles     32.1%  
Women's Doubles   21.6%  
Mixed Doubles     29.3%

For men, singles and doubles are about the same. Perhaps the singles servers are a bit stronger, but the doubles returners are taking more chances, trying to avoid feeding weak returns to aggressive netmen. With women, you're more likely to see a return in play in a doubles match than in singles. Unless you're a connoisseur of powerful serves, you'll probably find higher rates of returns in play to be more enjoyable to watch.

The same applies to winners, compared to unforced errors. (Forced errors are a bit tricky--sometimes they are as exciting and indicative of quality as a winner; other times they're just an out-of-position unforced error.) Let's see what fraction of points end in various ways, for each of the five events:

Event            Unforced%  Forced%  Winner%  
Men's Singles        25.6%    16.2%    21.3%  
Women's Singles      28.9%    16.0%    23.4%  
Men's Doubles        12.8%    17.2%    29.9%  
Women's Doubles      20.9%    18.0%    32.1%  
Mixed Doubles        14.5%    17.0%    29.5%

Here, doubles is the clear winner. For both men and women, more doubles points than singles points end in winners, and fewer points end in unforced errors. Some of that reflects the much higher rate of net play, since it's easier to execute an unreturnable shot from just a few feet behind the net. There are a few more forced errors in doubles, perhaps representing failed attempts to handle volleys that almost went for winners, but no matter how we interpret them, the difference in forced errors is not enough to offset the differences in winners and unforced errors.

The hipsters weren't wrong

The numbers aren't as conclusive as I expected them to be. Yes, doubles points are shorter, but not so much so that the format is reduced to only serving and returning. (Though some men's matches are close.) As usual, our data has limitations, but the information available for each point suggests that there's plenty of high-quality, entertaining tennis to be seen on doubles courts, even if it's usually limited to four or five shots at a time.

Unmixing the Gender Gap in Mixed Doubles

Doubles has long been a sort of final frontier in tennis analytics. Double is interesting, at least in part, for the same reason that all team sports are compelling–contributions can come from either player, or a combination of the two. From an analytics perspective, that poses a challenge: Can we isolate what each player brings to the court? I’ve tried to do so with my doubles Elo ratings, but that method relies on players changing partners. It’s not possible to identify how much each half contributed simply by looking at match results.

The problem, as usual, is limited data availability. To know how much value to assign to each player, we need to know what he or she did, even at the basic level of aces, double faults, winners, and errors. The tours report matchstats for many doubles contests, but do not separate the players. Knowing that the Bryan brothers hit 12 aces doesn’t tell us anything about Bob or Mike. The grand slam websites have been better, often providing sequential point-by-point data for some matches, but the same problem persists: They don’t differentiate between players.

That is, until now! The Australian Open website specified the server for each point of every doubles match. (It doesn’t identify the returner on each point, but … baby steps.) That opens up whole new vistas for analytics to separate the contributions of each player.

There’s no I in mixed

A natural place to start is mixed doubles, an event that, due to lack of data, has been almost entirely ignored by analysts. Yet mixed doubles is one of things that everyone seems to have at least a moderate interest in, either because it’s a popular amateur pastime, or because gender differences in sport are inherently fascinating. Due to the variety of skillsets on court at all times, mixed doubles presents tactical puzzles that are different from those posed by same-gender matches.

Let’s start with the basics. There are only 32 teams in a grand slam mixed doubles event, so it’s possible to extend the dataset even further by manually recording which players returned from which sides. (Thanks to Jeff M for a big assist with this.) Thus, for over 3,000 points, we have the gender of the server and the returner. The following table shows several aggregates: Overall mixed doubles averages, typical performance for male and female servers, and rates for male and female returners, including serve points won, first-serve-in rates, and average first serve speed:

Subset           Hold%    SPW  First In  Avg 1st  
Average          76.0%  63.3%     66.2%    103.1  
Men serving      78.6%  65.1%     65.0%    110.2  
Women serving    72.4%  61.3%     67.6%     94.9  
Men returning        -  60.4%     64.6%    103.5  
Women returning      -  65.9%     67.6%    102.8

I was a bit surprised by how narrow the gap is between men and women serving. In men’s doubles at the Australian Open, servers won 67.8% of points, and in women’s doubles, servers won 58.5%. The pool of players is very similar, but in the mixed event, men won fewer serve points and women won more.

