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.

Podcast Episode 40: Fed Cup, the ATP Tour Finals, and a Sandbox Full of Rule Changes

Episode 40 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, starts with the Czech Republic’s victory in the Fed Cup final, and quickly diverts to a discussion of how we can evaluate players, and whether stylistic varietey is all it’s cracked up to be.

We preview the ATP Tour Finals, with a look at Djokovic, Federer, and a half-dozen dark horses, then discuss the plethora of experiments in progress at the NextGen Finals in Milan, including a fast-four-like scoring system, which neither of us are all that excited about, even if it’s supposed to make things more, well, exciting.

Thanks for listening!

(Note: this week’s episode is about 57 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

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Podcast Episode 39: Khachanov’s Paris Title, and WTA Finals in Review

Episode 39 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, covers the breakthrough Masters title of Karen Khachanov, along with the memorable semi-final between Novak Djokovic and Roger Federer. We also give an update on Jack Sock’s career choices and the career accomplishments of doubles whiz Rajeev Ram.

The second half of the episode is our recap of the WTA Finals in Singapore and the Elite Trophy in Zhuhai. We get distracted from our discussion of Svitolina, Sabalenka, and Barty by delving into the weeds of tournament formats, considering the pros and cons of the various round-robin and wild-card approaches that events use this time of year.

Thanks for listening!

(Note: this week’s episode is 61 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

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Podcast Episode 38: A Look at the WTA Finals Field

Episode 38 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, is our preview of the WTA tour championships. We look at Sloane’s weak position on the Elo table, Wozniacki’s comments about the strength of the field, and the strongest tacticians of the elite eight. We also consider the shifting career forecast of the resurgent Luxembourg finalist, Belinda Bencic.

We also have quick takes on Ivo Karlovic, who is setting records both in age and tiebreak frequency, and the new fifth-set tiebreak rule at Wimbledon. Thanks for listening!

(Note: this week’s episode is about 65 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

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Ivo Karlovic and the Odds-On Tiebreak

Italian translation at settesei.it

Ivo Karlovic is on track to accomplish something that no player has ever done before. Over the course of his career, Karlovic, along with John Isner, has set a new standard for one-dimensional tennis playing. The big men win so many service points that they are almost impossible to break, making their own service-return limitations manageable. With a player on court who maximizes the likelihood of service holds, tiebreaks seem inevitable.

This season, Karlovic has taken tiebreak-playing to a new level. Through last night’s semi-final at the Calgary Challenger (final score: 7-6, 7-6), the 6-11 Croatian has played 42 matches, including 115 sets and 61 tiebreaks. In percentage terms, that’s a tiebreak in 53% of all sets. Among player-seasons with at least 30 matches across the ATP, ATP qualifying, and ATP Challenger levels since 1990, no one has ever before topped 50%.

Even approaching the 50% threshold marks someone as very unusual. Less than 20% of tour-level sets reach 6-6, and it’s rare for any single player to top 30%. This year, only Isner and Nick Kyrgios have joined Karlovic in the 30%-plus club. Even Reilly Opelka, the seven-foot American prospect, has tallied only 31 tiebreaks in 109 sets this season, good for a more modest rate of 28.4%.

Karlovic is in truly uncharted territory. Isner came very close in his breakthrough 2007 season on the Challenger tour, playing 51 tiebreaks in 102 sets. The rest of the all-time top ten list starts to get a little repetitive:

Rank  Year  Player        Sets  TBs    TB%  
1     2018  Ivo Karlovic   115   61  53.0%  
2     2007  John Isner     102   51  50.0%  
3     2005  Ivo Karlovic   118   56  47.5%  
4     2016  Ivo Karlovic   146   68  46.6%  
5     2017  Ivo Karlovic    91   42  46.2%  
6     2006  Ivo Karlovic   106   48  45.3%  
7     2015  Ivo Karlovic   168   76  45.2%  
8     2018  John Isner     149   65  43.6%  
9     2001  Ivo Karlovic    78   34  43.6%  
10    2004  Ivo Karlovic   140   61  43.6%

* Karlovic’s and Isner’s 2018 totals are through matches of October 20th. 

