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.

How Important is the Seventh Game of the Set?

Few nuggets of tennis’s conventional wisdom are more standard than the notion that the seventh game of each set is particularly crucial. While it’s often difficult to pin down such a well-worn conceit, it seems to combine two separate beliefs:

  1. If a set has reached 3-3, the pressure is starting to mount, and the server is less likely to hold serve.
  2. The seventh game is somehow more important than its immediate effect on the score, perhaps because the winner gains momentum by taking such a pivotal game.

Let’s test both.

Holding at 3-3

Drawing on my database of over 11,000 ATP tour-level matches from the last few years, I found 11,421 sets that reached three-all. For each, I calculated the theoretical likelihood that the server would hold (based on his rate of service points won throughout the match) and his percentage of service games won in the match. If the conventional wisdom is true, the percentage of games won by the server at 3-3 should be noticeably lower.

It isn’t. Using the theoretical model, these servers should have held 80.5% of the time. Based on their success holding serve throughout these matches, they should have held 80.2% of the time. At three-all, they held serve 79.5% of the time. That’s lower, but not enough lower that a human would ever notice. The difference between 80.2% and 79.5% is roughly one extra break at 3-3 per Grand Slam. Not Grand Slam match–an entire tournament.

None of that 0.7% discrepancy can be explained by the effect of old balls [1]. Because new balls are introduced after the first seven games of each match, the server at three-all in the first set is always using old balls, which should, according to another bit of conventional wisdom, work against him. However, the difference between actual holds and predicted holds at 3-3 is slightly greater after the first set: 78.9% instead of the predicted 79.8%. Still, this difference is not enough to merit the weight we give to the seventh game.

The simple part of our work is done: Servers hold at three-all almost as often as they do at any other stage of a match.

Momentum from the seventh game

At 3-3, a set is close, and every game matters. This is especially true in men’s tennis, where breaks are hard to come by. Against many players, getting broken so late in the set is almost the same as losing the set.

However, the focus on the seventh game is a bit odd. It’s important, but not as important as serving at 3-4, or 4-4, or 4-5, or … you get the idea. The closer a game to the end of the set, the more important it is–theoretically, anyway. If 3-3 is really worth the hoopla, it must grant the winner some additional momentum.

To measure the effect of the seventh game, I took another look at that pool of 11,000-plus sets that reached three-all. For each set, I calculated the two probabilities–based on each player’s service points won throughout the match–that the server would win the set:

  1. the 3-3 server’s chance of winning the set before the 3-3 game
  2. his chance of winning the set after winning or losing the 3-3 game

In this sample of matches, the average server at three-all had a 48.1% chance of winning the set before the seventh game. The servers went on to win 49.4% of the sets [2].

In over 9,000 of our 3-3 sets, the server held at 3-3. These players had, on average, a 51.3% chance of winning the set before serving at 3-3, which rose to an average of a 57.3% chance after holding. In fact, they won the set 58.6% of the time.

In the other 2,300 of our sets, the server failed to hold. Before serving at three-all, these players had a 35.9% chance of winning the set, which fell to 12.6% after losing serve. These players went on to win the set 13.7% of the time. In all of these cases, the model slightly underestimates the likelihood that the server at 3-3 goes on to win the set.

There’s no evidence here for momentum. Players who hold serve at three-all are slightly more likely to win the set than the model predicts, but the difference is no greater than that between the model and reality before the 3-3 game. In any event, the difference is small, affecting barely one set in one hundred.

When a server is broken at three-all, the evidence directly contradicts the momentum hypothesis. Yes, the server is much less likely to win the set–but that’s because he just got broken! The same would be true if we studied servers at 3-4, 4-4, 4-5, or 5-5. Once we factor in the mathematical implications of getting broken in the seventh game, servers are slightly more likely to win the set than the model suggests. Certainly the break does not swing any momentum in the direction of the successful returner.