Perhaps there is more insight to be gained by looking at more specific matchups:

Server  Returner    SPW  First In  Avg 1st  
Male      Male    61.7%     63.5%    111.0  
Male      Female  68.1%     66.3%    109.5  
Female    Male    58.9%     66.0%     94.6  
Female    Female  63.3%     69.0%     95.1 

Tactics appear to change a bit depending on the gender of the returner. Both men and women land more first serves when facing a female returner. However, first serve speed doesn’t vary much. This suggests that David Marrero–who got himself in hot water by possibly fixing a 2016 Australian Open mixed match and then making some questionable comments about inter-gender competition afterward–is unusual in his reluctance to hit hard against female opponents.

Interestingly, the averages from same-gender doubles matches pop up in this table. When men serve to women in mixed doubles, they win 68.1% of points, almost exactly the same rate of serve points won in men’s doubles. When women serve to men, they take 58.9% of points, just a bit higher than the usual rate in women’s doubles. This suggests that while the server-returner matchup is important, the gender of the net player is a key factor as well.

Beware of Melichar

Individual player results against each gender will tell us more, but a single tournament worth of no-ad, third-set super-tiebreak matches doesn’t give us a lot of data on many players. Many members of first-round losing teams served only 20-25 points each. Of the finalists, John Patrick Smith had the biggest gender gap, winning 54.9% of service points against men and 74.4% against women, and his opponent Barbora Krejcikova was similar, winning 59.6% against men and 73.0% against women. Their partners, Astra Sharma and Rajeev Ram, both had narrower gaps of just a few percentage points.

Over the course of the entire event, Sharma was the best server of the four, winning 69.7% of total service points compared to Ram’s 69.0%. But neither came close to semi-finalist Nicole Melichar, who won a whopping 78.4%, narrowly besting her partner, Bruno Soares, who won 77.7%. The Melichar/Soares duo appears to be particularly effective as a unit: Melichar won only 72.6% of service points in her three women’s doubles matches, and Soares won only 70.2% in his men’s doubles quarter-final run alongside Jamie Murray.

The first step toward analyzing any sporting event is simply understanding what’s going on. In the case of mixed doubles, a big part of that is getting a sense of the gender gap on both serve and return. There’s still a painful dearth of data–we now have a mere 31 matches with servers and returners identified for each point–but the next time you watch a mixed doubles match, you’ll be that much smarter about what to expect and what sorts of performances are worthy of further study.

Jürgen Melzer and Singles Players Who Care About Doubles

This is a guest post by Peter Wetz.

Italian translation at settesei.it

Three weeks ago, Jürgen Melzer played his last singles tournament on home turf at the Erste Bank Open in Vienna. His low singles ranking, caused by injury setbacks and a mediocre comeback campaign, required him to enter into the tournament as a wild card. Melzer drew Milos Raonic in the first round; bookmakers and fans alike predicted that this would be Melzer’s last singles match.

However, things went differently. In front of a packed arena (at least by tournament-Monday standards) Melzer squeezed out a two set win to face Kevin Anderson in the round of 16. That match never happened, though, after a suddenly occurring gastritis forced him to withdraw. As weird as it sounds, this means that Melzer did not lose the last match of his singles career, a feat only a few players can put on their CV.