For more variety, here are the 15 different players with the highest single-season tiebreak rates:

Rank  Year  Player           Sets  TBs    TB%  
1     2018  Ivo Karlovic      115   61  53.0%  
2     2007  John Isner        102   51  50.0%  
3     2004  Amer Delic         95   37  38.9%  
4     2008  Michael Llodra    117   45  38.5%  
5     2008  Chris Guccione    173   65  37.6%  
6     2002  Alexander Waske   109   40  36.7%  
7     1993  Greg Rusedski      99   35  35.4%  
8     2017  Reilly Opelka     115   40  34.8%  
9     2005  Wayne Arthurs      95   33  34.7%  
10    2004  Dick Norman        97   33  34.0%  
11    2001  Ivan Ljubicic     148   50  33.8%  
12    2004  Max Mirnyi        137   46  33.6%  
13    2014  Samuel Groth      172   57  33.1%  
14    2005  Gregory Carraz     98   32  32.7%  
15    2007  Fritz Wolmarans    80   26  32.5%

Karlovic is truly in a class by himself. He’ll turn 40 next February, but age has had little impact on the effectiveness of his serve. While he reached his career peak ranking of No. 14 back in 2008, it was more recently that his serve was at its best. In 2015, he won more than three-quarters of his service points and held 95.5% of his serve games. Both of those marks were career highs. His recent serve stats have remained among his career bests, winning 73.5% of service points in 2018, though as his ranking has tumbled, these feats have come against weaker competition, in ATP qualifying and Challenger matches.

Age has taken its toll, however, and Ivo’s return game is the victim. From 2008-12, he broke serve in more than one out of ten chances, while in 2016-18, it has fallen below 8%. Neither mark is particularly impressive–Isner and Kyrgios are the only tour regulars to break in less than 17% of games this season–but the difference, from a peak of 12.0% in 2011 to a low of 7.1% this year, helps explain why the Croatian is playing more tiebreaks than ever.

Karlovic has long been one of the most unique players on tour, thanks to his height, his extreme statistical profile, and his willingness (or maybe his need) to approach the net. As he gets older and his game becomes even more one-dimensional, it’s only fitting that he breaks some of his own records, continuing past the age when most of his peers retire in order to hit even more aces and play even more tiebreaks.

Daniil Medvedev’s Leading Elo Indicator

Italian translation at settesei.it

It is shaping up to be a breakthrough season for 22-year-old Russian Daniil Medvedev. His Tokyo title two weeks ago was his first at the ATP 500 level and his third on the season, after earlier triumphs in Sydney and Winston-Salem. The run in Japan was a particularly notable step, since he knocked out three top-20 players along the way. He had only four top-20 victories in the entire season leading up to Tokyo, and two of those were against the slumping Jack Sock.

His ATP ranking is rising alongside his results. The Winston-Salem title moved him into the top 40, and the Tokyo trophy resulted in a leap to No. 22. After a first-round win in Shanghai last week, Medvedev crept to his current career-high of No. 21. With a couple of wins in Moscow this week, he could overtake Milos Raonic and reach the top 20.

The improvement on the ATP ranking table is nothing next to the Russian’s race to the top of the Elo list. Last Monday, with the Japanese title in the books, Medevdev rose to No. 8 on my men’s Elo ranking. Since then, he has dropped two places but remains in the top ten, ahead of Marin Cilic, Kevin Anderson, and a host of others who outrank him on the official ATP list.

Given the discrepancy, what do we believe? Is Medvedev inside the top 10 or outside the top 20? Is Elo a leading indicator–that is to say, an early-warning signal for future ATP ranking milestones–or a misleading one? Elo is designed to be forward-looking, tuned to forecast upcoming match outcomes and weighting wins and losses based on the quality of the opponent. The official rankings explicitly consider a year’s worth of results, with no adjustments for quality of competition. In theory, Elo should be the better of the two measures for predicting longer-term results, but that assumes the algorithm works well, and that it doesn’t overreact to short-term successes. Let’s take a look at past differences between the two systems and see what the future might hold for the 22-year-old.

