451 Games in 10 Days

When Margaret Court won her first major title at the 1960 Australian Championships, the wonder isn’t that she broke through as a 17 year-old. It’s that she remained standing at all.

The news coverage ahead of the final praised Court’s game and foresaw great things for her future, but it also predicted a win for her opponent, 18-year-old Jan Lehane, who had beaten Court 6-1 6-0 in the 1959 juniors final. While Court (then unmarried, playing as Margaret Smith) had posted a more recent win over her rival, the issue that led the pundits to favor Lehane was scheduling. Court had barely stepped off the court for two weeks.

That’s where my title comes from: A preview of the final claimed that the teenager had played 451 games in 10 days. Unlike Lehane, who entered only the adult singles event, Court played singles and doubles, as well as girls’ singles and doubles. She reached the finals in women’s doubles and girls’ singles, as well as the semi-final in junior doubles.*

** one news report claimed she reached three other finals, but I have a score from the girls’ doubles semi-final showing Court and her partner, Val Wicks, as the losers.

She lost her first two finals, including the junior singles to another future tour stalwart, Lesley Turner, which suggested that fatigue was a factor. Making matters worse, both of those championship matches went three sets.

451 games?

In those days, the Australian Championships were a more modest affair than the present-day Australian Open. The field was mostly Australian, though in 1960, two elite foreigners, Brazilian Maria Bueno and Britain’s Christine Truman, made the trip. Bueno and Truman won the doubles, while Bueno lost to Court in their singles quarter-final, and Lehane saw off Truman in the semis. Still, the singles draw was only five rounds.

Since early-round matches were often blowouts (Court won her opener 6-1 6-0), I struggled to come up with those 451 games. Here’s a quick rundown of Court’s known matches in the tournament:

Sum it up, and we have 292 games, plus the total from two more probable rounds of girls’ doubles. (It’s also conceivable that there is one more early round of junior singles, though it seems unlikely that the juniors draw would be bigger than the adult field.) But even in the pre-tiebreak era, a few doubles matches probably didn’t account for more than 150 games.

One event is not enough

Just like today, the top players of six decades ago carefully managed their schedules. For instance, they might play only doubles in the week before Wimbledon. But in January 1960, Court was not a top player, and her schedule was largely at the whim of her state federation.

For Australian juniors, the few days before the Championships were given over to the Wilson Cup, an interstate team event. (Boys played a parallel Linton Cup event.) The 1960 Wilson Cup was a Fed Cup-style round robin among six Australian states, with each tie consisting of two singles and one doubles match.

Court, representing Victoria, got her fair share of warmup matches. I’ve found results from three days of Wilson Cup play. (There were likely five rounds, partly because that is the logical number in a six-team round robin, partly because the first day of results I found are listed as the “third round.”) Here are Court’s results:

  • Jan 19th vs New South Wales: singles d. Lehane, 6-1 6-3; doubles loss to Lehane/Dawn Robberds, 6-3 6-2.
  • Jan 20th vs Tasmania: singles d. Gourlay, 6-0 6-0. (Court didn’t play the doubles rubber.)
  • Jan 21st vs South Australia: singles d. Felicity Harris, 6-0 6-0. (I didn’t find a doubles result, and several matches that day appear to have been unplayed or unfinished due to rain.)

That’s 57 more games. A post-Wilson Cup note reported that Court dropped only eight games in her singles matches. If she played one more match, that’s another 16 games (say, a 6-2 6-2 win); if she played two, it’s 28 (for instance, 6-0 6-1 and 6-3 6-0). It also seems likely that she participated in another doubles match or two. Wilson Cup play started on the 18th and the “third round” took place on the 19th, so it’s possible that she three or four matches on the first day alone.

A fortnight to remember

While I can’t account for all 451 games (plus 20 more in the women’s singles final), we do have records of Court playing 13 singles matches, almost definitely 14, and possibly 15. We have scores for 5 doubles matches, almost definitely 7, and possibly as many as 10. We can be confident of a total of at least 365 games, with several more scores unaccounted for. All of this happened between the opening of the Wilson Cup on January 18th and the adult singles finals on February 1st.

