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

How Elo Rates US Open Finalists Flavia Pennetta and Roberta Vinci

Among the many good things that have happened to Flavia Pennetta and Roberta Vinci after reaching the final of this year’s US Open, both enjoyed huge leaps in Monday’s official WTA rankings. Pennetta rose from 26th to 8th, and Vinci jumped from 43rd to 19th.

Such large changes in rankings are always a little suspicious and expose the weakness of systems that award points based on round achieved. A lucky draw or one incredible outlier of a match doesn’t mean that a player is suddenly massively better than she was a couple of weeks ago.

To put it another way: As they are, the official rankings do a decent job of representing how a player has performed. What they don’t do so well is represent how well someone is playing, or the closely related issue of how well she will play.

For that, we can turn to Elo ratings, which Carl Bialik and Benjamin Morris used at the beginning of the US Open to compare Serena Williams to other all-time greats [1]. Elo awards points based on opponent quality, not the importance of the tournament or round. As such, the system provides a better estimate of the current skill level of each player than the official rankings do.

Sure enough, Elo agrees with my hypothesis, that Pennetta didn’t suddenly become the 8th best player in the world. Instead, she rose to 17th, just behind Garbine Muguruza (another Slam finalist overestimated by the rankings) and ahead of Elina Svitolina. Vinci didn’t really return to the top 20, either: Elo places her 34th, between Camila Giorgi and Barbora Strycova.

While her official ranking of 8th is Pennetta’s career high, Elo disagrees again. The system claims that Pennetta peaked during the US Open six years ago, after a strong summer that involved semifinal-or-better showings in four straight tournaments, plus a fourth-round win over Vera Zvonareva in New York. She’s more than 100 points below that career-high level, equivalent to the present gap between her and 7th-Elo-rated Angelique Kerber.

The current Elo rankings hold plenty of surprises like this, having little in common with the official rankings:

Rank  Player                 Elo  
1     Serena Williams       2460  
2     Maria Sharapova       2298  
3     Victoria Azarenka     2221  
4     Simona Halep          2204  
5     Petra Kvitova         2174  
6     Belinda Bencic        2144  
7     Angelique Kerber      2130  
8     Venus Williams        2126  
9     Caroline Wozniacki    2095  
10    Lucie Safarova        2084

Rank  Player                 Elo   
11    Ana Ivanovic          2078  
12    Carla Suarez Navarro  2062  
13    Agnieszka Radwanska   2054  
14    Timea Bacsinszky      2041  
15    Sloane Stephens       2031  
16    Garbine Muguruza      2031  
17    Flavia Pennetta       2030  
18    Elina Svitolina       2023  
19    Madison Keys          2019  
20    Jelena Jankovic       2016

While Victoria Azarenka is still nearly 200 points shy of her peak, Elo gives her credit for the extremely tough draws that have met her return from injury. Another player rated much higher here than in the WTA rankings is Belinda Bencic, whose defeat of Serena launched her into the top ten.

The oldest final

Pennetta and Vinci are both unusually old for Slam finalists, not to mention players who reached that milestone for the first time. Elo doesn’t consider them among the very best players active today, but next to other 32- and 33-year-olds in WTA history, they compare very well indeed.

Among players 33 or older, Pennetta’s current rating is sixth best in the last thirty-plus years [2]. As the all-time list shows, that puts her in extraordinarily good company:

Rank  Player                Age   Elo  
1     Martina Navratilova  33.4  2527  
2     Serena Williams      33.9  2480  
3     Chris Evert          33.4  2412  
4     Venus Williams       33.3  2175  
5     Nathalie Tauziat     33.9  2088  
6     Flavia Pennetta      33.5  2030  
7     Wendy Turnbull       33.1  2018  
8     Conchita Martinez    33.3  2014

In the 32-and-over category, Vinci stands out as well. Her lower rating, combined with the somewhat larger pool of players who remained competitive to that ago, means that she holds 24th place in this age group. For a player who has never cracked the top ten, 24th of all time is an impressive accomplishment.

Keep an eye out for more Elo-based analysis here. Soon, I’ll be able to post and update Elo ratings on Tennis Abstract and, once a few more kinks are worked out, use them to improve the WTA tournament forecasts on the site as well.

Continue reading How Elo Rates US Open Finalists Flavia Pennetta and Roberta Vinci

Is Kevin Anderson Developing Into an Elite Player?

With his upset win over Andy Murray on Monday, Kevin Anderson reached his first career Grand Slam quarterfinal. At age 29, he’ll ascend to a new peak ranking, and with a bit of cooperation from the rest of the draw, one more win could put him in the top ten for the first time.