Precedents

Since 1988, 102 men have debuted in the ATP top ten. A slightly larger number, 113, have shown up in the top ten of my Elo ratings. There’s a very substantial overlap between the two, with 94 names appearing in both categories. Thus, 8 players have reached the ATP top ten without clearing the Elo threshold, while 19 have rated a spot in the Elo top ten without convincing the ATP computer to agree.

Here are the eight ATP top-tenners whose Elos have never merited the same status:

Player               ATP Top Ten Debut  ATP Top Ten Weeks  
Jonas Svensson                19910325                  5  
Nicolas Massu                 20040913                  2  
Radek Stepanek                20060710                 12  
Jurgen Melzer                 20110131                 14  
Juan Monaco                   20120723                  8  
Kevin Anderson                20151012                 31  
Pablo Carreno Busta           20170911                 17  
Lucas Pouille                 20180319                  1

A few of these players could still make progress on the Elo list, especially Kevin Anderson, who is currently 11th, a miniscule five points behind Medvedev.

Here is the longer list of Elo top-ten players without any weeks in the official top ten:

Player                 Elo Top Ten Debut  Elo Top Ten Weeks  
Carl Uwe Steeb                1989/05/22                  3  
Andrei Cherkasov              1990/12/11                  1  
Goran Prpic                   1991/05/20                  1  
David Wheaton                 1991/07/08                  9  
Jerome Golmard                1999/05/03                  2  
Dominik Hrbaty                2001/01/15                  2  
Jan Michael Gambill           2001/04/06                  6  
Nicolas Escude                2002/02/25                  4  
Younes El Aynaoui             2002/05/20                  2  
Paul Henri Mathieu            2002/10/14                  8  

Player                 Elo Top Ten Debut  Elo Top Ten Weeks
Agustin Calleri               2003/05/19                  2  
Taylor Dent                   2003/10/06                 10  
Andrei Pavel                  2004/05/10                  2  
Robby Ginepri                 2005/10/24                  1  
Ivo Karlovic                  2007/11/12                  3  
Roberto Bautista Agut         2016/02/22                  1  
Nick Kyrgios                  2016/03/04                 62  
Stefanos Tsitsipas            2018/08/13                  3  
Daniil Medvedev               2018/10/08                  2

* I define ‘weeks’ a little differently for Elo ratings, as ratings are generated only for those weeks with an ATP-level tournament or Davis Cup tie.

Most of these guys came very close to cracking the ATP top ten. For example, David Wheaton’s peak ranking was No. 12. With the exception of Nick Kyrgios, no one spent more than ten weeks in the Elo top ten without eventually reaching the same standard according to the ATP formula. This list shows that it’s possible to have a brief peak that cracks the Elo top ten but doesn’t last long enough to reflect the kind of success that the official ranking system was designed to reward. About one in six players with a top-ten Elo rating never reached the ATP top ten, though as we can see, the odds of remaining an Elo-only star fall quickly with each additional week in the top ten.

Kyrgios is a perfect example of the differences between the two approaches to player ranking. The Australian has recorded a number of high-profile upsets, which are the fastest way to climb the Elo list. But knocking out the second-ranked player in the world, as Kyrgios did to Novak Djokovic at Indian Wells last year, doesn’t have much impact on the ATP ranking when it happens in the fourth round. Usually, a player who can oust the elites will start piling up wins in a form that the official computer will appreciate. But Kyrgios, unlike just about every player in history with his talent, hasn’t done that.

In short, Elo will always elevate a few players to top-ten status even if they’ll never deserve the same treatment from the ATP formula. It’s too early to say whether Medvedev fits that mold. But where Elo really excels is identifying top players before the ATP computer does. Of the 94 cases since 1988 in which a man debuted in both top tens, Elo was first to anoint the player a top-tenner in 76 of them–better than 80%. The official rankings were first 10 times, and the two systems tied in the other eight instances. On average, players reached the Elo top ten about 32 weeks before the ATP top ten.

