Category Archives: Serve statistics

Ivo Karlovic and His Remarkable 10,466* Aces

Here’s the official story: This week, Ivo Karlovic crossed the much-heralded 10,000-ace milestone. Next up is the all-time record of 10,183 aces, held by Goran Ivanisevic.

Karlovic is one of the greatest servers in the game’s history, and he has in fact hit more than 10,000 aces. Ivanisevic was really good at serving, too, and he might even hold the all-time record. But when it comes down to the details in this week’s ATP press releases, all the numbers are wrong.

Last year, Carl Bialik laid out the two main problems with ATP ace records:

  • The ATP doesn’t have any stats from before 1991. (Ivanisevic started playing tour-level matches in 1988.)
  • ATP totals don’t include aces from Davis Cup matches, even though Davis Cup results are counted toward won-loss records and rankings.

I’ll add one more: There are plenty of other matches since 1991 with no recorded ace counts, too. By my count, we don’t have stats for 14 of Ivanisevic’s post-1991 matches. (They’re not on the official ATP site, anyway.) That doesn’t count Davis Cup, the Olympics (also no stats), and the now-defunct Grand Slam Cup.

If you like tracking records and comparing the best players from different eras, tennis might not be your sport. All of these problems exist for players who retired only recently, and some of the issues persist to the present day. And if you want to compare Federer or Ivanisevic with, say, Boris Becker or–it’s tough to write this without laughing–Pancho Gonzalez, you’re completely out of luck.

We’ll probably never find ace totals from all of the missing matches. But it seems silly to pretend we can identify the true record-holder and celebrate when these “records” are broken when we so obviously cannot.

Approximate* career* totals*

What we can do is estimate the number of missing aces for each of the top contenders. In Ivanisevic’s case, his 1988-90 seasons, combined with Davis Cup and other gaps in the record, total nearly 200 matches. Even if we can’t pinpoint the exact number of uncounted aces, we can come up with a number that demonstrates just how far ahead of Karlovic he currently stands.

To fill in the gaps, I calculated each player’s rate of aces per game for each surface for every season he played. For 1988-90, I used 1991 rates. (This post at First Ball In, which I discovered after writing mine, suggests that players improve their ace rates the first few seasons of their careers, so we should adjust a bit downward. That may be right. A 5% penalty for Goran’s 1988-90 knocks off about 60 aces from his total below.)

Once we crunch the numbers, we get an estimated 2,368 aces in Ivanisevic’s 195 “missing” matches. That gives him a career total of 12,551–a mark Karlovic couldn’t achieve until the end of 2017, if then.

But wait–Ivo has some missing matches, too! The gaps in his record only amount to 21 matches, mostly Davis Cup. The same approximation method adds 466 aces to his record, meaning he hit that 10,000th ace back in June, in his second-rounder against Alexander Zverev. Even with those nearly 500 “extra” aces, Ivanisevic’s record is almost surely out of reach.

What about Pete Sampras? Officially, Pete is fifth on the all-time list, with 8,858 aces. But like Goran, he played a lot of matches before record-keeping began in 1991. His ace record is missing nearly 200 matches, as well.

In Sampras’s case, we can estimate that he hit 1,815 aces that aren’t reflected in his official total. (In line with the caveat regarding Goran’s total above, we might want to knock that total down by 50 to reflect the possibility that he hit more aces in 1991 than in 1988-90.)

Making similar minor adjustments to the other members of the top five, Federer and Andy Roddick, here’s what the all-time list should look like, at least in general terms:

Player      Official  Est Missing  Est Total  
Ivanisevic     10183         2368      12551
Sampras         8858         1815      10673  
Karlovic       10022          466      10488  
Federer         9279          524       9803  
Roddick         9074          694       9768  

Coincidentally, Karlovic is officially within 200 aces of  Ivanisevic’s all-time record, and while he really isn’t anywhere near the record, he is that close our estimate of Sampras’s second-place total.

We can be confident that Ivo is a great server. But if we can’t be sure of his own ace total, mostly amassed in the last decade, it seems foolish to pretend that we’ll know when–or even if–he breaks the all-time record.

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Filed under Records, Serve statistics

The Almost Neutral Let Cord

Once I started charting matches–carefully watching and notating every shot–I thought I noticed a trend after “let” serves. It seemed that players missed far more first serves than usual after a let, and when players landed a post-let first serve, their offering was weaker than usual.

Now that we have nearly 500 pro matches in the Match Charting Project database, including at least 200 each from both the ATP and the WTA, there’s plenty of data with which to test the hypothesis.