There you have it. Players hold serve about as often as usual at three-all (whether they’re serving with new balls or not), and winning or losing the seventh game doesn’t have any discernible momentum effect on the rest of the set [3]. Be sure to tell your friendly neighborhood tennis pundits.

Continue reading How Important is the Seventh Game of the Set?

Should Andy Murray Skip the Tour Finals to Prepare for Davis Cup?

After advancing to the Davis Cup final, Andy Murray floated the idea that he might skip the World Tour Finals to prepare. The Belgian hosts are likely to choose clay for November’s Davis Cup tie (in part to make Murray less comfortable), and if Murray reached the final round in London the week before, he would have only four days off to recover and adjust to the different surface.

A lot of factors will go into Murray’s ultimate decision: how much importance he gives each event, how much he thinks fatigue will affect him, and how likely it is that the ATP would sanction him for skipping a required event. For today, I’ll have to ignore all of those and focus on the one most amenable to analysis: The effect of switching surfaces right before a Davis Cup tie.

Shifting from one surface to another immediately before Davis Cup is common. From 2009 to the present, there have been just over 2,000 World Group, Group 1, and Group 2 Davis Cup singles rubbers, and almost 450 of those involved at least one player who had played the previous week [1] on a different surface. It’s very rare that both players switched surfaces, so we have a sample of 432 matches in which one player changed surfaces from the previous week, and the other player either played or (presumably) prepared on the same surface.

At the simplest level of analysis, the switchers have been surprisingly effective. In those 432 matches between switchers and non-switchers, the switchers won 275, or 63.6% of the time. When we narrow the sample to the 130 times the switcher reached at least the round of 16 the week before Davis Cup (and, thus, had even less time to adjust), the results are surprisingly similar: 82 wins, or 63.1% in favor of the switchers.

Of course, there are all sorts of biases that could be working in favor of the switchers. The better the player, the less likely he can change his schedule to better prepare for Davis Cup, leaving him stuck on the “wrong” surface the week before a tie. And the better the player, the more likely he was a switcher in the smaller sample, one of those who reached the round of 16 the week before.

To evaluate the effect of switching, then, we must proceed with more subtlety. If switchers are more likely to be the favorites, we need to consider each player’s skill level and estimate how often switchers should have won. To do that, we can use JRank, my player rating system with surface-specific estimates for each competitor.

Immediately, we lose about 15% of our sample due to matches involving at least one player who didn’t have a rating at the time [2]. These are almost all Group 2 matches, so its doubtful that we lose very much. In the slightly smaller pool of 361 matches, the switcher won 62.0%, and when the switcher reached the round of 16 the previous week, he won 60.0%.

JRank confirms that the sample is strongly biased toward switchers. The player changing surfaces was favored in 69.8% of these contests. To take an extreme example, Murray went from hard courts at the 2013 US Open to clay courts in the World Group playoff against Croatia. Against Borna Coric, who hadn’t played the week before, Murray was a 99.1% favorite, and of course he won the match.

Once we calculate the probability that the switcher won each of the 361 matches, it turns out that the switchers “should have” won 227, or 62.8% of the time. That’s almost indistinguishable from the historical record, when the switchers won 224 matches. In the smaller sample of 120 matches when the switcher reached the round of 16 the previous week, switchers “should have” won 72 matches. As it happened, they won exactly 72.

In other words, it doesn’t appear to be a disadvantage to play Davis Cup matches on an unfamiliar surface. JRank-based predictions are primarily based on “regular” matches, so if switchers are performing at the level that JRank forecasts for them, they’re playing as well as they would at, say, the third round of a Slam, when the surface is familiar.

This isn’t a clear answer to Murray’s dilemma, of course. If he plays, say, Roger Federer and Novak Djokovic in back-to-back three-setters on Saturday and Sunday, then travels to a different venue, handles tons of press, and practices with a different set of coaches and fellow players before a big match the following Friday, he faces more of a challenge than your typical surface-switcher in our dataset.

However, there’s little evidence that surface-switching alone is a good reason to skip the Tour Finals. If history is any guide, Murray will play very well on the Belgian clay–just as well as he would at the same venue in the middle of the clay season.

