Unlikely Davis Cup Finalists and an Early Forecast for Ghent

Among nations that have reached Davis Cup finals, neither Great Britain or Belgium quite fits the mold.

The fortunes of the UK team depend almost entirely on Andy Murray. If you have to choose one player, you couldn’t do much better, but it’s hardly a strategy with lots of room for error. While the Belgian team is a bit more balanced, it doesn’t boast the sort of superstar singles player that most successful nations can send into battle.

Thanks to injury and apathy, the Brits and the Belgians haven’t defeated the level of competition usually required of Davis Cup finalists. Belgium hasn’t had to face any singles player better than Leonardo Mayer, and the only top-ten singles player to show up against Britain was Gilles Simon.

Measured by season-best singles rankings, these are two of the weakest Davis Cup finalists in the modern era [1]. The last time a finalist didn’t have two top-50 singles players was 1987, when the Indian team snuck past the Australians in the semifinals, only to be trounced by a powerhouse Swedish side in the final. This year, neither side has two top-50 players [2].

It’s even worse for the Belgians: David Goffin, their best singles player, has never topped 14th in the rankings. Only three times since 2000 has a nation reached the final without a top-ten player, and to find a side that won the Davis Cup without a top-tenner, we must go back to 1996, when the French team, headed by Arnaud Boetsch and Cedric Pioline, claimed the Cup.

Even when a nation reaches the final without a top-ten singles player, they typically have another singles player in the same range. Yet Belgium’s Steve Darcis has only now crept back into the top 60.

Despite a widespread belief that you can throw logic out the window in the riot that is Davis Cup, the better players still tend to win. Here are Elo-rating-based predictions for the four probable rubbers on clay:

  • Murray d. Darcis (94.3%)
  • Goffin d. GBR-2 (90.1%)
  • Murray d. Goffin (86.7%)
  • Darcis d. GBR-2 (78.1%)

Predicting the outcome of any doubles matches–let alone best-of-five-setters with players yet to be determined, probably including one very good but low-ranked player in Andy Murray–is beyond me. But based on the Murray brothers’ performance against Australia and the Belgians’ lack of a true doubles specialist, the edge has to go to Britain–let’s say 65%.

If we accept these individual probabilities, Great Britain has a 65.2% chance of winning the Davis Cup. That doesn’t take into account home court advantage, which will probably be a factor and favor the Belgians [3].

It’s a huge opportunity for the Brits, but it’s still quite a chance for Belgium, which hasn’t been this close to the Davis Cup for a century.  After all, the Cup is inscribed with country names, not judgments about that nation’s easy path to the final.

Continue reading Unlikely Davis Cup Finalists and an Early Forecast for Ghent

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

The Pivotal Point of 15-30

According to nearly every tennis commentator I’ve ever heard, 15-30 is a crucial point, especially in men’s tennis, where breaks of serve are particularly rare. One reasonable explanation I’ve heard is that, from 15-30, if the server loses either of the next two points, he’ll face break point.

Another way of looking at it is with a theoretical model. A player who wins 65% of service points (roughly average on the ATP tour) has a 62% chance of winning the game from 15-30. If he wins the next point, the probability rises to 78% at 30-all, but if he loses the next point, he will only have a 33% chance of saving the game from 15-40.

Either way, 15-30 points have a lot riding on them. In line with my analysis of the first point of each game earlier this week, let’s take a closer look at 15-30 points–the odds of getting there, the outcome of the next point, and the chances of digging out a hold, along with a look at which players are particularly good or bad in these situations.

Reaching 15-30

In general, 15-30 points come up about once every four games, and no more or less often than we’d expect. In other words, games aren’t particularly likely or unlikely to reach that score.

On the other hand, some particular players are quite a bit more or less likely.  Oddly enough, big servers show up at both extremes. John Isner is the player who–relative to expectations–ends up serving at 15-30 the most often: 13% more than he should. Given the very high rate at which he wins service points, he should get to 15-30 in only 17% of service games, but he actually reaches 15-30 in 19% of service games.

