Measuring the Clutchness of Everything

Matches are often won or lost by a player’s performance on “big points.” With a few clutch aces or un-clutch errors, it’s easy to gain a reputation as a mental giant or a choker.

Aside from the traditional break point stats, which have plenty of limitations, we don’t have a good way to measure clutch performance in tennis. There’s a lot more to this issue than counting break points won and lost, and it turns out that a lot of the work necessary to quantify clutchness is already done.

I’ve written many times about win probability in tennis. At any given point score, we can calculate the likelihood that each player will go on to win the match. Back in 2010, I borrowed a page from baseball analysts and introduced the concept of volatility, as well. (Click the link to see a visual representation of both metrics for an entire match.) Volatility, or leverage, measures the importance of each point–the difference in win probability between a player winning it or losing it.

To put it simply, the higher the leverage of a point, the more valuable it is to win. “High leverage point” is just a more technical way of saying “big point.”  To be considered clutch, a player should be winning more high-leverage points than low-leverage points. You don’t have to win a disproportionate number of high-leverage points to be a very good player–Roger Federer’s break point record is proof of that–but high-leverage points are key to being a clutch player.

(I’m not the only person to think about these issues. Stephanie wrote about this topic in December and calculated a full-year clutch metric for the 2015 ATP season.)

To make this more concrete, I calculated win probability and leverage (LEV) for every point in the Wimbledon semifinal between Federer and Milos Raonic. For the first point of the match, LEV = 2.2%. Raonic could boost his match odds to 50.7% by winning it or drop to 48.5% by losing it. The highest leverage in the match was a whopping 32.8%, when Federer (twice) had game point at 1-2 in the fifth set. The lowest leverage of the match was a mere 0.03%, when Raonic served at 40-0, down a break in the third set. The average LEV in the match was 5.7%, a rather high figure befitting such a tight match.

On average, the 166 points that Raonic won were slightly more important, with LEV = 5.85%, than Federer’s 160, at LEV = 5.62%. Without doing a lot more work with match-level leverage figures, I don’t know whether that’s a terribly meaningful difference. What is clear, though, is that certain parts of Federer’s game fell apart when he needed them most.

By Wimbledon’s official count, Federer committed nine unforced errors, not counting his five double faults, which we’ll get to in a minute. (The Match Charting Project log says Fed had 15, but that’s a discussion for another day.) There were 180 points in the match where the return was put in play, with an average LEV = 6.0%. Federer’s unforced errors, by contrast, had an average LEV nearly twice as high, at 11.0%! The typical leverage of Raonic’s unforced errors was a much less noteworthy 6.8%.

Fed’s double fault timing was even worse. Those of us who watched the fourth set don’t need a fancy metric to tell us that, but I’ll do it anyway. His five double faults had an average LEV of 13.7%. Raonic double faulted more than twice as often, but the average LEV of those points, 4.0%, means that his 11 doubles had less of an impact on the outcome of the match than Roger’s five.

Even the famous Federer forehand looks like less of a weapon when we add leverage to the mix. Fed hit 26 forehand winners, in points with average LEV = 5.1%. Raonic’s 23 forehand winners occurred during points with average LEV = 7.0%.

Taking these three stats together, it seems like Federer saved his greatness for the points that didn’t matter as much.

The bigger picture

When we look at a handful of stats from a single match, we’re not improving much on a commentator who vaguely summarizes a performance by saying that a player didn’t win enough of the big points. While it’s nice to attach concrete numbers to these things, the numbers are only worth so much without more context.

In order to gain a more meaningful understanding of this (or any) performance with leverage stats, there are many, many more questions we should be able to answer. Were Federer’s high-leverage performances typical? Does Milos often double fault on less important points? Do higher-leverage points usually result in more returns in play? How much can leverage explain the outcome of very close matches?

These questions (and dozens, if not hundreds more) signal to me that this is a fruitful field for further study. The smaller-scale numbers, like the average leverage of points ending with unforced errors, seem to have particular potential. For instance, it may be that Federer is less likely to go for a big forehand on a high-leverage point.

Despite the dangers of small samples, these metrics allow us to pinpoint what, exactly, players did at more crucial moments. Unlike some of the more simplistic stats that tennis fans are forced to rely on, leverage numbers could help us understand the situational tendencies of every player on tour, leading to a better grasp of each match as it happens.

Winning Return Points When It Matters

In my post last week about players who have performed better than expected in tiebreaks (temporarily, anyway), I speculated that big servers may try harder in tiebreaks than in return games.

If we interpret “try harder” as “win points more frequently,” we can test it. With my point-by-point dataset, we can look at every top player in the men’s game and compare their return-point performance in tiebreaks to their return-point performance earlier in the set.