Here are the 11 most extreme gaps in which Elo got there first, along with the top-ten debuts of the Big Four:

Player               ATP Debut   Elo Debut  Week Diff  
Mariano Puerta      2005/07/25  2000/06/12        267  
Marc Rosset         1995/07/10  1990/11/05        244  
Fernando Gonzalez   2006/04/24  2002/10/07        185  
Guillermo Canas     2005/05/09  2002/08/05        144  
Mikhail Youzhny     2007/08/13  2004/11/15        143  
Gaston Gaudio       2004/06/07  2002/04/29        110  
Richard Gasquet     2007/07/09  2005/06/20        107  
Tomas Berdych       2006/10/23  2004/10/11        106  
Robin Soderling     2009/10/19  2007/10/08        106  
Mark Philippoussis  1999/03/29  1997/03/24        105  
Jack Sock           2017/11/06  2016/01/18         94  
                                                       
Player               ATP Debut   Elo Debut  Week Diff  
Roger Federer       2002/05/20  2001/02/19         65  
Andy Murray         2007/04/16  2006/08/21         34  
Novak Djokovic      2007/03/19  2006/07/31         33  
Rafael Nadal        2005/04/25  2005/02/21          9

And in case you’re curious, the ten cases in which the ATP computer beat Elo to the punch:

Player              ATP Debut   Elo Debut  Week Diff  
Stan Wawrinka      2008/05/12  2010/10/25        128  
David Ferrer       2006/01/30  2007/05/28         69  
Janko Tipsarevic   2011/11/14  2012/05/13         26  
Rainer Schuettler  2003/06/09  2003/08/25         11  
Tommy Robredo      2006/05/08  2006/07/24         11  
Fernando Verdasco  2009/02/02  2009/04/06          9  
Albert Costa       1997/04/21  1997/05/26          5  
Nicolas Almagro    2011/04/25  2011/05/22          4  
John Isner         2012/03/19  2012/04/15          4  
Jiri Novak         2002/10/14  2002/10/21          1

The 32-week average difference is suggestive. As I’ve noted, Elo ratings are optimized to forecast the near future, so at least in theory, they reflect each player’s level right now. The ATP algorithm tallies each man’s performance over 52 weeks, with equal weight given to the first and last weeks in that timeframe. Setting aside improvement and decline due to age, that means the ATP computer is telling us how each player was performing, on average, 26 weeks ago. If Medvedev continues to oust top-20 players on a regular basis and claims another 500-level title or two, he could well be 26 or 32 weeks away from a top-ten debut.

Elo isn’t designed to make long-term forecasts–the tools needed to do so, for the most part, have yet to be invented. And the system occasionally gives high ratings to players who don’t sustain them for very long. But in general, a superlative Elo rating is a sign that a similar mark on the ATP ranking list isn’t far behind. So far, Kyrgios has managed to defy the odds, but the smart money still points to an eventual ATP top-ten debut for Medvedev.

Podcast Episode 37: Djokovic and Halep Pad Their Career Totals

Episode 37 of the Tennis Abstract Podcast, with Carl Bialik of the Thirty Love podcast, opens with a discussion of Borna Coric’s future, along with the difficulty of forecasting 21 year olds in an era when men don’t peak until much later. We touch on Roger Federer’s unusually weak performance in the Shanghai semi-final, as well as Novak Djokovic’s dominant return of serve and his growing pile of Masters trophies.

We also look ahead to the year-end championship fields in London and Singapore, and consider Simona Halep’s place in history, now that she has sealed the year-end number one ranking for the second consecutive season.

Thanks for listening!

(Note: this week’s episode is about 62 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

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

Update: Episode index with links, thanks to FBITennis:

Forecasting young players 1:07
Assessing Roger Federer after Shanghai 8:53
How good is Djokovic’s return game? 16:16
Adjusting titles for strength of opponent 24:10
Do the Masters’ surfaces suppress Fed’s achievements? 30:20
Who is the favorite for the ATP Tour Finals (London)? 36:18
Who is the favorite for the WTA Finals (Singapore)? 41:30
Is Halep an all-time Top 10 WTA player? 49:58
ELO as a leading indicator of (next) year-end ranking 58:50

The Rosy Forecast of Arnya Sabalenka’s Elo Rating

Italian translation at settesei.it

It’s been almost two weeks since Aryna Sabalenka’s last title, and the next one is starting to feel overdue. With respect to Naomi Osaka’s ascent, the Belarussian is the hottest rising star on the women’s tour right now, with two titles in the last two months, plus two more finals earlier in the season. The 20-year-old is 8-4 against the top ten this year, with wins over Caroline Wozniacki, Petra Kvitova, Elina Svitolina, and Karolina Pliskova.