The list of players who serve at 15-30 more often than they should is a very mixed crew. I’ve extended this list to the top 13 in order to include another player in Isner’s category:

Player                 Games  ExpW  ActW  Ratio  
John Isner             3166    537   608   1.13  
Joao Sousa             1390    384   432   1.12  
Janko Tipsarevic       1984    444   486   1.09  
Tommy Haas             1645    368   401   1.09  
Lleyton Hewitt         1442    391   425   1.09  
Tomas Berdych          3947    824   894   1.08  
Vasek Pospisil         1541    361   390   1.08  
Rafael Nadal           3209    661   713   1.08  
Pablo Andujar          1922    563   605   1.08  
Philipp Kohlschreiber  2948    652   698   1.07  
Gael Monfils           2319    547   585   1.07  
Lukasz Kubot           1360    381   405   1.06  
Ivo Karlovic           1941    299   318   1.06

(In all of these tables, “Games” is the number of service games for that player in the dataset, minimum 1,000 service games. “ExpW” is the expected number of occurences as predicted by the model, “ActW” is the actual number of times it happened, and “Ratio” is the ratio of actual occurences to expected occurences.)

While getting to 15-30 this often is a bit of a disadvantage, it’s one that many of these players are able to erase. Isner, for example, not only remains the favorite at 15-30–his average rate of service points won, 72%, implies that he’ll win 75% of games from 15-30–but from this score, he wins 11% more often than he should.

To varying extents, that’s true of every player on the list. Joao Sousa doesn’t entirely make up for the frequency with which he ends up at 15-30, but he does win 4% more often from 15-30 than he should. Rafael Nadal, Tomas Berdych, and Gael Monfils all win between 6% and 8% more often from 15-30 than the theoretical model suggests that they would. In Nadal’s case, it’s almost certainly related to his skill in the ad court, particularly in saving break points.

At the other extreme, we have players we might term “strong starters” who avoid 15-30 more often than we’d expect. Again, it’s a bit of a mixed bag:

Player                 Games  ExpW  ActW  Ratio  
Dustin Brown           1013    249   216   0.87  
Victor Hanescu         1181    308   274   0.89  
Milos Raonic           3050    514   462   0.90  
Dudi Sela              1066    297   270   0.91  
Richard Gasquet        2897    641   593   0.93  
Juan Martin del Potro  2259    469   438   0.93  
Ernests Gulbis         2308    534   500   0.94  
Kevin Anderson         2946    610   571   0.94  
Nikolay Davydenko      1488    412   388   0.94  
Nicolas Mahut          1344    314   297   0.94

With some exceptions, many of the players on this list are thought to be weak in the clutch. (The Dutch pair of Robin Haase and Igor Sijsling are 12th and 13th.) This makes sense, as the pressure is typically lowest early in games. A player who wins points more often at, say, 15-0 than at 40-30 isn’t going to get much of a reputation for coming through when it counts.

The same analysis for returners isn’t as interesting. Juan Martin del Potro comes up again as one of the players least likely to get to 15-30, and Isner–to my surprise–is one of the most likely. There’s not much of a pattern among the best returners: Novak Djokovic gets to 15-30 2% less often than expected; Nadal 1% less often, Andy Murray exactly as often as expected, and David Ferrer 3% more often.

Before moving on, one final note about reaching 15-30. Returners are much less likely to apply enough pressure to reach 15-30 when they are already in a strong position to win the set. At scores such as 0-4, 0-5, and 1-5, the score reaches 15-30 10% less often than usual. At the other extreme, two of the games in which a 15-30 score is most common are 5-6 and 6-5, when the score reaches 15-30 about 8% more often than usual.

The high-leverage next point

As we’ve seen, there’s a huge difference between winning and losing a 15-30 point. In the 290,000 matches I analyzed for this post, neither the server or returner has an advantage at 15-30. However, some players do perform better than others.