As it turns out, top players post better return numbers in tiebreaks than they do earlier in the set. I looked at every match in my dataset (most tour-level matches from the last few seasons) for the ATP top 50, and found that these players, on average, won 5.2% more return points than they did earlier in those sets.

That same group of players saw their serve performance decline slightly, by 1.1%. Since the top 50 frequently play each other, it’s no surprise that the serve and return numbers point in different directions. However, the return point increase and the serve point decrease don’t cancel each other out, suggesting that the top 50 is winning a particularly large number of tiebreaks against the rest of the pack, mostly by improving their return game once the tiebreak begins.

(There’s a little bit of confirmation bias here, since some of the players on the edge of the top 50 got there thanks to good luck in recent tiebreaks. However, most of top 50–especially those players who make up the largest part of this dataset–have been part of this sample of players for years, so the bias remains only minor.)

My initial speculation concerned big servers–the players who might reasonably relax during return games, knowing that they probably won’t break anyway. However, big servers aren’t any more likely than others to return better in tiebreaks. (Or, put another way, to return worse before tiebreaks.) John Isner, Ivo Karlovic, Kevin Anderson, and Roger Federer all win slightly more return points in tiebreaks than they do earlier in sets, but don’t improve as much as the 5.2% average. What’s more, Isner and Anderson improve their serve performance for tiebreaks slightly more than they do their return performance.

There are a few players who may be relaxing in return games. Bernard Tomic improves his return points won by a whopping 27% in tiebreaks, Marin Cilic improves by 16%, and Milos Raonic improves by 11%. Tomic and Raonic, in particular, are particularly ineffective in return games when they have a break advantage in the set (more on that in a moment), so it’s plausible they are saving their effort for more important moments.

Despite these examples, this is hardly a clear-cut phenomenon. Kei Nishikori, for example, ups his return game in tiebreaks almost as much as Cilic does, and we would never think of him as a big server, nor do I think he often shows signs of tactically relaxing in return games. We have plenty of data for most of these players, so many of these trends are more than just statistical noise, but the results for individual players don’t coalesce into any simple, overarching narratives about tiebreak tendencies.

There is one nearly universal tendency that turned up in this research. When leading a set by one break or more, almost every player returns worse. (Conversely, when down a break, almost every player serves better.) The typical top 50 player’s return game declines by almost 5%, meaning that a player winning 35% of return points falls to 33.4%.

Almost every player fits this pattern. 48 of the top 50–everyone except for David Ferrer and Aljaz Bedene–win fewer return points when up a break, and 46 of 50 win more service points when down a break.

Pinning down exactly why this is the case is–as usual–more difficult than establishing that the phenomenon exists. It may be that players are relaxing on return. A one-break advantage, especially late, is often enough to win the set, so it may make sense for players to conserve their energy for their own service games. Looking at it from the server’s perspective, that one-break disadvantage might remove some pressure.

What’s clear is this: Players return worse than usual when up a break, and better than usual in tiebreaks. The changes are much more pronounced for some ATPers than others, but there’s no clear relationship with big serving. As ever, tiebreaks remain fascinating and more than a little inscrutable.

The Luck of the Tiebreak, 2015 in Review

Tiebreak outcomes are influenced by luck a lot more than most people think. All else equal, big servers aren’t any more successful than weak servers, and one season’s tiebreak king is often the next season’s tiebreak chump.

I’ve written a lot about this in the past, so I won’t repeat myself too much. (If you want to read more, here’s a good place to start.) In short, the data shows this: Good players win more tiebreaks than bad players do, but only because they’re better in general, not because they have special tiebreak skills. Very few players perform better or worse than they usually do in tiebreaks.

In the past, I’ve found that three players–Roger Federer, Rafael Nadal, and John Isner–consistently increase their level in tiebreaks. In other words, when you calculate how many tiebreaks Federer (or Nadal, or Isner) should win based on his overall rate of serve and return points won, you discover than he wins even more tiebreaks than that.

In any given year, some players score very high or very low–winning or losing far more tiebreaks than their overall level of play would suggest that they should. But the vast majority of those players regress back to the mean in subsequent years.

Here’s a look at which players outperformed the most in 2015 (minimum 20 tiebreaks). TBExp is the number of tiebreaks we would expect them to win, given their usual rate of serve and return points won. TBOE (Tie Breaks Over Expectations) is the difference between the number they won and the number we’d expect them to win, and TBOR is that difference divided by total tiebreaks.