Another unique thing about Melzer is that he is one of the last players to reach an elite level in singles as well as in doubles. To underline this characteristic let’s start by looking at singles (ChS) and doubles (ChD) career high rankings of  recently-retired1 top ten singles players. The following table shows each player’s peak singles and doubles rankings, sorted by the date at which each player recorded their best singles ranking:

Player			ChS	ChS Date  ChD	ChD Date
Paradorn Srichaphan	9	2003-05	  79	2003-09
Juan Carlos Ferrero	1	2003-09	  198	2003-02
Andy Roddick		1	2003-11	  50	2010-01
Rainer Schuettler	5	2004-04	  40	2005-07
Guillermo Coria		3	2004-05	  183	2004-03
Nicolas Massu		9	2004-09	  31	2005-07
Joachim Johansson	9	2005-02	  108	2005-09
Gaston Gaudio		5	2005-04	  78	2004-06
Guillermo Canas		8	2005-06	  47	2002-07
Mariano Puerta		9	2005-08	  68	1999-08
David Nalbandian	3	2006-03	  105	2009-10
Ivan Ljubicic		3	2006-05	  70	2005-05
Mario Ancic		7	2006-07	  47	2004-06
Radek Stepanek		8	2006-07	  4	2012-11
Nikolay Davydenko	3	2006-11	  31	2005-06
James Blake		4	2006-11	  31	2003-03
Fernando Gonzalez	5	2007-01	  25	2005-07
Robin Soderling		4	2010-11	  109	2009-05
Jürgen Melzer           8       2011-04   6     2010-10
Nicolas Almagro		9	2011-05	  48	2011-03
Mardy Fish		7	2011-08	  14	2009-07
Janko Tipsarevic	8	2012-04	  46	2011-04
Juan Monaco		10	2012-07	  41	2009-01

The data shows that top ten singles players rarely climb up to the very top in doubles. Of course, there can be several reasons for this: scheduling (playing a full singles schedule can be exhausting) or skill (being a good singles player doesn’t necessarily mean that you are also a good doubles player), among others. The fact that the best doubles career high ranking by the Big Four is Roger Federer’s rank of 24 reached in 2003 further underlines that top singles players have better things to do than practicing their volleying skills.

So, as the table above already suggests, Melzer is one of the last of the breed of players that–ranking-wise–made it until the very top in both singles and doubles. The following table shows players who reached a top-ten career high in both rankings, sorted by when they achieved their high in doubles back until 1990.

Player		    ChS	ChS Date   ChD	ChD Date
Petr Korda	    2	1998-02	   10	1990-06
Michael Stich	    2	1993-11	   9	1991-03
Marc Rosset	    9	1995-09	   8	1992-11
Yevgeny Kafelnikov  1	1999-05	   4	1998-03
Patrick Rafter	    1	1999-07	   6	1999-02
Wayne Ferreira	    6	1995-05	   9	2001-03
Jiri Novak	    5	2002-10	   6	2001-07
Jonas Björkman	    4	1997-11	   1	2001-07
Arnaud Clement	    10	2001-04	   8	2008-01
Jürgen Melzer	    8	2011-04	   6	2010-10
Radek Stepanek	    8	2006-07	   4	2012-11
Fernando Verdasco*  7	2009-04	   8	2013-11
Jack Sock*	    8	2017-11	   2	2018-09

* Active singles player

Since 1990 there have only been 13 players who reached a doubles and singles career high inside the top ten. The last number one with a top ten doubles ranking was Patrick Rafter. Currently there are only two active singles players part of this group. As has already been mentioned on this blog several times, Jack Sock’s doubles prowess is an exception no matter how you look at it. And the time between Fernando Verdasco’s singles high and doubles high shows that he reached them at two completely different stages of his career, which brings us to the final measure: Which players held a top ten spot in both rankings at the same time? The following table shows players, weeks spent in the singles top ten (weeksS), weeks spent in the doubles top ten (weeksD) and weeks spent in both singles and doubles top ten at the same time (weeksS+D) sorted by the date the doubles career high was reached.