Measured by their success rate serving at 15-30 relative to their typical rate of service points won, here is the top 11, a list unsurprisingly dotted with lefties:

Player             Games  ExpW  ActW  Ratio  
Donald Young       1298    204   229   1.12  
Robin Haase        2134    322   347   1.08  
Steve Johnson      1194    181   195   1.08  
Benoit Paire       1848    313   336   1.08  
Fernando Verdasco  2571    395   423   1.07  
Thomaz Bellucci    1906    300   321   1.07  
John Isner         3166    421   449   1.07  
Xavier Malisse     1125    175   186   1.06  
Vasek Pospisil     1541    243   258   1.06  
Rafael Nadal       3209    470   497   1.06  
Bernard Tomic      2124    328   347   1.06

There’s Isner again, making up for reaching 15-30 more often than he should.

And here are the players who win 15-30 points less often than other service points:

Player                  Games  ExpW  ActW  Ratio  
Carlos Berlocq          1867    303   273   0.90  
Albert Montanes         1183    191   173   0.91  
Kevin Anderson          2946    377   342   0.91  
Guillermo Garcia-Lopez  2356    397   370   0.93  
Roberto Bautista-Agut   1716    264   247   0.93  
Juan Monaco             2326    360   338   0.94  
Matthew Ebden           1088    186   176   0.94  
Grigor Dimitrov         2647    360   341   0.95  
Richard Gasquet         2897    380   360   0.95  
Andy Murray             3416    473   449   0.95

When we turn to return performance at 15-30, the extremes are less interesting. However, returning at this crucial score is something that is at least weakly correlated with overall success: Eight of the current top ten (all but Roger Federer and Milos Raonic) win more 15-30 points than expected. Djokovic wins 4% more than expected, while Nadal and Tomas Berdych win 3% more.

Again, breaking down 15-30 performance by situation is instructive. When the server has a substantial advantage in the set–at scores such as 5-1, 4-0, 3-2, and 3-0–he is less likely to win the 15-30 point. But when the server is trailing by a large margin–0-3, 1-4, 0-4, etc.–he is more likely to win the 15-30 point. This is a bit of evidence, though peripheral, of the difficulty of closing out a set–a subject for another day.

Winning the game from 15-30

For the server, getting to 15-30 isn’t a good idea. But compared to our theoretical model, it isn’t quite as bad as it seems. From 15-30, the server wins 2% more often than the model predicts. While it’s not a large effect, it is a persistent one.

Here are the players who play better than usual from 15-30, winning games much more often than the model predicts they would:

Player             Games  ExpW  ActW  Ratio  
Nikolay Davydenko  1488    194   228   1.17  
Steve Johnson      1194    166   190   1.14  
Donald Young       1298    163   185   1.13  
John Isner         3166    423   470   1.11  
Nicolas Mahut      1344    172   188   1.09  
Benoit Paire       1848    266   288   1.08  
Lukas Lacko        1162    164   177   1.08  
Rafael Nadal       3209    450   484   1.08  
Martin Klizan      1534    201   216   1.08  
Feliciano Lopez    2598    341   367   1.07  
Tomas Berdych      3947    556   597   1.07

Naturally, this list has much in common with that of the players who excel on the 15-30 point itself, including many lefties. The big surprise is Nikolay Davydenko, a player who many regarded as weak in the clutch, and who showed up on one of the first lists among players with questionable reputations in pressure situations. Yet Davydenko–at least at the end of his career–was very effective at times like these.

Another note on Nadal: He is the only player on this list who is also near the top among men who overperform from 15-30 on return. Rafa exceeds expectations in that category by 7%, as well, better than any other player in the last few years.

And finally, here are the players who underperform from 15-30 on serve:

Player               Games  ExpW  ActW  Ratio  
Dustin Brown         1013    122   111   0.91  
Tommy Robredo        2140    289   270   0.93  
Alexandr Dolgopolov  2379    306   288   0.94  
Federico Delbonis    1110    157   148   0.94  
Juan Monaco          2326    304   289   0.95  
Simone Bolelli       1015    132   126   0.96  
Paul-Henri Mathieu   1083    155   148   0.96  
Gilles Muller        1332    179   172   0.96  
Carlos Berlocq       1867    256   246   0.96  
Grigor Dimitrov      2647    333   320   0.96  
Richard Gasquet      2897    352   339   0.96

Tentative conclusions

This is one subject on which the conventional wisdom and statistical analysis agree, at least to a certain extent. 15-30 is a very important point, though in context, it’s no more important than some of the points that follow.