I have no idea if this is a record. One challenger immediately springs to mind: The John IsnerNicolas Mahut match totaled 183 games, but Mahut lost his first-round doubles with another 46 games played. (Isner withdrew from doubles, and neither played mixed.)

Another contender is Martina Navratilova‘s 1986 Wimbledon campaign. As she tells it, rain forced her to play a whopping 17 matches in the second week alone. Yet despite reaching the finals in women’s singles, women’s doubles, and mixed doubles, she played “only” 333 games over the fortnight. (Her per-day rate in the second week might have surpassed Court’s.)

At least Court had the good sense not to enter mixed.

I don’t have a comprehensive doubles database, and junior records are even more sparse, so it’s not an easy record to confirm. A man, playing best-of-five in singles and (for many years) best-of-five in doubles, would be more likely to reach 400 or 500 games at a single major. It’s also possible that Navratilova tallied more games at a different major with fewer memorable scheduling problems; her 1986 effort easily cleared 300 games despite every match being settled in straight sets.

As for Court, she celebrated with a well-deserved break … of about one week. Within ten days, she was in New Zealand, where she lost to Ruia Morrison (a Maori tennis great, and a good story for another day) in another final. The national federation didn’t send her abroad that year, so she played a modest schedule for the remainder of the season. With our modern understanding of the importance of recovery, it seems like that was an excellent idea.

The Rarity of Winning Two Titles at One Tournament

This is a guest post by Peter Wetz.

With all the drama in the tennis world right now–paradoxically despite the lack of official match results–a dry analytical article might be just what you need. And what better opportunity than quarantine to work through my long list of articles to write?

In June 2019, Feliciano Lopez had to complete five matches in two days. Not because he had to hop between tournaments as a 22-year-old Jo-Wilfried Tsonga did in 2007, but because Lopez went deep into both the singles and doubles draws on the grass courts at Queen’s Club, ultimately winning both titles.

Lopez won all four of his singles matches in the deciding set, and there was not much time to celebrate and recover after the final, because the doubles title match awaited. Partnering a rehabilitating Andy Murray seems to have been a sensible decision based on the fact that Murray’s most lopsided head-to-head of 11-0 is against Lopez. By doing so, Lopez could be guaranteed to avoid facing Murray in the doubles draw. An unusual strategy–and probably not his top consideration in choosing a partner–but it worked.

Lifting two trophies on finals day happens quite often at the Challenger tour, but is unusual on the main tour, where the best singles players often skip the doubles draw entirely. But how rare is it? And has it changed over the years? Longtime fans will immediately think of John McEnroe and his nearly equal tally of doubles titles (78) and singles titles (77). The modest title counts of Roger Federer (6) and Rafael Nadal (11) pale in comparison, even though the Spaniard is an exceptional doubles player.

Let’s take a look at the instances when a player won both trophies at the same tournament since 2005.

Year	Tournament	Player (Partner)
2005	Dusseldorf	Tommy Haas (Alexander Waske)
2005	Halle		Roger Federer (Yves Allegro)
2005	Basel		Fernando Gonzalez (Agustin Calleri)
2006	Vina del Mar	Jose Acasuso (Sebastian Prieto)
2007	Chennai		Xavier Malisse (Dick Norman)
2007	Delray Beach	Xavier Malisse (Hugo Armando)
2007	Munich		Philipp Kohlschreiber (Mikhail Youzhny)
2007	Dusseldorf	Agustin Calleri (Juan Ignacio Chela)
2008	Monte Carlo	Rafael Nadal (Tommy Robredo)
2008	Dusseldorf	Robin Soderling (Robert Lindstedt)
2009	Costa Do Sauipe	Tommy Robredo (Marcel Granollers)
2009	San Jose	Radek Stepanek (Tommy Haas)
2009	Newport		Rajeev Ram (Jordan Kerr)
2010	Memphis		Sam Querrey (John Isner)
2010	Marseille	Michael Llodra (Julien Benneteau)
2010	Bucharest	Juan Ignacio Chela (Lukasz Kubot)
2011	Tokyo		Andy Murray (Jamie Murray)
2012	Zagreb		Mikhail Youzhny (Marcos Baghdatis)
2013	Newport		Nicolas Mahut (Edouard Roger Vasselin)
2014	Newport		Lleyton Hewitt (Chris Guccione)
2017	Montpellier	Alexander Zverev (Mischa Zverev)
2018	Gstaad		Matteo Berrettini (Daniele Bracciali)
2019	London		Feliciano Lopez (Andy Murray)

