Category: Clutch

Digging Out of the Holes of 0-40 and 15-40

In the men’s professional game, serving at 0-40 isn’t a death sentence, but it isn’t a good place to be. An average player wins about 65% of service points, and at that rate, his chance of coming back from 0-40 is just a little better than one in five.

Some players are better than others at executing this sort of comeback. Tommy Robredo, for instance, has come back from 0-40 nearly 60% more often than we’d expect, while Sam Querrey digs out of the 0-40 hole one-third less often than we would predict.

Measuring a player’s success rate in these scenarios isn’t simply a matter of counting up 0-40 games. That’s what we saw on the ATP official site last week, and it’s woefully inadequate. That article marvels at Ivo Karlovic‘s “clutch” accomplishments from 0-40 and 15-40, when we could easily have guessed that Ivo would lead just about any serving category. Big serving isn’t clutch if it’s what you always do.

Statistics are only valuable in context, and that is particularly true in tennis. Simply counting 0-40 games and reporting the results hides a huge amount of potential insight. Whether a player wins or loses (a game, a set, a match, or a stretch of matches) is only the first question. To deliver any kind of meaningful analysis, we need to adjust those results for the competition and consider what we already know about the players we’re studying.

Rather than tear apart that article, though, let’s do the analysis correctly.

The number of times a player comes back from 0-40 or 15-40 isn’t what’s important. As we’ve seen, big servers will dominate those categories. That doesn’t tell us who is particularly effective (or, dare we say, “clutch”) in such a situation, it only identifies the best servers. What matters is how often players come back compared to how often we would expect them to, taking into consideration their serving ability.

Karlovic is an instructive example. Over the last few years–the time span available in this dataset of point-by-point match records–Ivo has gone down 0-40 56 times, holding 17 of those games, a rate of 30.4%. That’s third-best on tour, behind John Isner and Samuel Groth. But compared to how well we would expect Karlovic to serve, he’s only 7% better than neutral, right in the middle of the ATP pack.

Before diving into the results, a few more notes on methodology. For each 0-40 or 15-40 game, I calculated the server’s rate of service points won in that match. Since we would expect 0-40 games to occur more often in matches with good returners, in-match rates seem more accurate than season-long aggregates. Given the in-match rate of serve points won, I then determined the odds that the server would come back from the 0-40 or 15-40 score. For each game, then, we have a result (came back or didn’t come back) and an estimate of the comeback’s likelihood. Combining both numbers for all of a player’s service games tells us how effective he was at these scores.

For 30 of the players best represented in the dataset, here are their results at 0-40, showing the number of games, the number of successful comebacks, the rate of successful comebacks, and the degree to which the player exceeded expectations from 0-40:

Player                  0-40  0-40 W  0-40 W%  W/Exp  
Tommy Robredo            110      30    27.3%   1.59  
Denis Istomin            114      26    22.8%   1.36  
John Isner                87      31    35.6%   1.34  
Guillermo Garcia-Lopez   161      29    18.0%   1.32  
Kevin Anderson           130      38    29.2%   1.28  
Bernard Tomic            110      24    21.8%   1.25  
Fernando Verdasco        141      30    21.3%   1.17  
Rafael Nadal             140      32    22.9%   1.15  
Kei Nishikori            122      23    18.9%   1.15  
Marin Cilic              125      26    20.8%   1.14  
                                                      
Player                  0-40  0-40 W  0-40 W%  W/Exp  
Jo-Wilfried Tsonga       124      29    23.4%   1.14  
Novak Djokovic           124      34    27.4%   1.12  
Andreas Seppi            145      24    16.6%   1.09  
Grigor Dimitrov          115      22    19.1%   1.08  
Philipp Kohlschreiber    146      28    19.2%   1.08  
Roger Federer            107      26    24.3%   1.07  
Ivo Karlovic              56      17    30.4%   1.07  
Santiago Giraldo         113      18    15.9%   1.06  
Alexandr Dolgopolov      141      25    17.7%   1.03  
Milos Raonic              82      23    28.0%   1.01  
                                                      
Player                  0-40  0-40 W  0-40 W%  W/Exp  
Tomas Berdych            149      30    20.1%   1.01  
Jeremy Chardy            122      21    17.2%   0.98  
Feliciano Lopez          136      26    19.1%   0.97  
Fabio Fognini            211      24    11.4%   0.97  
Mikhail Youzhny          155      18    11.6%   0.92  
David Ferrer             203      32    15.8%   0.89  
Richard Gasquet          152      25    16.4%   0.87  
Andy Murray              164      24    14.6%   0.80  
Gilles Simon             158      16    10.1%   0.72  
Sam Querrey               84      12    14.3%   0.68

As I mentioned above, Robredo has been incredibly effective in these situations, coming back from 0-40 30 times instead of the 19 times we would have expected. Some big servers, such as Isner and Kevin Anderson, are even better than their well-known weapons would leads us to expect, while others, such as Karlovic and Milos Raonic, aren’t noticeably more effective at 0-40 than they are in general.