These numbers show that some players are better than others at certain stages within each game. In some cases, the strengths balance out with other weaknesses; in others, the stats may expose pressure situations where a player falters.

While many of the extremes I’ve listed here are significant, it’s important to keep them in context. For the average player, games reach 15-30 about one-quarter of the time, so performing 10% better or worse in these situations affects only one in forty games.

Over the course of a career, it adds up, but we’re rarely going to be able to spot these trends during a single match, or even within a tournament. While outperforming expectations on 15-30 points (or any other small subset) is helpful, it’s rarely something the best players rely on. If you play as well as Djokovic does, you don’t need to play even better in clutch situations. Simply meeting expectations is enough.

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

How Important is the First Point of Each Game?

A common belief among players, coaches, and commentators is that the first point of each game is of particular importance. It’s often suggested that the first point sets the tone for the entire game.

Of course, winning the first point is better than losing it, but that’s not what I’m talking about.  Winning any point is better than losing it. If the first point is more important than the others, winning it would have to give a player even more of an advantage than the simple fact of having reached 15-0 instead of 0-15.

The difference between 15-0 and 0-15–apart from any momentum it generates–is a substantial one. Using a theoretical model that treats each point as independent, a player who typically wins 60% of service points will hold about 74% of the time, meaning that at love-all, they have a 74% of winning the game. At 15-0, that probability jumps to 84%. At 0-15, it’s only 58%.

To say that the first point is particularly important, then, is to say that the gap between winning and losing it is even greater than that. On the evidence of over 20,000 recent ATP and WTA matches, covering nearly half a million games, though, the first point is no more important than it should be. Except for, possibly, a few players and a few in-match situations, it gives no momentum to either player.

The basics

The broadest finding is perhaps the most surprising. Winning the first point fails to give the server any extra advantage, but losing the first point does. The results for ATP matches and WTA matches are the same. If the server loses the first point, he or she is then about one percent more likely to win the game than if points were truly independent of each other.

Naturally, this is not a recommendation that a server should lose the first point of any game! For our 60% server, winning the first point still improves her odds of a hold to 84%. But instead of the 58% chance at 0-15 that the theoretical model predicts, it’s really between 58.5% and 59%.

An effect of this size is not something that one would ever notice simply watching tennis matches. It probably doesn’t have any practical import, either. But over multiple very large samples of recent professional matches, the effect demonstrates that winning the first point of a game does not endow a player with any additional benefits.

Situations where it matters

In general, the first point is only as valuable as its immediate effect on the score. However, there are certain situations where winning it seems to give the server a bit more of an edge, or where losing it isn’t the disadvantage that it should be.

The latter situation is most pronounced. In both men’s and women’s tennis, servers outperform the theoretical model when serving down two breaks, at scores such as 0-4, 0-5, and 1-5. They beat the model to a much lesser, but still real, extent when serving down one break. This could be due to their acknowledgement that these games are “must wins,” or in the double-break situations, to a lack of effort on the part of the returner.

Regardless of the reason, with a double-break disadvantage, the effect of going down 0-15 is much less than in the model. Our 60% server, instead of facing a choice between an 84% chance of winning at 15-0 or 58% at 0-15, is looking at a 91% chance of winning at 15-0 or a 71% chance of winning at 0-15.

When serving with the break advantage, the situation is reversed, but it is much less pronounced. At scores such as 6-5 and 3-2, the model is a good predictor of win probability from 15-0, but servers underperform against the model from 0-15. The difference, though only a few percentage points, could be due to more aggression or focus on the part of the returner, or to the server feeling nerves.

At the majority of the most common scores, though, the effect of the first point is no different than the aggregate numbers, with the first point having almost no effect beyond the score.

