Smaller Swings In Big Moments

Despite the name, unforced errors aren’t necessarily bad. Sometimes, the right tactic is to play more aggressively, and in order to hit more winners, most players will commit more errors as well. Against some opponents, increasing the unforced error count–as long as there is a parallel improvement in winners or other positive point-ending shots–might be the only way to win.

Last week, I showed that one of the causes of Angelique Kerber’s first-round loss was her disproportionate number of errors in big moments. But as my podcasting partner Carl Bialik pointed out, that isn’t the whole story. If Kerber played more aggressively on the most important points–one possible cause of more errors–it might be the case that her winner rate was higher, as well. Since the 6-2 6-2 scoreline was so heavily tilted against her, it was a safe bet that Kerber recorded more high-leverage errors than winners. Still, Carl makes a valid point, and one worth testing.

To do so, let’s revisit the data: 500 women’s singles matches from the last four majors and the first four rounds of this year’s French Open. By measuring the importance of each point, we can determine the average leverage (LEV) of every point in each match, along with the average leverage of points which ended with a player hitting an unforced error, or a winner. Last week, we found that Kerber’s UEs in her first-round loss had an average LEV of 5.5%, compared to a LEV of 3.8% on all other points. For today’s purposes, let’s use match averages as a reference point: Her average UE LEV of 5.5% also compares unfavorably to the overall match average LEV of 4.1%.

What about winners? Kerber’s 15 winners came on points with an average LEV of 3.9%, below the match average. Case closed: On more important points, Kerber was more likely to commit an error, and less likely to hit a winner.

Across the whole population, players hit more errors and fewer winners in crucial moments, but only slightly. Points ending in errors are about one percent more important than average (percent, not percentage point, so 4.14% instead of 4.1%), and points ending in winners are about two percent less important than average. In bigger moments, players increase their winner rate about 39% of the time, and they improve their W-UE ratio about 45% of the time. Point being, there are tour-wide effects on more important points, but they are quite small.

Of course, Kerber’s first-round upset isn’t indicative of how she has played at Slams in general. In my article last week, I mentioned the four players who did the best job of reducing errors at big moments: Kerber, Agnieszka Radwanska, Timea Bacsinszky, and Kiki Bertens. Kerber and Radwanska both hit fewer winners on big points as well, but Bacsinszky and Bertens manage a perfect combination, hitting slightly more winners as the pressure cranks up. Among players with more than 10 Slam matches since last year’s French, Bacsinszky is the only one to hit winners on more important points than her unforced errors over 75% of the time.

Compared to her peers, Kerber’s big-moment tactics are remarkably passive. The following table shows the 21 women for whom I have data on at least 13 matches. “UE Rt.” (“UE Ratio”) is similar to the metric I used last week, comparing the average importance of points ending in errors to average points; “W Ratio” is the same, but for points ending in winners, and “W+UE Ratio” is–you guessed it–a (weighted) combination of the two. The combined measure serves as an rough approximation of aggression on big points, where ratios below 1 are more passive than the player’s typical tactics and ratios above 1 are more aggressive.

Player                     M  UE Rt.  W Rt.  W+UE Rt.  
Angelique Kerber          20    0.92   0.85      0.88  
Alize Cornet              13    0.92   0.87      0.94  
Agnieszka Radwanska       17    0.91   0.95      0.95  
Simona Halep              19    0.93   0.94      0.95  
Samantha Stosur           13    0.95   0.98      0.96  
Timea Bacsinszky          14    0.89   1.02      0.97  
Elina Svitolina           15    1.02   0.95      0.97  
Karolina Pliskova         18    0.97   0.98      0.97  
Caroline Wozniacki        14    0.93   1.00      0.97  
Johanna Konta             13    1.00   0.97      0.98  
Caroline Garcia           14    0.94   1.02      0.98  
Svetlana Kuznetsova       17    0.96   0.98      0.99  
Garbine Muguruza          20    1.02   0.94      0.99  
Venus Williams            25    1.00   0.97      0.99  
Elena Vesnina             13    0.96   1.03      0.99  
Anastasia Pavlyuchenkova  15    1.03   0.99      0.99  
Coco Vandeweghe           13    1.08   0.95      1.01  
Madison Keys              13    1.01   1.02      1.01  
Serena Williams           27    0.99   1.05      1.02  
Carla Suarez Navarro      14    1.00   1.14      1.05  
Dominika Cibulkova        14    1.11   1.03      1.07

Kerber’s combined measure stands out from the pack. Her point-ending shots–both winners and errors, but especially winners–occur disproportionately on less important points, and the overall effect is double that of the next most passive big-moment player, Alize Cornet. Every other player is close enough to neutral that I would hesitate before making any conclusions about their pressure-point tactics.