Many of these extremes don’t hold up when we turn to the results from 15-40. Quite a few more games reach 15-40 than 0-40, so the more limited variation at 15-40 suggests that many of the extreme results from 0-40 can be ascribed to an inadequate sample. For instance, Robredo–our 0-40 hero–falls to neutral at 15-40. Here is the complete list:

Player                  15-40  15-40 W  15-40 W%  W/Exp  
John Isner                238      122     51.3%   1.33  
Milos Raonic              215       98     45.6%   1.18  
Feliciano Lopez           304      108     35.5%   1.17  
Jo-Wilfried Tsonga        301      119     39.5%   1.17  
Denis Istomin             304      101     33.2%   1.17  
Rafael Nadal              320      118     36.9%   1.16  
Ivo Karlovic              148       68     45.9%   1.15  
Kevin Anderson            338      132     39.1%   1.15  
Guillermo Garcia-Lopez    405      106     26.2%   1.14  
Andreas Seppi             396      113     28.5%   1.12  
                                                         
Player                  15-40  15-40 W  15-40 W%  W/Exp  
Bernard Tomic             273       86     31.5%   1.12  
Kei Nishikori             298       96     32.2%   1.10  
Novak Djokovic            348      132     37.9%   1.07  
Richard Gasquet           325      106     32.6%   1.07  
Roger Federer             281      109     38.8%   1.07  
Fernando Verdasco         306       94     30.7%   1.06  
Philipp Kohlschreiber     352      110     31.3%   1.06  
Andy Murray               431      135     31.3%   1.06  
Santiago Giraldo          331       86     26.0%   1.05  
Tomas Berdych             398      131     32.9%   1.05  
                                                         
Player                  15-40  15-40 W  15-40 W%  W/Exp  
Marin Cilic               357      109     30.5%   1.05  
Sam Querrey               244       78     32.0%   1.04  
Jeremy Chardy             300       91     30.3%   1.04  
Fabio Fognini             422       98     23.2%   1.03  
Tommy Robredo             285       78     27.4%   0.99  
Grigor Dimitrov           307       89     29.0%   0.99  
David Ferrer              498      138     27.7%   0.98  
Alexandr Dolgopolov       299       77     25.8%   0.95  
Mikhail Youzhny           339       77     22.7%   0.94  
Gilles Simon              426       93     21.8%   0.91

The big servers are better represented at the top of this ranking. Even though Isner is expected to come back from 15-40 nearly 40% of the time–better than almost anyone on tour–he exceeds that expectation by one-third, far more than anyone else considered here.

Finally, let’s look at comebacks from 0-30:

Player                  0-30  0-30 W  0-30 W%  W/Exp  
John Isner               338     229    67.8%   1.19  
Bernard Tomic            299     146    48.8%   1.15  
Grigor Dimitrov          342     166    48.5%   1.11  
Novak Djokovic           409     235    57.5%   1.10  
Santiago Giraldo         344     142    41.3%   1.10  
Fernando Verdasco        373     175    46.9%   1.10  
Rafael Nadal             376     194    51.6%   1.09  
Tomas Berdych            492     262    53.3%   1.09  
Tommy Robredo            296     132    44.6%   1.08  
Roger Federer            344     193    56.1%   1.08  
                                                      
Player                  0-30  0-30 W  0-30 W%  W/Exp  
Feliciano Lopez          326     161    49.4%   1.07  
Alexandr Dolgopolov      347     154    44.4%   1.07  
Marin Cilic              378     179    47.4%   1.06  
Jo-Wilfried Tsonga       357     185    51.8%   1.06  
Guillermo Garcia-Lopez   380     146    38.4%   1.06  
Ivo Karlovic             186     118    63.4%   1.04  
Philipp Kohlschreiber    395     185    46.8%   1.03  
Denis Istomin            314     135    43.0%   1.03  
Kei Nishikori            341     145    42.5%   1.03  
David Ferrer             529     227    42.9%   1.02  
                                                      
Player                  0-30  0-30 W  0-30 W%  W/Exp  
Kevin Anderson           361     181    50.1%   1.02  
Mikhail Youzhny          390     142    36.4%   1.00  
Andy Murray              419     185    44.2%   1.00  
Andreas Seppi            418     164    39.2%   0.99  
Jeremy Chardy            316     132    41.8%   0.99  
Milos Raonic             246     139    56.5%   0.99  
Fabio Fognini            478     153    32.0%   0.99  
Sam Querrey              292     131    44.9%   0.97  
Gilles Simon             442     155    35.1%   0.96  
Richard Gasquet          370     159    43.0%   0.95

Isner still stands at the top of the leaderboard, while Bernard Tomic and Grigor Dimitrov give us a mild surprise by filling out the top three. Again, as the sample size increases, the variation decreases even further, illustrating that, over the long term, players tend to serve about as well at one score as they do at any other.