Continue reading Should Andy Murray Skip the Tour Finals to Prepare for Davis Cup?

The Pivotal Point of 15-30

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

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

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

Reaching 15-30

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

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

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

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

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

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

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

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

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

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

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

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

The high-leverage next point

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

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

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

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

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

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

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

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

Winning the game from 15-30

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

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

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

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

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

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

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

Tentative conclusions

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

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

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

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

How Important is the First Point of Each Game?

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

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

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

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

The basics

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

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

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

Situations where it matters

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

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

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

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

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

Susceptible servers

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

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

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

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

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

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

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

Conventional overstatement

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

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

The Effects (and Maybe Even Momentum) of a Long Rally

In yesterday’s quarterfinal between Simona Halep and Victoria Azarenka, a highlight early in the third set was a 25-shot rally that Vika finished off with a forehand winner. It was the longest point of the match, and moved her within a point of holding serve to open the set.

As very long rallies often do, the point seemed like it might represent a momentum shift. Instead, Halep sent the game back to deuce after a 10-stroke rally on the next point. If there was any momentum conferred by these two points, it disappeared as quickly as it arose. It took eight more points before Azarenka finally sealed the hold of serve.

Does a long rally tell us anything at all? Does it have predictive value for the next point, or even the entire game, or is it just highlight-reel fodder that is forgotten as soon as the umpire announces the score?

To answer those questions, I delved into the shot-by-shot data of the Match Charting Project, which now contains point-by-point accounts of nearly 1,100 matches. I identified the longest 1% of points–17 shots or longer for women, 18 shots for men–and analyzed what happened afterwards, looking for both fatigue and momentum effects.

The next point

There’s one clear effect of a long rally: The next point will be shorter than average. The 10-shot rally contested by Vika and Simona yesterday was an outlier: Women average 4.45 shots on the point after a long rally, while the overall average (controlled for server and first or second serve) is 4.85. Men average 4.03 shots on the following point, compared to an average of 4.64.

For women, fatigue is also a factor for the server. Following a long rally, women land only 61.3% of first serves, compared to an average of 64.6%. Men don’t exhibit the same fatigue effect; the equivalent numbers are 62.3% and 62.2%.

There’s more evidence of an immediate fatigue factor for women, as well. The players who win those long rallies are slightly better than their opponents, winning 50.7% of points on average. Immediately after a long rally, however, players win only 49% of points.  It’s not obvious to me why this should be the case. Perhaps the player who won the long rally worked a bit harder than her opponent, maybe putting all of her remaining effort into a groundstroke winner, or finishing the point with a couple of athletic shots at the net.

In any case, there’s no equivalent effect for men.  After winning a long rally, players win 51.1% of their next points, compared to an expected 50.8%. That’s either a very small momentum effect or, more likely, a bit of statistical noise.

Both men and women double fault more often than usual after a long rally, though the effect is much greater for women. Immediately following these points, women double fault 4.7% of the time, compared to an average of 3.3%. Men double fault 4.5% of the time after a long rally, compared to an expected rate of 4.2%.

Longer-term momentum

Beyond a slightly effect on the characteristics of the next point, does a long rally influence the outcome of the game? The evidence suggests that it doesn’t.

For each long rally, I identified whether the winner of the rally went on to win the game, as Vika did yesterday. I also combined the score after the long rally with the average rate of points won on the appropriate player’s serve to calculate the odds that, from such a score, the player who won the rally would go on to win the game. To use yesterday’s example, when Azarenka held game point at AD-40, her chances of winning the game were 77.6%.

For both men and women, there is no significant effect. Women who won long rallies went on to win 66.2% of those games, while they would have been expected to win 65.7%. Men won 64.4% of those games, compared to an expected rate of 64.1%.

With a much larger dataset, these findings might indicate a very slight momentum effect. But limited to under 1,000 long-rally points for each gender, the differences represent only a few games that went the way of the player who won the long point.