Susceptible servers

There are a few players for whom the first point does seem to have an extra effect. These fall into two categories: players who fit the conventional wisdom, doing much better (compared to the model) from 15-0 than from 0-15, and those who are the opposite, reducing the gap between the likely outcomes from 15-0 and 0-15.

Among the 38 ATPers for whom I have more than 2,000 recorded service games, the player in the first category who sees the greatest first-point effect is Richard Gasquet. From 15-0, he beats the model by about one percent, but from 0-15, he underperforms by five percent. He’s the only male player whose gap between these two figures is more than five percent.

At the other end of the spectrum is Santiago Giraldo, who from 15-0 underperforms against the model by two percent, but from 0-15, beats the model by seven percent.

The rest of Giraldo’s category is where things get interesting. The other four players with a gap of four percent or greater are Feliciano Lopez, John Isner, Juan Martin del Potro, and Rafael Nadal. It’s no surprise to see two lefties here, as left-handers typically win more points in the ad court. Every other lefty in the dataset fits the same pattern, though their gaps are smaller.

The presence of big servers at this end of the list is a bit tougher to explain. Because they are so likely to hold in any given service game, perhaps they are sometimes unfocused on the first point of a game and become more serious after falling to 0-15.

Among WTA players, the distribution is about the same. The most extreme effect is on the serve of Sorana Cirstea, who, like Giraldo, is much more effective (compared to the model) from 0-15 than from 15-0. The other women in this category with more than a five percent gap are Flavia Pennetta, Ekaterina Makarova, and Ana Ivanovic.

At the other extreme, in Gasquet’s category, are Francesca Schiavone, Li Na, Julia Goerges, and Eugenie Bouchard, all of whom are about two percent more effective than expected from 15-0, and four percent less effective than expected from 0-15.

Conventional overstatement

As is so often the case, the conventional wisdom proves to have a grain of truth in it … sometimes, maybe, and to a much lesser extent than is generally claimed. Even the most extreme effect on tour, like that of Gasquet or Cirstea, doesn’t change the result of a game more than once every two or three matches.

The first point of a game is quite meaningful, because 15-0 is so much better than 0-15. But except for a few players and a few situations–some of which actually shrink the gap between 15-0 and 0-15–there’s little truth to the common claim that the first point is more important than its mere effect on the scoreline.

Break Point Conversions and the Close Matches Federer Isn’t Winning

The career head-to-head between Roger Federer and Novak Djokovic sits at 21-21, but the current era of this rivalry is hardly even. Since the beginning of 2011, Djokovic has won 15 of 23, including last night’s US Open final.

These matches tend to be close ones. In only 7 of the 23 matches has either player won more than 55% of points, and in more than half (12 of 23), neither player has won more than 53% of points, fitting my proposed definition of lottery matches.

In the 12 lottery matches between Fed and Novak since 2011, the player who won the most points always won the match. Yet Djokovic wins far more (9 of 12) of these close matches. Last night was a perfect example: Federer won more return points than his opponent, and it was the third time since the 2012 Tour Finals that the Novak beat Fed while winning 50.3% of points.

When a player wins 50.3% of points, he wins the match only 59% of the time. Even at 51.8%, Novak’s total points won in three other Federer matches, the player with more points wins only 91% of the time.

If many of the matches are close, and one player is winning so many of the matches, there must be more to the story.

Back to break points

Clearly, Novak is winning more big points than Roger is. Since Federer has won more than half of the tiebreaks between them, the next logical place to look is break points.

Federer’s perceived inability to convert break points has been a concern for years. Early last year, I wrote about his success rate on break points, and found that while he does, in fact, convert fewer break points than expected, it’s only a few percentage points. Further, it’s not a new problem: He was winning fewer break points than he should have been back when he was the unchallenged top player in the game.

Against Novak, though, it’s another story, and since they’ve faced each other so often, we can no longer write off a poor break-point performance as an outlier.

In these last 23 matches–including last night’s 4-for-23 on break points–Federer has converted 15% fewer break points than expected, twice as bad as his worst single-season mark. Djokovic, on the other hand, has converted break points at almost the same rate as other return points.