Two things may catch one’s eye when looking at the list: First, since 2011 the double-title feat occurred slightly less than once per year. But before that it happened several times a year with the sole exception of 2006. Second, the only player who managed to win both titles at a Masters event is Nadal at Monte Carlo in 2008.

It is obvious, and a frequent topic of tennis hipster talk, that top singles players do not care as much about doubles anymore, certainly not as much as McEnroe and his peers did. One line of argument is that the way that modern doubles tennis has evolved to become more and more different from the singles game. In order to keep up with that, singles players would need to adapt their practice routine, which might detract from potential singles success. Long story short, the argument is that doubles became too “difficult” for singles players.

But let’s look at the numbers. The following graphs show the composition of draws since the year 2000. We see the percentage of players in singles draws, who also entered the doubles draw of the same tournament for three different categories (A = All, M = Masters, G = Grand Slams). The first graph shows the numbers for top 50 singles players and the second graph for top 10 singles players.

Percentage of top 50 players entering doubles draws per 5 years
Percentage of top 10 players entering doubles draws per 5 years

The first graph is not very dramatic, but it establishes that the habits of top 50 singles players have been quite steady over the past 20 years among all tournament categories. Since the year 2000, irrespective of event categories, between 41 and 47 percent of top 50 players entering a singles draw also entered the doubles draw of the same tournament.*

The second graph shows us that the numbers for top 10 players are a different story entirely. Ignoring tournament categories, the number of top 10 players participating in doubles draws has plummeted from 35 to 22 percent. While the numbers also decreased if we only look at Masters tournaments, it is interesting that it remains higher than the overall number. This can likely be explained by the fact that the prize money for doubles at Masters events is significantly higher than at regular tour events. Often the organizers of these tournaments also have the financial power to persuade top players to play doubles in order to–I am hypothesizing here–increase ticket sales or attendance in the early days of a tournament. See the Indian Wells Masters for instance, which is known for its stellar doubles draw every year.

The most drastic decline in doubles attendance by top 10 singles players can be seen at the Grand Slams, however. While in the period between the years 2000 and 2004 every fifth singles player took part in the doubles, in the past five years only one out of 183 singles entries also appeared in the doubles draw. The sole exception (of course!) was Dominic Thiem, who entered the 2016 US Open doubles competition ranked number 10 in singles with his countryman Tristan Samuel Weissborn.

As with many analyses it is difficult to provide a definitive answer to the question at hand. But the numbers help us to see the size of the effects and theorize about its causes. That doubles competition has become more and more specialized certainly has its validity. At the same time, the numbers also suggest that top singles players simply optimize for prize money, which means focusing on singles, not doubles. If there was a McEnroe-esque player on tour today (as Rafa might be), he just wouldn’t play enough doubles to win nearly 80 titles.

However, it is hard to tell which was first: The decline of singles players playing doubles due to reasons such as financial motivation (among possibly many others), or the players’ realization that they simply cannot keep up with the elite doubles competition? One thing may be for sure though: Had TennisTV already existed a few decades ago, it would have shown a lot more doubles than it does now.

* Note that there is the possibility that a few singles players might have been willing to enter the doubles draw of a tournament, but couldn’t, because their ranking was too low among other reasons. However, I think this affects the analysis only marginally, if at all.

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

Grand Slam Prize Money Whack-a-Mole

Eagle-eyed Twitterer @juki_tennis noticed the following tweaks to the rules for the 2020 grand slams:

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

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

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

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

Paid withdrawals

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

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

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

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

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

One of two prongs

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

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

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

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

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

I promised to talk about doubles

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

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

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

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

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

Incentives and intentions

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

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

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

Salary, not prize money

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

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

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

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.


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

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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  
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.