Even when Kerber wins, she does so with effective defense at key points. In only two of her last 20 matches at majors did her winners occur on particularly important points. (Incidentally, one of those two was last year’s US Open final.) In general, her brand of passivity works–she won 16 of those matches. But defensive play doesn’t leave very much room for error–figuratively or literally. The tactics were familiar and proven, but against Makarova, they were poorly executed.

Angelique Kerber’s Unclutch Unforced Errors

It’s been a rough year for Angelique Kerber. Despite her No. 1 WTA ranking and place at the top of the French Open draw, she lost her opening match on Sunday against the unseeded Ekaterina Makarova. Adding insult to injury, the loss goes down in the record books as a lopsided-looking 6-2 6-2.

Andrea Petkovic chimed in with her diagnosis of Kerber’s woes:

She’s simply playing without confidence right now. It was tight, even though the scoreline was 2 and 2 but everyone who knows a thing about tennis knew that Angie made errors whenever it mattered because she’s playing without any confidence right now – errors she didn’t make last year.

This is one version of a common analysis: A player lost because she crumbled on the big points. While that probably doesn’t cover all of Kerber’s issues on Sunday–Makarova won 72 points to her 55–it is true that big points have a disproportionate effect on the end result. For every player who squanders a dozen break points yet still wins the match, there are others who falter at crucial moments and ultimately lose.

This family of theories–that a player over- or under-performed at big moments–is testable. For instance, I showed last summer that Roger Federer’s Wimbledon loss to Milos Raonic was due in part to his weaker performance on more important points. We can do the same with Kerber’s early exit.

Here’s how it works. Once we calculate each player’s probability of winning the match before each point, we can assign each point a measure of importance–I prefer to call it leverage, or LEV–that quantifies how much the single point could effect the outcome of the match. At 3-0, 40-0, it’s almost zero. At 3-3, 40-AD in the deciding set, it might be over 10%. Across an entire tournament’s worth of matches, the average LEV is around 5% to 6%.

If Petko is right, we’ll find that the average LEV of Kerber’s unforced errors was higher than on other points. (I’ve excluded points that ended with the serve, since neither player had a chance to commit an unforced error.) Sure enough, Kerber’s 13 groundstroke UEs (that is, excluding double faults) had an average LEV of 5.5%, compared to 3.8% on points that ended some other way. Her UE points were 45% more important than non-UE points.

Let’s put that number in perspective. Among the 86 women for whom I have point-by-point UE data for their first-round matches this week*, ten timed their errors even worse than Kerber did. Magdalena Rybarikova was the most extreme: Her eight UEs against Coco Vandeweghe were more than twice as important, on average, as the rest of the points in that match. Seven of the ten women with bad timing lost their matches, and two others–Agnieszka Radwanska and Marketa Vondrousova–committed so few errors (3 and 4, respectively), that it didn’t really matter. Only Dominika Cibulkova, whose 15 errors were about as badly timed as Kerber’s, suffered from unclutch UEs yet managed to advance.

* This data comes from the Roland Garros website. I aggregate it after each major and make it available here.

Another important reference point: Unforced errors are evenly distributed across all leverage levels. Our instincts might tell us otherwise–we might disproportionately recall UEs that came under pressure—-but the numbers don’t bear it out. Thus, Kerber’s badly timed errors are just as badly timed when we compare her to tour average.

They are also poorly timed when compared to her other recent performances at majors. Petkovic implied as much when she said her compatriot was making “errors she didn’t make last year.” Across her 19 matches at the previous four Slams, her UEs occurred on points that were 11% less important than non-UE points. Her errors caused her to lose relatively more important points in only 5 of the 19 matches, and even in those matches, the ratio of UE leverage to non-UE leverage never exceeded 31%, her ratio in Melbourne this year against Tsurenko. That’s still better than her performance on Sunday.

Across so many matches, a difference of 11% is substantial. Of the 30 players with point-by-point UE data for at least eight matches at the previous four majors, only three did a better job timing their unforced errors. Radwanska heads the list, at 16%, followed by Timea Bacsinszky at 14% and Kiki Bertens at 12%. The other 26 players committed their unforced errors at more important moments than Kerber did.

As is so often the case in tennis, it’s difficult to establish if a stat like this is indicative of a longer-trend trend, or if it is mostly noise. We don’t have point-by-point data for most of Kerber’s matches, so we can’t take the obvious next step of checking the rest of her 2017 matches for similarly unclutch performances. Instead, we’ll have to keep tabs on how well she limits UEs at big moments on those occasions where we have the data necessary to do so.

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.