To my surprise, there’s no such trend. If anything, players–men in particular–are more likely to make a first serve after a let cord. When they do, they are at least as likely to win the point as in non-let points, suggesting that the serve is no weaker than usual.

Let’s start with the ATP numbers. In over 1,100 points in the charting database, the server began with a let. He eventually landed a first serve 62.8% of the time, compared to 62.0% of the time on non-let points. When he made the first serve, he won 73.3% of points that began with a let serve, compared to only 70.6% of first-serve points when there was no let.

More first serves in, and more success on first serves. The latter finding, with its difference of 2.7 percentage points, is particularly striking.

Of the trends I had expected to see, only one is borne out by the data. Since a net cord let is only millimeters away from a fault into the net, it seems logical that net faults would be more common immediately after a let than otherwise. That is the case: 15.7% of men’s first serves result in faults into the net, but after a let,  that figure jumps to 17.0%.

When we turn to WTA matches with available data, we find that the post-let effect is even stronger. In non-let points, first serves go in at a 62.8% rate. After a first-serve let, players record a 65.3% first-serve percentage. Given that first-serve percentages are usually concentrated in a relatively small range, a difference of 2.5 percentage points is quite significant.

The WTA data tells a different story than the ATP numbers do when we look at the end result of those first serves. On non-let points, WTA players win first-serve points at a 62.8% rate, while after a first-serve let, they win these points at only a 61.8% clip. It may be that some women approach post-let first serves a bit more conservatively, and they pay the price by winning fewer of those points.

WTA players also appear to miss a few more post-let first serves into the net, though the difference is not as striking as it is for men. On non-let points, net faults make up 16.2% of the total, and after first-serve lets, net faults account for 16.7% of first serves. Of all the numbers presented here, this one is most likely to be no more than random noise.

It turns out that let serves don’t have much to tell us about the next serve or its outcome–and that’s not much of a surprise. What I didn’t expect was that, after a let serve, professionals are a bit more likely than usual to find success with their next offering.

If you like watching tennis and think this kind of research is worth reading, please consider lending a hand with the Match Charting Project. There’s no other group effort of its kind, and the more matches in the database, the more valuable the analysis.

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Filed under Match charting, Serve statistics

Donald Young’s Perpetual Hopes and the Lefty Serve That Isn’t

Donald Young celebrated his 25th birthday last week, and if you’ve been following the ATP for any part of the last decade, you know all about his talent, his potential, and his underwhelming results. Every time he goes deep in a tournament–as he has in Washington this week, upsetting Kevin Anderson in three sets today–all that upside talk gets dredged up again.  Is this finally the breakthrough for which we’ve waited so long?

In general, it’s a safe bet to watch longer-term trends more closely than short-term peaks and valleys. So the short, obvious answer is: No, it’s unlikely to be a sign of much greater things to come. Still, Young has beaten three top-50 players this week, and it’s a good time to take a closer look at what might be holding him back.

A prime obstacle isn’t hard to identify. Donald has one of the weakest serves on the ATP tour. While that doesn’t automatically keep him out of the top fifty in the world, it sure doesn’t help. Young’s year-to-date ace percentage, 3.4%, is among the ten worst on tour, and with the exception of David Ferrer and Roberto Bautista Agut, none of the other players on that list are inside the top 35. This year’s number is no slump, as Young’s ace rate has been below 4% every year since 2009.

Another metric to indicate the effectiveness of a player’s service game is the ratio of service winning percentage to return winning percentage (SW/RW). If a player wins lots of service points, it might be due to a good serve, or it might owe to a strong overall game. This ratio gives us a rough measure of how much a player’s success on serve is due to the serve itself.

Coming into Washington this week, Young’s SW/RW was 1.49, one of the lowest marks of any left-handed tour regular in the last ten years. A few right-handers succeed while winning only 50% more service points than return points–including Ferrer and, for one season, Andy Murray–but the average player on tour wins roughly 73% more serve points than return points. Even Rafael Nadal hasn’t fallen below the 1.5 mark since 2005.

As Ferrer has demonstrated, a player with Young’s level of service success can have a very good career on tour. Yet Ferrer’s skillset is unusual, and importantly, he’s a righty.

Not every successful ATP left-hander is a big server. Nadal won dozens of titles before fully developing the serve he uses today. Neither Fernando Verdasco nor Jurgen Melzer, two lefties who cracked the top ten, are known for overpowering deliveries. But in the last decade, Nadal is the only left-hander to consistently succeed with a SW/RW under 1.6.

It’s a different story for righties. As we’ve seen, Ferrer is a perennial top player despite Young-like serve stats. Fabio Fognini, Nikolay Davydenko, and Lleyton Hewitt have all enjoyed solid seasons without greater serve dominance than Young. (Though Hewitt has racked up better ace totals.)