Player		weeksS	weeksD	weeksS+D Chd Date
John Mcenroe	208	96	74	 1983-01
Pat Cash	89	14	5	 1984-08
Anders Jarryd	82	379	78	 1985-08
Mats Wilander	227	72	72	 1985-10
Stefan Edberg	452	122	117	 1986-06
Guy Forget	79	119	5	 1986-08
Yannick Noah	157	87	84	 1986-08
Andres Gomez	143	62	31	 1986-09
Boris Becker	530	21	21	 1986-09
Joakim Nystrom	72	57	33	 1986-11
Miloslav Mecir	109	19	19	 1988-03
Emilio Sanchez	57	138	44	 1989-04
Jakob Hlasek	37	132	10	 1989-11
Yevgeny Kafeln.	388	157	148	 1998-03
Patrick Rafter	156	33	26	 1999-02
Jonas Björkman	43	462	29	 2001-07
Jürgen Melzer	14	50	14	 2010-09

With Melzer’s retirement, there is no active player who held a top ten ranking in singles and doubles at the same week. In other words, he is the last player who held simultaneous top ten rankings in singles and doubles. With Jonas Björkman this makes him one of only two players in this group for the past 18 years! Even in the nineties there were only two players–Rafter and Yevgeny Kafelnikov–reaching this feat, whereas in the eighties there were many others.

Even if this stream of trivia does not tell us much analytically, we can see that players peaking with and without partners on their side of the court are becoming a rare species. The times when they have done so simultaneously are long gone.

Footnotes

1. We look at retired players, because their career high rankings are not subject to change anymore.

Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.

Forecasting the 2018 Laver Cup

Embed from Getty Images

Italian translation at settesei.it

It’s that time of year again: group selfies in suits, dodgy Davis Cup excuses, and a reminder that it takes more than six continents just to equal Europe. That’s right, it’s Laver Cup.

Last year, I worked out a forecast of the event, walking through a variety of ways in which captains Bjorn Borg and John McEnroe could use their rosters and ultimately predicting a 16-8 win for Team Europe. As it happened, both captains intelligently deployed their stars, and the result was 15-9. This year, the competitors are a little different and the home court has moved from Prague to Chicago, but the format remains the same.

Let’s start with a look at the rosters. I’ve included two additional players for reference: Juan Martin del Potro, scheduled to play for Team World, but withdrew; and Pierre Hugues Herbert, the doubles specialist Borg hasn’t realized he needs. Each player is shown alongside his surface-weighted singles Elo rating and surface-weighted doubles “D-Lo” rating:

EUROPE                       Singles Elo  Doubles D-Lo  
Novak Djokovic                      2137          1667  
Roger Federer*                      2097          1700  
Alexander Zverev                    1971          1690  
David Goffin                        1960          1582  
Grigor Dimitrov                     1928          1719  
Kyle Edmund                         1780          1542  
                                                        
WORLD                        Singles Elo  Doubles D-Lo  
Kevin Anderson                      1914          1692  
Nick Kyrgios                        1910          1668  
John Isner                          1887          1800  
Diego Sebastian Schwartzman         1814          1540  
Frances Tiafoe                      1772          1544  
Jack Sock                           1724          1925  
                                                        
ALSO                                                    
Juan Martin Del Potro               2062          1678  
Pierre Hugues Herbert               1691          1890

* Federer has played very little tour-level doubles for a long time. Last year I estimated his D-Lo at 1650; he played rather well last year, so I’ll bump him up to 1700 this time around.

Especially with Delpo on the sidelines, Europe looks to dominate the singles. The doubles leans in World’s favor, largely because Jack Sock is so good, especially in comparison with guys who have focused on singles.

Format review

Let’s do a quick refresher on the format. Laver Cup takes place over three days, each of which has three singles matches and one doubles match. Each player must play singles at least once, and no doubles pairing can repeat itself. Day 1 matches are worth one point each, day 2 matches are worth 2 points each, and day 3 matches are worth 3 points each. If there’s a 12-12 tie at the end of day 3, a single doubles set–in which a previously-used team may compete–will decide it all.

Given that format, the best way for the captains to use their rosters is to stick their three worst singles players on day 1 duty, then use their best three on both day 2 and day 3. For doubles, they should use their best doubles player every day, with the best partner on day 3, next best on day 2, and third best on day 1. As I’ve mentioned, Borg and McEnroe came close to this last year, although Borg didn’t use Rafael Nadal (his best doubles player) in day 3 doubles, and he generally overused Tomas Berdych. Both decisions are understandable, as Nadal may not have been physically able to play every possible match, and Berdych was in front of a Czech crowd.