Anderson has been a stalwart in the top 20 for two years now, but this additional step comes as a bit of a surprise. Despite the overall aging of the ATP tour and the emergence of Stan Wawrinka as a multi-Slam champion, it’s still a bit difficult to imagine a player in his late twenties taking major steps forward in his career.

What’s more, Anderson’s game is very serve-dependent. With an excellent backhand, he isn’t as one-dimensional a player as John Isner, Ivo Karlovic, or perhaps even Milos Raonic, but it’s much easier to categorize him with those players than with more baseline-oriented peers.

In today’s game, it is very difficult to reach the very top ranks without a quality return game. Tiebreaks are too much of a lottery to depend on in the long-term; you have to consistently break serve to win matches. As I wrote in a post about Nick Kyrgios earlier this year, almost no players have finished a season in the top ten without winning at least 37% of return points. Anderson has achieved that mark only once, in 2010. Entering the US Open this year, he was winning only 34.2% of return points.

The only top-ten player this year with a lower rate of return points won is Raonic, at 30.2%. Raonic is a historical anomaly, and as his tiebreak winning percentage has tumbled, from a near-record 75% last year to a more typical 51% this year, his place in the top ten is in jeopardy as well. In other words, the only servebot in the top ten has to rely on plenty of luck–or outstanding, perhaps one-of-a-kind skills in the clutch–to remain among the game’s elite.

Anderson is a more well-rounded player than Raonic, and he wins more return points than that. But he still falls well short of the next-worst return game in the top ten, Wawrinka’s 36.7%. The 2.5 percentage points between Anderson and Wawrinka represent a big gap, almost one-fifth of the entire range between the game’s best and worst returners.

The less effective a player’s return game, the more he must rely on tiebreaks to win sets, and that’s one explanation for Anderson’s success this season. His 62%(26-16) tiebreak winning percentage in 2015 is the best of his career, and considerably higher than his career tiebreak winning percentage of 54%. Again, it sounds like a small difference, but take away three or four of the tiebreaks he’s won this year, and he no longer reached the final at Queen’s Club … or might not be preparing for a quarterfinal in New York.

Very few players have managed to spend meaningful time in the top ten while depending so heavily on winning tiebreaks. Another metric to help us see this is the percentage of sets won that are won in tiebreaks. Entering the US Open, just over 25% of Anderson’s sets won were won in tiebreaks. Only four times since 1991 has a player sustained a rate that high and ended the year in the top ten: Raonic last year, Andy Roddick in 2007 and 2009, and Greg Rusedski in 1998.

In fact, between 1991 and 2014, only 17 times did a player finish a season in the top ten with this rate above 20%. Roddick represents five of those times, and almost all, except for Roddick at his peak, were players who finished outside the top five. Wawrinka’s and Raonic’s 2014 seasons were the only occurrences in the last decade.

The one ray of light in Anderson’s statistical profile this season is a significantly improved first serve. His 2015 ace rate is over 18%, compared to the 2014 (and career average) rate of 14%. His percentage of first-serve points won is up to 78.8%, from last season’s 75.4% and a career average of 75.8%.

This is a major improvement, and is the reason why he is one of only five players on tour (along with Isner, Karlovic, Roger Federer, and Novak Djokovic) winning more than 69% of service points this year. In many ways, Anderson’s stats are similar to those of Feliciano Lopez, but the Spaniard–another player who has long stood on the fringes on the top ten–has never topped 68% of service points won for a full season.

If Anderson can sustain this new level of first-serve effectiveness, he will–at the very least–continue to see a bit more success in tiebreaks. A tiebreak winning percentage higher than his career average of 54% (though still probably below his 2015 rate of 62%) will help keep him in the top 15. However, even for the best servers, tiebreaks are often little more than coin flips, and players don’t join the game’s elite by relying on coin flips.

As his quarterfinal appearance at the Open shows, Anderson is moving in the right direction. It’s easy to see a path for him that involves ending the season in the top ten. But to move up to the level above that, following the path of someone like Wawrinka, he’ll need to start serving like peak Andy Roddick, or–perhaps just as difficult–significantly improve his return game.

Tommy Robredo and the Men Who Beat Number One

Today in Cincinnati, Tommy Robredo took out the top-ranked player in the world, Novak Djokovic, in straight sets. Robredo has had a fine career, peaking in the top five and beating many of the world’s best, but it was only the second time in eight tries that he managed to defeat a reigning world number one.