I’m often hesitant to use the c-words, but the evidence is piling up that in these particular clutch situations, Roger is choking. At the very least, we can eliminate a couple of alternative explanations, those based on break point opportunities and on performance in the ad court.

Let’s start with break point opportunities. 4-for-23 on break points is painful to look at, but there is a positive: You have to play very well to generate 23 break point chances against a top player. In fact, there’s a very clear, almost linear relationship between return points won and break point chances generated, and Federer beat expectations by 77% yesterday. Over 21 return games, a player who won 39% of return points, as Roger did, would be expected to create only 13 break point opportunities. A 4-for-13 mark would still be disappointing, but it wouldn’t induce nearly as many grimaces.

In these 23 matches, Federer has generated exactly as many break point chances as expected. Djokovic has done the same. The story here is clearly about performance at 30-40 or 40-AD, not on anything earlier in the game. On non-break points yesterday, Fed returned more effectively.

The other explanation would be that Roger’s poor break point record has to do with the ad court. Against Rafael Nadal, that might be true: Much of the Spaniard’s effectiveness saving break points has to do with the way he skillfully uses left-handed serving in that court.

But in the Novak-Fed head-to-head, we can rule this out as well.  According to Match Charting Project data, which includes more than 40 Djokovic matches and 90 Federer matches, neither player performs much better in either half of the court. Djokovic wins more service points in the deuce court–65% to 64% in general, 66% to 64% on hard courts, and Federer wins return points at the same rate in both courts.

Pundits like to say that tennis is a game of matchups, and in this rivalry, both players defy their typical patterns. Over the course of his career, Novak has saved break points more effectively than average, but not nearly as well as he does against Federer. Federer, for his part, has turned in some of his best return performances against Djokovic … except for these dismal efforts converting break points, when he is far worse than his already-weak averages.

Perhaps the only solution for Roger is to find even more ways to improve his world-class service games. In the previous match against Novak, he converted only one of eight break point chances–the sort of stat that would easily explain a loss. That day in Cincinnati, though, Federer’s one break of serve was better than Djokovic’s zero.

Fed won 56.4% of total points in that match, his third highest rate against Djokovic since 2011. If Novak is going to play better clutch tennis and win the close matches, that leaves Federer with an unenviable alternative. To win, he must decisively outplay the best player in the world.

A New Way of Looking at Lottery Matches

When Rafael Nadal was eliminated from the US Open last week, a bit of bad luck was involved. He won only two fewer points than his opponent, Fabio Fognini, claiming 49.7% of the total points played. In his career up to that point, Rafa had won 8 of 18 matches in which he won between 49% and 50% of total points. It doesn’t take much to flip the result of such a match.

Matches in which neither player wins more than 51% of points represent nearly one in ten contests on the ATP tour. As Michael Beuoy demonstrated last year, those matches are very much up for grabs: the player with the most points wins less than 65% of the time.

In writing about the small subset of matches in which the loser wins a higher percentage of return points than the winner, Carl Bialik has coined the useful term “lottery matches.” However, Bialik has limited the term to those matches that have an unexpected result. I’d like to expand the definition a bit to all those tight matches that could go either way, even if the player who wins the most points ends up winning as expected.

(A quick side note: Bialik prefers comparing return points, the building blocks of his Dominance Ratio metric. Matches are won a bit more frequently when the winner’s DR is below 1.0 than when he wins fewer than 50% of total points played. These metrics often overlap, of course. To make this arcane subject a bit more accessible, I’m going to stick with the traditional total-points-won stat.)

As Beuoy showed, matches aren’t guaranteed to go to the player who wins the most points unless that guy wins at least 53% of points. (Even then, there’s a slight possibility of an upset, but it’s sufficiently rare that, for today’s purposes, I’m going to ignore it.) 52.5% is much better than 50.5%, but at 52.5%, you’re still going to lose about one of every 25 matches.

By extending the “lottery match” umbrella to all those matches in which neither player wins 51%, 52%, or even 53% of total points, we acknowledge that none of these matches are sure things, and we can look at a broader range of matches to determine whether players are winning as many tight matches as they should. Further, by considering such a category of tight matches, we’ll be able to identify those men who play a lot of them–and by doing so, leave themselves vulnerable to lucky upsets.