It takes time for all of these wins to show up in the WTA rankings. Sabalenka nudged into the top 20 after winning New Haven in August, and rose as high as 11th last Monday, though she is set to fall back to 14th after failing to defend her title in Tianjin this week. While the official ranking is a lagging indicator, Elo ratings react more quickly, especially to high-profile upsets like the ones Sabalenka has been recording almost every week.

Sabalenka’s Elo rating has rocketed to the top of the list. Through last week’s matches, she sits at second overall, behind Simona Halep, but closer to Halep than to third-place Wozniacki. After knocking out Caroline Garcia in Beijing last week, she briefly took over the Elo top spot before handing it back after her quarter-final loss to Qiang Wang. Still, an overall ranking of #2 is a lot more suggestive of future stardom than the WTA computer’s report of #11.

When Elo looks at hard court matches alone, it is even more optimistic, putting Sabalenka at the very top of the list. Elo would narrowly favor the Belarussian in a hard-court match against Halep and, assuming the draw treated both players equally, would make Sabalenka the early favorite for the 2019 Australian Open title.

What should we make of this? Is it time to appoint Sabalenka the next superstar, or ought we treat Elo ratings with more circumspection? Let’s take a look at players who have topped the Elo list in the past to get a better idea.

Since 1984, only 29 women (including Sabalenka) have reached the #1 or #2 spot on the overall Elo list. 19 of them got to #1 in the official rankings. Here are the other ten:

Player               Peak  
Petra Kvitova           2  
Conchita Martinez       2  
Jana Novotna            2  
Agnieszka Radwanska     2  
Elina Svitolina         3  
Gabriela Sabatini       3  
Elena Dementieva        3  
Samantha Stosur         4  
Johanna Konta           4  
Aryna Sabalenka        11

This is pretty good company. Svitolina could still reach #1, and several of the others were expected to attain even greater heights than they did. The only warning sign here is Johanna Konta, who isn’t the best comp for a young star, as she didn’t crack the top two until close to her 26th birthday.

The group of women who have ranked #1 on the hard-court specific Elo ranking table is even more select. Sabalenka is only the 17th player since 1984 to head the list, and 14 of the 17 have topped the official rankings as well. The only other exceptions are Svitolina and Konta.

If there’s ever a good time to anoint a 14th-ranked player the future of the sport, I’d say this is it. Elo isn’t perfect, and it’s possible that the algorithm has overreacted to a series of upsets in a season packed full of them. But if the system has made a mistake, it’s one that it doesn’t make very often. Sabalenka has only won four main-draw matches at majors, so maybe that 2019 Australian Open title is too much to ask. But in the long term, one grand slam title might be a mere harbinger of even greater things to come.

The All-Time ATP Masters Race Is Even Closer Than You Think

Italian translation at settesei.it

As I write this, Novak Djokovic has earned himself a place in the semi-finals at the Shanghai Masters, putting him two wins away from his 32nd career ATP Masters title. A championship this week would leave him one behind Rafael Nadal, the all-time leader with 33 Masters victories. Roger Federer, also in action today in Shanghai, is not far back, with a career total of 27.

Masters tallies aren’t as important as grand slam counts, but they make up an important part of an elite player’s resume. For one thing, there are more of them, and the mix of surfaces–more clay, no grass, and an indoor event–adds to our knowledge of a player’s range of skills. It’s no surprise that Nadal, Djokovic, and Federer are miles ahead of the pack on this list, as on so many others.

But all Masters aren’t created equal. At last year’s Madrid Masters, Nadal had to defeat Djokovic, as well as clay-court giant Dominic Thiem and the ever-threatening Nick Kyrgios. Six months later in Paris, Jack Sock earned the same number of Masters titles by coasting down a path that included only one player ranked in the top 35. Like major titles, Masters championships are heavily influenced by luck, and when we focus on raw totals, we trust that fortune tends to even out.

