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

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

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

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

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

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

Surface-specific Elo

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

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

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

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

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

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

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

The survivor

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

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

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

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

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

Current Elo ratings

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

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

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

Event History Pages at Tennis Abstract

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

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

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

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

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

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

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

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

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


Lleyton Hewitt and the Elusive Triple-Hundred

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

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

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

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

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

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

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

One Year of Heavy Topspin

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

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

Here’s to an even better year two!

Bernoulli and Court Tennis

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

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

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

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

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