The first time Robredo accomplished the feat was more than eleven years ago, at the 2003 French Open, where he upset Lleyton Hewitt in five sets. Since then, his only chances to beat number ones have come against Roger Federer, and he lost in all five tries. When the Spaniard finally scored a win over Fed in New York last year, Roger had long since fallen out of the top spot.

With today’s win, Robredo becomes the 66th man since the advent of the ATP ranking system who has beaten at least two different number ones. Only 13 active players have managed the feat.

23 players in ATP history have beaten at least three players who were ranked number one at the time. Coincidentally, the man who defeated the most number ones was present at today’s match. Boris Becker upset six different players in the top spot, compiling a very impressive 19-16 career record against players ranked number one.

Next on the list is Michael Chang, who beat five different number ones (though he only won 7 of 27 matches against them), while Federer, Andre Agassi, Greg Rusedski, and Dominik Hrbaty beat four. Four more active players have defeated three number ones: Andy Murray , David Ferrer, Juan Martin del Potro, and Jo-Wilfried Tsonga. Each of those four recorded their upsets against Rafael Nadal, Djokovic, and Federer, except for Ferrer, who has never beaten Fed but did defeat Agassi when the American held the top spot.

Becker’s 19 wins against top-ranked players is also a record, though he has to share this one with Nadal, who is 19-10 against number ones. Boris and Rafa tower far above the next players on the list, Djokovic and Bjorn Borg, who each have 11 career wins against number ones. Next on the list among active players are Murray (9), del Potro (6), Ferrer (5), and Federer (5).

Robredo doesn’t quite rank among this elite company, but his second top-ranked scalp adds a little more luster to an already lengthy list of career highlights.

Erratic Results and the Fate of Jerzy Janowicz

When Jerzy Janowicz defeated Victor Estrella in the first round at Roland Garros on Sunday, it was the Pole’s first win since Februrary, breaking a string of nine consecutive losses. Janowicz’s results have been rather pedestrian ever since his semifinal run at Wimbledon last year, yet the 720 points he earned for that single performance have kept his ranking in the top 25 and given him a seed at the Grand Slams.

As we’ve discussed many times on this site, occasional greatness trumps consistent mediocrity, at least as far as ranking points are concerned. The system rewards players who bunch wins together–Janowicz current holds about 1500 points, barely double what he earned from that single event last year.

In the short term, bunching wins is a good thing, as Janowicz has learned. But from an analytical perspective, how should we view players with recent histories like his? Does the Wimbledon semifinal bode well for the future? Does the mediocre rest of his record outweigh a single excellent result? Does it all come out in the wash?

It’s a question that doesn’t pertain only to Janowicz. While 48% of Jerzy’s points come from Wimbledon, 49% of Andy Murray‘s current ranking point total comes from winning Wimbledon. Another reigning Slam champion, Stanislas Wawrinka, owes 34% of his point total to a single event.  By contrast, for the average player in the top 50, that figure is only 21%. Rafael Nadal and Novak Djokovic are among the most consistent on tour, at 16% and 10%, respectively.

Since 2010, there has only been one top-40 player who earned more than half of his year-end ranking points from a single event: Ivan Ljubicic, whose 1,000 points for winning Indian Wells dominated his 1,965 point total. His top-16 ranking at the end of that year didn’t last. He didn’t defend his Indian Wells points or make up the difference elsewhere, falling out of the top 30 for most of 2011. Of course, he was in his 30s at that point, so we shouldn’t draw any conclusions from this extreme anecdote.

When we crunch the numbers, it emerges that there has been no relationship between “bunched” ranking points and success the following year. I collected several data points for every top-40 players from the 2010, 2011, and 2012 seasons: their year-end ranking, the percentage of ranking points from their top one, two, and three events, and the year-end ranking the following year.  If bunching were a signal of an inflated ranking–that is, if you suspect Janowicz’s abilities don’t jibe with his current ranking–we would see following-year rankings drop for players who fit that profile.

Take Jerzy’s 2012, for example. He earned 46% of his points from his top event (the Paris Masters final), 53% from his top two, and 57% from his top three.  (Corresponding top-40 averages are 21%, 34%, and 44%.)  He ended the year with 1,299 ranking points. At the end of 2013, his ranking no longer reflected his 600 points from Paris. But unlike Ljubicic in 2010, Janowicz boosted his ranking, improving 24% to 1,615 points.

The overall picture is just as cloudy as the juxtaposition of Ljubicic and Janowicz. There is no correlation between the percentage of points represented by a player’s top event (or top two, or top three) and his ranking point change the following year.