Now that we know the captains will act in a reasonably savvy way, we can forecast the second edition with a little more confidence than the inaugural one.

The forecast

Nadal’s absence this year will hurt the Europe squad on both singles and doubles. Combined with a small step backward for Federer’s singles game, this year’s Laver Cup figures to be closer than last year. Recall that my forecast a year ago called for a 16-8 Europe victory, and the result was 15-9.

Assuming optimal usage, the 2018 forecast gives Europe a 67.6% chance of winning, with a most likely final score of 14-10. There’s a nearly one-in-ten shot that we’ll see a 12-12 tie, in which the superior doubles capabilities of Team World give them the edge, with a 70.7% probability of winning the tie-breaking set.

Were del Potro not so fragile, this could get even more interesting. Swap out Frances Tiafoe for the Tower of Tandil, and Europe’s chances fall to 56.8%, with a most likely final score of 13-11.

Nothing McEnroe could have done, short of going to medical school a few decades ago, could have put the Argentine on his team this week. But Borg has less of an excuse for failing to maximize the potential of his team. Unlike World, with its world-beating doubles specialist, Europe has a stunning singles roster that rarely takes to the doubles court. As we’ve seen, one doubles player can take the court three times, plus the potential 12-12 tie-breaking set. The specialist would need to play singles only once, on the low-leverage first day.

The obvious choice is Pierre Hugues Herbert, a top-five doubles player with the ability to play respectable singles as well. The Frenchman would be considerably more valuable than Kyle Edmund, who is a better singles player, but not good enough to be of much help to an already loaded side. (I made a similar point last year and illustrated it with Herbert’s partner, Nicolas Mahut. Since then, Herbert has taken the lead over his Mahut in both singles and doubles Elo ratings.)

When we sub in Herbert for Edmund, the simulation spits out the best result yet for Europe. Against the actual World team (that is, no Delpo), the hypothetical Europe squad would have a 74.6% chance of winning, with the likely final score between 14-10 and 15-9. Herbert and a mediocre partner would still be the underdogs in a tie-breaking final set against Sock and John Isner, but the presence of a legitimate doubles threat would narrow the odds to about 58/42.

We won’t get to see either Delpo or Herbert in Chicago this year, but we can expect a slightly more competitive Laver Cup than last year. Add in home court advantage, and the result is even less of a foregone conclusion. It’s no match for last week’s Davis Cup World Group play-offs, but I suspect it’ll make for more compelling viewing this weekend than the final rounds in Metz and St. Petersburg.

Jack Sock, Doubles King Once Again

Embed from Getty Images

Italian translation at settesei.it

A couple of years ago, I wrote an article introducing D-Lo, an Elo-like rating system for doubles, which crowned Jack Sock as the best doubles player on the men’s tour. Sock grabbed the top spot in October 2016 and hung on for about nine months, largely by not playing very much. A couple of first-round losses in Washington and Montreal last summer sent him tumbling, landing at 8th after the US Open and as low as 14th going into this year’s Australian Open.

Despite his preference for singles, Sock has rocketed back into the lead, first pairing with John Isner for the Indian Wells title, and then partnering Mike Bryan (replacing injured brother Bob) to win both Wimbledon and the US Open. With the exception of one week immediately after Indian Wells, Sock sits at the head of the D-Lo table for the first time in more than a year. Here are the current top ten, along with their ratings:

Rank  Player                 D-Lo  
1     Jack Sock              1949  
2     Bob Bryan              1930  
3     Mike Bryan             1917  
4     Pierre Hugues Herbert  1906  
5     Nicolas Mahut          1893  
6     Jamie Murray           1886  
7     Bruno Soares           1883  
8     Oliver Marach          1867  
9     Robert Farah           1863  
10    Nikola Mektic          1863

Yes, that’s the injured Bob Bryan in the second spot. More on that in a moment.