Player              TBs  TBWon  TBExp  TBOE   TBOR  
Stan Wawrinka        46     34   24.9   9.1  19.8%  
Martin Klizan        25     17   12.2   4.8  19.0%  
Marin Cilic          35     26   21.0   5.0  14.2%  
Tomas Berdych        34     24   20.0   4.0  11.7%  
John Isner           64     39   31.7   7.3  11.3%  
Feliciano Lopez      42     27   22.4   4.6  11.0%  
Jiri Vesely          28     16   13.2   2.8  10.1%  
Sam Groth            31     18   14.9   3.1  10.1%  
Gilles Muller        45     27   22.7   4.3   9.5%  
Gael Monfils         28     18   15.4   2.6   9.4%

There are a lot of big servers here (more on that later) and a lot of new faces. Federer and Nadal were roughly neutral in 2015, winning exactly as many tiebreaks as we’d expect. Of the tiebreak masters, only Isner remained among the leaders. He has never posted a season below +5% TBOR, and only twice has he been below +11% TBOR. Just from this leaderboard, you can tell how elite that is.

Along with Isner, we have Marin Cilic, Feliciano Lopez, Sam Groth, and Gilles Muller, all players one would reasonably consider to be big servers. As I mentioned above, big serving doesn’t typically correlate with exceeding tiebreak expectations. It may just be a fluke: Lopez was roughly neutral in 2013 and 2014, and -15% in 2012; Groth doesn’t have much of a tour-level track record, but was -5% in 2014; Muller has been up and down throughout his career; and Cilic almost always underperformed until 2013.

Adding to the “fluke” argument is the case of Ivo Karlovic. His -14% TBOR this year was one of the worst among players who contested 20 or more tiebreaks, and he’s been exactly neutral over the last decade.

Let’s take a closer look at a few players.

Stan Wawrinka: For the second year in a row, he won at least 15% more tiebreaks than expected. Whether it’s clutch, focus, or dumb luck, the shift in his tiebreak fortunes dovetails nicely with his upward career trajectory. From 2006-13, he only posted one season at neutral or better, and his overall TBOR of -9% was one of the worst in the game for that span.

Cilic’s story is similar. Before 2013, he posted only one season above expectations. Since then, he’s won 19%, 16%, and 14% more tiebreaks than expected.

While only anecdotes, these two cases contradict an idea I’ve heard quite a bit, that players weaken in the clutch as they get older. The subject often comes up in the context of Karlovic’s tiebreak futility or Federer’s break point frustrations. It’s tough to prove one way or the other, in part because there’s no generally accepted measure of clutch in tennis. (If indeed there is any persistent clutch skill.) Using a measure like TBOR is dangerous, both because it is so noisy, and because of survivorship bias–players who get worse as they get older are more likely to fall in the rankings and play fewer tour matches as a result.

Another complicating factor is worthy of further study. To estimate how many tiebreaks a player should win, we need to take our expectation from somewhere. I’m using each player’s overall rates of serve and return points won. But if a player is trying harder in tiebreaks (assuming more effort translates into better results), we would expect that he would win more points in tiebreaks.

Isner has admitted to coasting on unimportant points, and for someone with his game style, a whole lot of return points can be classified as unimportant. Very generally speaking, the more one-dimensional the player, the more reason he has to take it easy during return games, and the more he does so, the more we would observe that he outperforms expectations in tiebreaks–simply because he sets expectations artificially low.

That might be an explanation for Isner’s consistent appearance on these leaderboards. And if we assume that players become more strategically sound as they age–or simply better at tactically conserving energy–we might have a reason why older players score higher in this metric.

Two more players worth mentioning are Milos Raonic and Kei Nishikori. They were 5th and 6th on the 2014 leaderboard, outperforming expectations by 15% and 14%, respectively. In 2015, Raonic fell to neutral, and Nishikori (in far fewer tiebreaks) dropped to -14%, nearly the bottom of the rankings. Taken together, it’s a good reminder of the volatility of these numbers. In Raonic’s case, it’s a warning that relying too much on winning tiebreaks (which, by extension, implies relying too little on one’s return game) is a poor recipe for long-term success.

Finally, some notes on the big four. Novak Djokovic and Andy Murray have never figured heavily in these discussions, both because they don’t play a ton of tiebreaks, and because they don’t persistently out- or underperform expectations. Federer and Nadal, however, were long among the best. Both have returned to the middle of the pack: Federer hasn’t posted a TBOR above 5% since 2011, and Nadal underperformed by 8.5% in 2014 before bouncing back to neutral last season.

Whatever tiebreak skill Roger and Rafa once had now eludes them. On the other hand, ten months of good tiebreak luck can happen to anyone, even a legend. If either player can recapture that tiebreak magic–even if it’s mere luck that allows them to do so–it might translate into a few more wins as they try to reclaim the top spot in the rankings.

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

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

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.