Winning the lottery (matches)

Let’s start with the broadest category: all matches in which neither player won more than 53% of total points. These represent everything from true toss-ups at 50% to near-guarantees at 52.9%. Using Beuoy’s model, we can take the total points won from each of these matches and calculate the likelihood that the player with the greater number of points won the match.

Nadal, for instance, is one of the more effective players in these tight matches. Going into the US Open, he had played 168 of them, winning 115. By taking the total points won from each of these matches, we find that he “should have” won only 102.5 of them, meaning that by some combination of clutch play and luck, he’s outperformed expectations by 12%.

Among active players with at least 100 of these matches, Nadal ranks an impressive fourth overall, behind John Isner, Fognini, and Jurgen Melzer. Novak Djokovic and Andy Murray are just inside the top 20, exceeding expectations by 6% and 5%, respectively, while Roger Federer is much further down the list, winning 7% fewer of these tight matches than he should.

Finding Fed on the negative end of this list is a surprise, since Federer, Nadal, and Isner are among the very, very few players who consistently beat expectations in tiebreaks. Tiebreak skill should be closely related to outperforming expectations in tight matches. In any event, my collaborator on a related project, Ryan Rodenberg, has written at length about Federer’s lack of success in some lottery matches.

When we narrow the focus to matches in which neither player won more than 51% of points–true toss-up matches–Nadal is still among the best. In fact, the top four of Rafa, Fognini, Melzer, and Isner remains the same, as each of those players has won between 36% and 38% more often than they should in contests with these extremely slim margins.  Once again, Djokovic and Murray are positive, at +16% and +6%, respectively, while Federer trails far behind, at -9%.

Careening downward

A big advantage of using the broader, 53-percent-of-points definition of lottery matches is that it gives us a larger sample to work with. Nadal has only played 27 matches in his career when the loser won more points than the winner did, and only 40 when neither player topped 51% of total points won.

In the 53% category, though, Nadal has amassed several matches each year of his career, allowing us to look at more meaningful trends. Each season from 2005-11, he averaged about 15 tight matches per year, and won at least one more than we would’ve expected of him, often two or three. Since the beginning of last year, though, he’s played 25, winning only 13 when he should have won 16.

Even with the bigger sample, these are small margins. If Nadal comes roaring back next year and beyond, again winning more close matches than expected, we’ll ultimately see these two seasons as outliers. Yet most of Nadal’s peers post surprisingly consistent records in tight matches. In the last decade, Djokovic and Murray have each had only one season each below -10%, and Federer has reliably underperformed, never reaching +7% for a full season. Not every player is as good in these matches as Nadal, but the ones who do excel post roughly similar numbers from one year to the next.

The bigger picture

Winning tight matches is useful, but as Federer’s experience demonstrates, it’s hardly necessary. And in the case of Fognini, exceeding expectations in lottery matches is hardly sufficient for more general success.

Even better than winning tight matches is winning easy matches, and a useful side effect of studying lottery matches is generating measurements of who plays them the most–and, of course, the least.

Lottery matches–again, those in which neither player wins more than 53% of points–represent fewer than 20% of Rafa’s career matches. His 19.7% rate of close contests is lower than any other player since 2000 (minimum 100 matches). In this category, the big four are bunched together as expected. Among active players, Federer is second lowest, Djokovic is third, and Murray is eighth. Kei Nishikori and David Ferrer are also among the top ten.

At the other end of the spectrum, we find the usual big-serving suspects. Vasek Pospisil tops the list at 49.5%, with Ivo Karlovic (44.5%), Isner (41.9%), and Jerzy Janowicz (40.5%) filling out the top four.

Analyzing the results of very close matches–whichever definition you prefer–is a useful way of identifying players on lucky or unlucky streaks, or even those who appear to play particularly well on big points. However, the more meaningful metric–certainly the one that more closely correlates with elite-level success–is the one that tells us who is avoiding tight matches. The only thing better than luck is not needing it.