A quick refresher on the D-Lo system: It mostly works like a standard Elo algorithm, in that players gain points for winning matches and lose points for losing them, based on the quality of the opponent and the amount of prior information already baked into their ratings. A big upset earns more points than a victory over an equal, and for players with fewer prior matches, the effect of each match is greater. Thus, Sock got a few more points than Mike did for winning the 12 matches at the last two slams, because we knew relatively less about him before those tournaments.

D-Lo assumes that the quality of each team is equal to the average of the two players. If a team wins, each member of the partnership gains points, with one tweak: If the two players have different ratings, their ratings slightly move toward the average of the two. This is because it’s impossible to know how much each player contributes to a win. The system is designed so that, after a year or so of playing together, the two mens’ ratings will meet in the middle. It’s an imperfect system, but it does a reasonably good job of forecasting results, which means it usually provides a solid representation of each player’s skill level.

Back to the matter at hand: Doubles ratings have been particularly volatile this year, with five different men (Sock, Bob, Pierre Hugues Herbert, Mate Pavic, and Henri Kontinen) holding the #1 spot, and two more (Nicolas Mahut and John Peers) peaking at #2. This parity means that no player has a particularly high rating. Two years ago, Sock’s mark of 1949 would have been good for only fourth (behind himself, Herbert, and Mahut), and several players (the Bryans, Herbert, and Daniel Nestor among them) have peaked with ratings above 2000.

Take a look at how much the rank order has fluctuated since the beginning of 2018:

2018 D-Lo leaders

For clarity’s sake, I’ve left off Oliver Marach (whose rating tracks closely with that of his partner, Pavic, and whose season hasn’t lived up to its early promise) and Peers (ditto, with Kontinen). Herbert has reached the highest level of anyone this season, but a rough second half so far has left him behind the American trio of Jack, Bob, and Mike.

Back to the curious case of Bob Bryan. The Bryan brothers’ title at the Madrid Masters this year gave the twins their highest D-Lo ratings in nearly two years. “Standard” Elo doesn’t penalize players for absence, so Bob’s mark has remained at 1930 ever since. (I’ve added an injury/absence penalty in my singles Elo ratings, but haven’t done so for D-Lo. I suspect there is less of an effect, but still a measureable one, in doubles.) Mike’s rating has slipped because of some bad results apart from the pair of majors, and only Sock has caught up.

If Bob is healthy enough to play this fall, the twins are expected to pair up for the World Tour Finals, once again leaving the best doubles player in the world out of the field. In that case, Sock, down to 157th in the ATP singles race, could end up spending that week playing the new ATP Challenger event in Houston. Without their young compatriot in the way, the Bryans will be back in familiar territory, headed to London as the favorites for another year-end title.

Men’s Doubles Season Starts and the Case of Oliver Marach and Mate Pavic

This is a guest post by Peter Wetz.

In recent years, the steady decline of the holders of 116 doubles titles–Bob and Mike Bryan–has resulted in more variety at the very top of the game. The 16-time Grand Slam champions won their last major at the US Open 2014. Since then, eight different teams have won their first title at the highest level of the sport.

Even though none of these debut winners emerged out of nowhere, the doubles team consisting of Oliver Marach and Mate Pavic, which formed in the middle of last season, has enjoyed an exceptional run at this year’s start of the season. This prompted me to take a closer look at the performance of doubles teams per season.

The following table shows each team’s won-loss record through the French Open for each season since 2000 . It’s sorted by number of  wins up to that point, and the last column displays the won-loss record for the complete season. Only teams that have won more than 30 matches until the French Open are listed.