For the most extreme players–the ten most “bunched” ranking point totals in this dataset–there’s a small indication that the following season might disappoint. Only three of the ten (including Janowicz in 2012-13) improved their ranking, while three others saw their point total decrease by more than 40%. On average, the following-year decrease of the ten most extreme player-seasons was approximately 20%. But that’s a small, noisy subset, and we should take the overall results as a stronger indication of what to expect from players who fit this profile.

There’s still a case to be made that Jerzy is heading for a fall. He hasn’t racked up many victories so far this year that would offset the upcoming loss of his Wimbledon points. And his Wimbledon success was particularly lucky, as he faced unseeded players in both the fourth round and the quarterfinals. Even if he is particularly effective on grass, it’s unlikely the draw will so heavily favor him again.

But however a player earns his disproportionately large point total, the points themselves are no harbinger of doom. On that score, anyway, Janowicz fans can expect another year in the top 25.

New Ranking Maps and Charts

I’m excited to share with you a couple of new features I’ve been working on for

First is an interactive ranking map:


The above map shows the geographic concentration of teenagers in the WTA top 1000.  Click through to the full-size map, and you can mouse over any country to find out how many players they have in that category.

More importantly, you can customize the map in a variety of ways.  Choose from either the ATP or WTA rankings, decide how deep you’d like to go in the rankings, and if you’d like, limit the age range.  It’s a great way to see which countries are most dominant on each tour, and it’s also an opportunity to visually investigate which nations are likely to hold that power in the near future.

Next is an interactive ranking history chart:


This chart shows ranking points for the big four over the past three years.  Again, if you click through to the full-size map, you’ll get more features: mouse over any line to see the date and the player’s ranking points at the date.

Like the map, the ranking chart is fully interactive.  You can select anywhere from one to four players–for now, only in the ATP top 100–choose a timeframe, and select either ranking or ranking points.

One option I want to call you attention to is one of the timeframes: “Year-end (by age).”  Here, instead of dates, the horizontal axis shows ages.  For instance, this graph shows the big four’s year-end rankings at each age.


Rafael Nadal, Top Twosomes, and the Future

The only match that either Rafael Nadal or Novak Djokovic lost in London was the final, when Nadal fell to Djokovic.  It was a good summary of the season as a whole.  The top two weren’t undefeated for the entire season, but they might as well have been.

Between them, Rafa and Novak lost only 16 matches this year, six of them to each other.  Fittingly, they split those six matches.  No single player poses a serious threat to their dominance.  Only Juan Martin del Potro defeated both this year, and he lost his five other encounters with the top-ranked duo.  The injured Andy Murray remains only a wildcard, having split Grand Slam finals with Djokovic this year but without having played Nadal since 2011.

Barring a huge upset loss in Davis Cup, Djokovic will end the season with the best-ever winning percentage for a #2-ranked player.  His 88.9% just edges out the 88.7% posted by Nadal in 2005, when he finished second to Roger Federer.  In the last thirty years, only five other #2’s won at least 85% of their matches.

Taking these six prior pairs as the best single-year twosomes the ATP has recently produced, it’s surprising to see what happened to them the following year.  In three of those seasons, neither of the ultra-dominant duos finished the next season at #1.  A third player overcame them both.

Here is the list of the seven most dominant twosomes of the last thirty years, along with their year-end rankings 12 months after the end of their notable seasons (Nx):

Yr  #1              W-L    Nx  #2              W-L    Nx  
83  John McEnroe    62-9    1  Mats Wilander   74-11   4  
85  Ivan Lendl      83-7    1  John McEnroe    72-10  14  
87  Ivan Lendl      70-7    2  Stefan Edberg   76-12   5  
89  Ivan Lendl      80-7    3  Boris Becker    58-8    2  
05  Roger Federer   81-4    1  Rafael Nadal    79-10   2  
12  Novak Djokovic  75-12   2  Roger Federer   74-13   6  
13  Rafael Nadal    76-7    ?  Novak Djokovic  72-9    ?

In 1988, Mats Wilander overcame both Ivan Lendl and Stefan Edberg to claim the #1 position.  In 1990, it was Edberg who leapfrogged Lendl and Boris Becker.  This year, of course, Nadal reclaimed the top spot from last year’s top two of Djokovic and Federer.

Those of us who watched the Tour Finals for the last week might find it hard to imagine that anyone–certainly not any of the other six men in London–would outperform either Rafa or Novak over the course of a season.  But injuries strike, slumps take hold, and–unlikely as it may seem in 2013–young players emerge and dominate. For all of the radical changes in the game since the late 80s, these precedents serve as an important reminder of the unpredictability of tennis.