The Odds of Successfully Serving Out the Set

Italian translation at settesei.it

Serving for the set is hard … or so they say. Like other familiar tennis conceits, this one is ripe for confirmation bias. Every time we see a player struggle to serve out a set, we’re tempted to comment on the particular challenge he faces. If he doesn’t struggle, we ignore it or, even worse, remark on how he achieved such an unusual feat.

My findings–based on point-by-point data from tens of thousands of matches from the last few seasons–follow a familiar refrain: If there’s an effect, it’s very minor. For many players, and for some substantial subsets of matches, breaks of serve appear to be less likely at these purportedly high-pressure service games of 5-4, 5-3 and the like.

In ATP tour-level matches, holds are almost exactly as common when serving for the set as at other stages of the match. For each match in the dataset, I found each player’s hold percentage for the match. If serving for the set were more difficult than serving in other situations, we would find that those “average” hold percentages would be higher than players’ success rates when serving for the set.

That isn’t the case. Considering over 20,000 “serving-for-the-set” games, players held serve only 0.7% less often than expected–a difference that shows up only once every 143 attempts. The result is the same when we limit the sample to “close” situations, where the server has a one-break advantage.

Only a few players have demonstrated any notable success or lack thereof. Andy Murray holds about 6% more often when serving for the set than his average rate, making him one of only four players (in my pool of 99 players with 1,000 or more service games) to outperform his own average by more than 5%.

On the WTA tour, serving for the set appears to be a bit more difficult. On average, players successfully serve out a set 3.4% less often than their average success rate, a difference that would show up about once every 30 attempts. Seven of the 85 players with 1,000 service games in the dataset were at least 10% less successful in serving-for-the-set situations than their own standard.

Maria Sharapova stands out at the other end of the spectrum, holding serve 3% more often than her average when serving for the set, and 7% more frequently than average when serving for the set with a single-break advantage. She’s one of 30 players for whom I was able to analyze at least 100 single-break opportunities, and the only one of them to exceed expectations by more than 5%.

Given the size of the sample–nearly 20,000 serving-for-the-set attempts, with almost 12,000 of them single-break opportunities–it seems likely that this is a real effect, however small. Strangely, though, the overall finding is different at the lower levels of the women’s game.

For women’s ITF main draw matches, I was able to look at another 30,000 serving-for-the-set attempts, and in these, players were 2.4% more successful than their own average in the match. In close sets, where the server held a one-break edge, the server’s advantage was even greater: 3.5% better than in other games.

If anything, I would have expected players at lower levels to exhibit greater effects in line with the conventional wisdom. If it’s difficult to serve in high-pressure situations, it would make sense if lower-ranked players (who, presumably, have less experience with and/or are less adept in these situations) were not as effective. Yet the opposite appears to be true.

Lower-level averages from the men’s tour don’t shed much light, either. In main draw matches at Challengers, players hold 1.4% less often when serving for the set, and 1.8% less often with a single-break advantage. In futures main draws, they are exactly as successful when serving for the set as they are the rest of the time, regardless of their lead. In all of the samples, there are only a handful of players whose record is 10% better or worse when serving for the set, and a small percentage who over- or underperform by even 5%.

The more specific situations I analyze, the more the evidence piles up that games and points are, for the most part, independent–that is, players are roughly as effective at one score as they are at any other, and it doesn’t matter a great deal what sequence of points or games got them there. There are still plenty of situations that haven’t yet been analyzed, but if the ones that we talk about the most don’t exhibit the strong effects that we think they do, that casts quite a bit of doubt on the likelihood that we’ll find notable effects elsewhere.

If there is any truth to claims like those about the difficulty of serving for the set, perhaps it is the case that the pressure affects both players equally. After all, if a server needs to hold at 5-4, it is equally important for the returner to seize the final break opportunity. Maybe the level of both players drops, something we might be able to determine by analyzing how these points are played.

For now, though, we can conclude that players–regardless of gender or level–serve out the set about as often as they successfully hold at 1-2, or 3-3, or any other particular score.

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.

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

Italian translation at settesei.it

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

Italian translation at settesei.it

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.