Year	Team		W-L (%) Start	W-L (%) Full
2013	Bryan/Bryan	40-4  (91%)	71-11 (87%)
2002	Knowles/Nestor	38-7  (84%)	66-14 (82%)
2007	Bryan/Bryan	37-5  (88%)	73-10 (88%)
2008	Bryan/Bryan	37-9  (80%)	63-17 (79%)
2009	Bryan/Bryan	37-9  (80%)	68-18 (79%)
2014	Bryan/Bryan	36-6  (86%)	64-12 (84%)
2018	Marach/Pavic	36-7  (84%)	tbd
2010	Nestor/Zimonjic	35-7  (83%)	57-19 (75%)
2012	Mirnyi/Nestor	34-9  (79%)	43-18 (70%)
2003	Knowles/Nestor	34-9  (79%)	57-16 (78%)
2006	Bryan/Bryan	33-9  (79%)	65-15 (81%)
2004	Bryan/Bryan	32-8  (80%)	57-17 (77%)
2010	Bryan/Bryan	31-7  (82%)	67-13 (84%)
2011	Bryan/Bryan	31-7  (82%)	59-16 (79%)
2009	Nestor/Zimonjic	31-8  (79%)	57-17 (77%)
2014	Nestor/Zimonjic	31-8  (79%)	42-18 (70%)
2003	Bryan/Bryan	31-12 (72%)	54-20 (73%)

As we can see, Marach/Pavic come in seventh with a very healthy 36-7 won-loss record this year. Their first loss came in the Rotterdam final, their fourth tournament after collecting titles in Doha, Auckland, and at the Australian Open–a streak of 17 consecutive match wins. If we ignore the all-time greats, there hasn’t been a better start to a men’s doubles season in the past 16 years.

The fact that the Bryan twins show up ten out of seventeen times in the table underlines just how dominant they were. And even though they did not win a Grand Slam in the last three years, they still had the best season starts in 2015 and 2016 (just barely missing the table, because they did not reach 30 match wins).

The last column gives a clue of what to expect from Marach and Pavic for the rest of the year. Most of the time, the teams at the very top only slightly decline. Notably, in 2007 the Bryan brothers maintained a win percentage of 88%, which led to the best doubles season in the dataset, measured by won-loss record.

After losing their seventh match this season at the 2018 French Open final to Herbert/Mahut and therefore missing the chance to win the first two majors of the season–a feat achieved in the open era only by the Bryans in 2013–it will be interesting to see if they will be able to sustain their level over a full season.

Peter Wetz is a computer scientist interested in racket sports and data analytics based in Vienna, Austria.

Men’s Doubles On the Dirt

Angelique Kerber wasn’t the only top seed to crash out early at this year’s French Open. In the men’s doubles draw, the top section opened up when Henri Kontinen and John Peers, the world’s top-ranked team, lost to the Spanish pair of David Marrero and Tommy Robredo. It’s plausible to attribute the upset to the clay, as Kontinen-Peers have tallied a pedestrian five wins against four losses on the dirt this season and one could guess that the Spaniards are at their strongest on clay.

Fortunately we don’t have to guess. Using a doubles variant of sElo–surface-specific Elo, which I began writing about a few days ago in the context of women’s singles–we can make rough estimates of how Kontinen/Peers would fare against Marrero/Robredo on each surface. The top seeds are solid on all surfaces–less than a year ago, they won a clay title in Hamburg–but stronger on hard courts. sElo ranks them 4th and 8th on hard, but 10th and 13th on clay among tour regulars.  Marrero is the surface-specialist of the bunch, ranking 37th on clay and 78th on hard. Robredo throws a wrench into the exercise, as he has played very little doubles recently, only eight events since the beginning of 2016.

Using these numbers–including those derived from Robredo’s limited sample–we find that sElo would have given Kontinen/Peers a 73.6% chance of winning yesterday, compared to a 78.3% advantage on a hard court. Even if we adjust Robredo’s clay-court sElo to something closer to his all-surface rating, the top seeds still look like 69% favorites.

A more striking example comes from yesterday’s other big upset, in which Julio Peralta and Horacio Zeballos took out Feliciano Lopez and Marc Lopez. On any surface, the Lopezes are the superior team, but Peralta and Zeballos have a much larger surface differential:

Player    Hard sElo  Clay sElo  
M Lopez        1720       1804  
F Lopez        1713       1772  
Zeballos       1651       1756  
Peralta        1517       1770

On a hard court, sElo gives the Lopezes a 68.1% chance of winning this matchup. But on clay, the gap narrows all the way to 53.6%. It’s still a bit of an upset for the South Americans, but not one that should come as much of a surprise.