It doesn’t even out, even for the top players who have played Masters events for more than a decade and racked up dozens of titles. To account for opponent quality and the difficulty of each title, I applied the same algorithm I’ve used in the past to rate slam titles. [1] The formula spits out a number for each Masters title, where 1 is average, less than 1 is easier than the norm, and greater than 1 is more difficult. Sock’s Paris trophy was the luckiest in recent years, clocking in at 0.39, while David Nalbandian’s 2007 Madrid title was the most difficulty, rating 1.92. These extremes nothwithstanding, almost every championship comes in between 0.5 and 1.5.

The all-time tally

Let’s start by looking at the top ten in “adjusted Masters.” The table below shows the results of my formula, alongside each player’s actual Masters count, and the average rating of the tournaments he has won:

Player          Adj Masters  Masters  Average  
Rafael Nadal           35.4       33     1.07  
Novak Djokovic         35.0       31     1.13  
Roger Federer          28.0       27     1.04  
Andre Agassi           15.0       17     0.88  
Andy Murray            15.0       14     1.07  
Pete Sampras           11.2       11     1.02  
Thomas Muster           7.5        8     0.94  
Michael Chang           6.4        7     0.91  
Boris Becker            5.4        5     1.08  
Jim Courier             5.0        5     1.00

Boris Becker and Jim Courier aren’t the only men to have recorded five Masters titles, but they are only ones who have done so against average or better competition. Andy Roddick won five, but the algorithm gives him credit for just under four, and it is even more harsh on Marat Safin, whose five victories translate into only 3.2 adjusted Masters.

The real story is at the top of the list, where adjusting for competition almost eliminates the gap between Nadal and Djokovic. Both men have won their titles against more difficult than average competition (often, by beating each other), but Djokovic has faced the tougher paths. If he wins on Sunday in Shanghai, he’ll overtake Nadal’s adjusted tally.

Also of note is the near-tie between Andre Agassi and Andy Murray. Agassi holds three more trophies, but won them against the weakest competition of anyone in the top ten. Murray has dealt with much of the same field that Nadal and Djokovic have, so it’s no surprise to see his difficulty rating well above 1.0.

The Paris swoon

Sock’s title last year was unquestionably weak, but not entirely out of character for Bercy. With the exception of the short-lived Essen Masters, Paris titles have come the cheapest of any other tour stop at this level:

Tournament            Years  Average Rating  
Madrid (clay)            10            1.18  
Rome Masters             29            1.09  
Indian Wells Masters     29            1.07  
Stuttgart Masters         6            1.05  
Stockholm Masters         5            1.04  
Hamburg Masters          19            1.02  
Miami Masters            29            1.01  
Monte Carlo Masters      29            0.98  
Canada Masters           29            0.97  
Cincinnati Masters       29            0.97  
Madrid (hard)             7            0.97  
Shanghai Masters          9            0.95  
Paris Masters            28            0.84  
Essen Masters             1            0.80

Paris was played on carpet until 2006, and that may be a factor. When I first ran the numbers, I used carpet-specific Elo ratings, which are limited by a relatively small sample. I tried again using hard-court ratings for carpet events, and while individual numbers shifted up and down, the overall results were about the same. Bercy was particularly weak during the carpet era, and it has gotten stronger, but I’m confident this is a feature of the results in the 1990s and early 2000s, not merely an artifact of Elo rating quirks.

Still, broadly speaking, fast courts seem to result in lower ratings. I suspect that’s because at predominantly best-of-three events, early-round upsets are more likely to occur on the quickest surfaces. Fast courts, then, effectively gut the field for the eventual champion. It certainly worked for Sock last year. But it’s no guarantee–the five most difficult Masters titles all came on hard courts, and one of them took place in Paris.

Peak Nalbandian

At the end of 2007, Nalbandian enjoyed two of the most glorious weeks of tennis ever played. In Madrid, he defeated Nadal in the quarters, Djokovic in the semis, and Federer in the final, not to mention Tomas Berdych and Juan Martin del Potro in the early rounds. Two weeks later, he beat Federer and Nadal again in Paris, along with wins over David Ferrer, Richard Gasquet, and Carlos Moya. Those two titles rate 1.92 and 1.70, respectively, and are two of the three most difficult since the Masters series began.