For now, we’ll have to conclude that the aftereffects of a long rally have a very short lifespan: barely one point for women, perhaps not even that long for men. These points may well have a greater effect on fans than they do on the players themselves.

Break Point Persistence: Why Venus is Better Than Her Ranking

Some points matter a lot more than others. A couple of clutch break point conversions or a well-played tiebreak make it possible to win a match despite winning fewer than half of the points. Even when such statistical anomalies don’t occur, one point won at the right time can erase the damage done by several other points lost.

Break points are among the most important points, and because tennis’s governing bodies track them, we can easily study them. I’ve previously looked at break point stats, with a special emphasis on Federer, here and here. Today we’ll focus on break points in the women’s game.

The first step is to put break points in context. Rather than simply looking at a percentage saved or converted, we need to compare those rates to a player’s serve or return points won in general. Serena Williams is always going to save a higher percentage of break points than Sara Errani does, but that has much more to do with her excellent service game than any special skills on break points.

Once we do that, we have two results for each player: How much better (or worse) she is when facing break point on serve, and how much better (or worse) she is with a break point on return.

For instance, this year Serena has won 2.8% more service points than average when facing break point, and 7.5% more return points than average with a break point opportunity. The latter number is particularly good–not only compared to other players, but compared to Serena’s own record over the last ten years, when she’s converted break points exactly as often as she has won other break points.

Serena’s experience isn’t unusual. From one year to the next, these rates aren’t persistent, meaning that most players don’t consistently win or lose many more break points than expected. Since 2006, Maria Sharapova has converted 1% fewer break points than expected. Caroline Wozniacki has recorded exactly the same rate, while Victoria Azarenka has converted 2% fewer break points than expected.

On serve, the story is similar, with a slight twist. Inexperienced players seem to perform a little worse when trying to convert a break point against a more experienced opponent, so most top players save break points about 4% more often than they win other service points. Serena, Sharapova, Wozniacki, Azarenka, and Petra Kvitova all have career rates at about this level.

Unlike in the men’s game, there’s little evidence that left-handers have a special advantage saving break points on serve. Angelique Kerber is a few percentage points above average, but Kvitova, Lucie Safarova, and Ekaterina Makarova are all within one percentage point of neutral.

While a few marginal players are as much as ten percentage points away from neutral saving break points or converting them, the main takeaway here is that no one is building a great career on the back of consistent clutch performances on break points. Among women with at least 250 tour-level matches in the last decade, only Barbora Strycova has won more than 3% more break points (serve and return combined) than expected. Maria Kirilenko is the only player more than 3% below expected.

This analysis doesn’t tell us anything very interesting about the intrinsic skills of our favorite players, but that doesn’t mean it’s without value. If we can count on almost all players posting average numbers over the long term, we can identify short-term extremes and predict that certain players will return to normal.

And that (finally) brings us to Venus Williams. Since 2006, Venus has played break points a little bit worse than average, saving 2% more break points than typical serve points (compared to +4% for most stars) and winning break points on return 3% less often than other return points.

But this year, Venus has saved break points 17% less often than typical service points, the lowest single-season number from someone who played more than 20 tour-level matches. That’s roughly once per match this year that Venus has failed to save a break point that–in an average year–she would’ve saved.

There’s no guarantee that saving those additional break points would’ve changed many of Venus’s results this year, but given the usual strength of her service game, holding serve even a little bit more would make a difference.

This type of analysis can’t say whether a rough patch like Venus’s is due to bad luck, mental lapses, or something else entirely, but it does suggest very strongly than she will bounce back. In fact, she already has. In her successful US Open run, she’s won about 66% of service points while saving 63% of break points. That’s not nearly as good as Serena’s performance this year, but it’s much closer to her own career average.

Like so many tennis stats that fluctuate from match to match or year to year, this is another one that evens out in the end. A particularly good or bad number probably isn’t a sign of a long-term trend. Instead, it’s a signal that the short-term streak is unlikely to last.