Mismatches

I’ve speculated in the past that surface preferences aren’t as pronounced in doubles as they are in singles. Regardless of surface, points are shorter, and many teams position one player at the net even on the dirt. While some hard-courters are probably uncomfortable on clay (and vice versa), I wouldn’t expect the effects to be as substantial as they are in singles.

The numbers tell a different story. Here are the top ten, ranked by hard court sElo:

Rank  Player          Hard sElo  
1     Jack Sock            1947  
2     Nicolas Mahut        1893  
3     Marcelo Melo         1883  
4     Henri Kontinen       1879  
5     P-H Herbert          1862  
6     Bob Bryan            1851  
7     Mike Bryan           1846  
8     John Peers           1842  
9     Bruno Soares         1829  
10    Jamie Murray         1828

By clay court sElo:

Rank  Player                Clay sElo  
1     Mike Bryan                 1950  
2     Bob Bryan                  1950  
3     P-H Herbert                1894  
4     Nicolas Mahut              1889  
5     Jack Sock                  1887  
6     Robert Farah               1850  
7     Juan Sebastian Cabal       1849  
8     Pablo Cuevas               1824  
9     Rohan Bopanna              1812  
10    John Peers                 1810

Jamie Murray and Bruno Soares, who appear in the hard court top ten, sit outside the top 25 in clay court sElo. Robert Farah and Juan Sebastian Cabal are 41st and 42nd in hard court sElo, despite ranking in the clay court top seven. Pablo Cuevas, another clay court top-tenner, is 87th on the hard court list.

To go beyond these anecdotes–noteworthy as they are–we need to compare the level of surface preference in men’s doubles to other tours. To do that, I calculated the correlation coefficent between hard court and clay court sElo for the top 50 players (ranked by overall Elo) in men’s doubles, men’s singles, and women’s singles. (I don’t yet have an adequate database to generate ratings for women’s doubles.)

In other words, we’re testing how much a player’s results on one surface predict his or her results on the other major surface. The higher the correlation coefficient, the more likely it is that a player will have similar results on hard and clay. Here’s how the tours compare:

Tour             Correl  
Men's Singles     0.708  
Women's Singles   0.417  
Men's Doubles     0.323

In contrast to my hypothesis above, surface preferences in men’s doubles appear to be much stronger than in either men’s or women’s singles. (And there’s a huge difference between men’s and women’s singles, but that’s a subject for another day.)

Randomness

I suspect that the low correlation of surface-specific Elos in men’s doubles is partly due to the more random nature of doubles results. Because the event is more serve-dominated, there are more close sets ending in tiebreaks, and because of the no-ad, super-tiebreak format used outside of Slams, tight matches are decided by a smaller number of points. Thus, every doubles player’s results–and their various Elo ratings–reflect the influence of chance more than the singles results are.

Another consideration–one that I haven’t yet made sense of–is that surface-specific ratings don’t improve doubles forecasts they way that they do men’s and women’s singles predictions. As I wrote on Sunday, sElo represents a big improvement over surface-neutral Elo for women’s forecasts, and in an upcoming post, I’ll be able to make some similar observations for the men’s game. Using Brier score, a measure of the calibration of predictions, we can see the effect of using surface-specific Elo ratings in 2016 tour-level matches:

Tour             Elo Brier  sElo Brier  
Men's Singles        0.202       0.169  
Women's Singles      0.220       0.179  
Men's Doubles        0.171       0.181

The lower the Brier score, the more accurate the forecasts. This isn’t a fluke of 2016: The differences in men’s doubles Brier scores are around 0.01 for each of the last 15 seasons. By this measure, Elo does a very good job predicting the outcome of men’s doubles matches, but the surface-specific sElo represents a small step back. It could be that the smaller sample–using only one surface’s worth of results–is more damaging to forecasts in doubles than it is in singles.

Doubles analytics is particularly uncharted territory, and there’s plenty of work remaining for researchers even in this narrow subtopic. There’s lots of work to do for the world’s top doubles players as well, now that we can point to a noticeably weaker surface for so many of them.