(Oddly enough, the only man who could stop Nalbandian that fall was Stan Wawrinka, who beat him both in Vienna and Basel. Wawrinka’s slam titles rate as the most difficult in that category.)

Here are the 20 most difficult Masters titles, along with their ratings:

Year  Event         Surface  Champion            Rating  
2007  Madrid        Hard     David Nalbandian      1.92  
2014  Canada        Hard     Jo Wilfried Tsonga    1.78  
2007  Paris         Hard     David Nalbandian      1.70  
2007  Canada        Hard     Novak Djokovic        1.68  
2009  Indian Wells  Hard     Rafael Nadal          1.61  
2009  Madrid        Clay     Roger Federer         1.52  
2017  Madrid        Clay     Rafael Nadal          1.52  
2016  Madrid        Clay     Novak Djokovic        1.51  
2011  Indian Wells  Hard     Novak Djokovic        1.50  
2013  Indian Wells  Hard     Rafael Nadal          1.50  
                                                         
Year  Event         Surface  Champion            Rating  
2010  Canada        Hard     Andy Murray           1.48  
2011  Rome          Clay     Novak Djokovic        1.48  
2012  Rome          Clay     Rafael Nadal          1.47  
2010  Indian Wells  Hard     Ivan Ljubicic         1.45  
2004  Hamburg       Clay     Roger Federer         1.44  
2015  Cincinnati    Hard     Roger Federer         1.44  
2013  Rome          Clay     Rafael Nadal          1.43  
2015  Canada        Hard     Andy Murray           1.43  
2008  Monte Carlo   Clay     Rafael Nadal          1.42  
2015  Madrid        Clay     Andy Murray           1.42

Nalbandian and Jo Wilfried Tsonga stand out at the top, but after that, it’s a whole lot of Big Four. Even in the next ten toughest paths, Djokovic, Nadal, and Federer account for seven.

Like just about any adjustment to high-profile counting stats, tweaking Masters titles for difficulty doesn’t exactly clear up the debate over the greatest players of all time. This is only one small part of that conversation. However, seeing the wide range of challenges faced by Masters champions is a necessary reminder that not all titles are the same, even if they all count for one thousand ATP ranking points.

[1] Here’s how I first described the algorithm:

To evaluate the overall difficulty of grand-slam titlists’ draws, I used Elo—a rating system that assesses a player’s strength based on his won-lost record and the quality of his opponents—to measure the skill of an average major champion. I then estimated the probability that such a player would have won all seven matches against the opponents that each tournament’s victor had to face. For each win, I credit the champion with the difference between one and the Elo forecast: If an average slam champion on the tournament’s surface had a 90% chance of winning the match, the player gets 0.1 points (1 – 0.9); if a typical major winner would have gone in with a 20% shot, he’s assigned 0.8. Summing all the matches for each winner and applying the algorithm to the last several decades of grand slams results in an average credit of 1.23 per titlist, so I then divided each sum by 1.23 to normalise the results.

For Masters events, it’s five or six matches instead of seven, and the final step involves dividing by 1.34 instead of 1.23.

Podcast Episode 36: Knights of the Federer Roundtable

Episode 36 is a very special edition of the Tennis Abstract Podcast. I’m joined (in person!) by my co-host Carl Bialik ,of the Thirty Love podcast, along with Federer super-fans and stats junkies Edo Salvati (of settesei.it) and Sulaiman Ijaz.

With this overwhelming amount of analytical enthusiasm gathered around a conference room table in Helsingør, Denmark, we delve into the GOAT debate, trying to take a balanced approach despite our likely Fed bias. We consider the value of weighting slam titles for draw difficulty, the importance of weeks at number one, the surface balance of Masters tournaments … even the doubles prowess of the men in the conversation. We also speculate about the eventual career tallies of Nadal and Djokovic, and what might tilt the debate in a new direction.

This was a really fun episode to record, so I hope you’ll enjoy it as much as we did.

(Note: this week’s episode is about 94 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

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