Surprisingly, it isn’t that lefties are bigger servers. On average, both lefties and righties win about 73% more service points than return points. The tentative conclusion I see from these numbers is that lefties–with the typical exception of Rafa–can’t get away with a weak serve the way that right-handers can.

Young’s SW/RW this week of 1.69 suggests that, despite only 13 aces in four matches, he’s playing well behind his serve, and the results have followed.  It may be, though, that a modest improvement to his serve–or perhaps his tactics behind the serve–would be particularly valuable, seizing whatever specific advantages worked for guys like Verdasco and Melzer.

If Young is (finally) to take a big step forward, he’ll need to do more with his serve for a season–not just a week. He doesn’t need to become the next Feliciano Lopez; he just needs to be a little less like a left-handed Fognini.

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Filed under American tennis, Serve statistics, Washington

Bouchard, Radwanska, and Second Serve Futility

In yesterday’s women’s semifinals, we were treated to some impressive return-of-serve performances. Li Na won almost 65% of points on Eugenie Bouchard‘s serve–a higher percentage than she won on her own.

A less positive view of the situation is that we saw some dreadful serving performances. In particular, both Bouchard and Agnieska Radwanska struggled to win any points at all on their second serves. Genie won just 5 of 27 after missing her first serve, while Aga won only 2 of 16.

You don’t need an IBM Key to the Match to realize that those numbers aren’t going to cut it.

The WTA features a more return-oriented game and more breaks of serve than the ATP does, but these numbers are far out of the ordinary, especially for a solid server such as Bouchard. Here are some circuit-wide averages, derived from about 1,000 tour-level matches played last season:

  • WTA players win 55.5% of service points: 62.3% on first serves and 44.6% on second serves.
  • When the second serve lands in play–in other words, excluding double faults, players win 51.8% of second-serve points.
  • In the average losing performance, players won 57.1% of first-serve points, 40.0% of second-serve points, and 47.2% of second-serve points in play.

Then again, Li and Dominika Cibulkova–especially the Slovakian–aren’t average returners. In 16 Cibulkova wins for which I have serve statistics, she never failed to win at least half of second-serve return points. Only once did she win less than 58% of them, and her median performance was a whopping 63% of second-serve points won. In 7 of the 16 matches, she won second-serve return points at a higher rate than her own first-serve points.

Domi’s dismantling of Radwanska’s second serve still stands out, but in this context, it doesn’t look quite so unusual. When Cibulkova is hitting the ball well, you might as well be throwing batting practice once you miss your first offering.

While Li’s best return performances don’t quite stack up with Cibulkova’s, she has little trouble neutralizing her opponents in Melbourne. In six matches, she has won more than half of second-serve return points in every match, peaking with a 12-of-15 performance in the fourth round against Ekaterina Makarova. Overall, Li has won 86 of 136 second-serve return points in the tournament, good for 63%.

On Saturday, one of these powerful forces will have to give way to the other. The last time Li and Cibulkova met, in Toronto last summer, Domi had one of her worst serving performances of the year, winning only 35.5% of second-serve points, 44.0% of those that landed in play. In that match, Cibulkova failed to display the dominating return game that has been her trademark in Australia, winning barely half of Li’s second offerings, and only 41% when excluding double faults.

But as Cibulkova showed by crushing Radwanska for only the second time in six career meetings, her performances aren’t predictable. Her all-or-nothing style guarantees that we’ll see some fireworks in the final from both servers and returners. And at the rate she’s going, Domi might set some more records in the process.

For even more detailed analysis of yesterday’s semifinals, check out the charting-based analysis of Li-Bouchard and Radwanska-Cibulkova.

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Filed under Australian Open, Serve statistics, WTA

Novak Djokovic and Neutralizing the Second Serve

When Novak Djokovic stands on the other side of the court, you’d better make some first serves.

Djokovic is one of only two players this year to win more than 55% of second-serve-return points (David Ferrer is the other).  When you consider that he also wins more than 35% of first-serve-return points, it’s less clear that the server has much of an advantage.  In fact, when Novak is performing at that level, if his opponent goes through a bad patch and only makes a quarter of his first serves, Djokovic has a better than 50% chance of breaking serve.

Commentators often refer to Djokovic’s return as a weapon, and they’re not joking.  Only six players (including Novak himself and, invariably, John Isner) won as many second-serve points as Novak won second-serve-return points.

What’s most remarkable about his return game is how quickly he neutralizes the second serve, often using tactics that, in the hands of lesser mortals, would be more appropriate for service points.  Unlike other returners, he is somewhat more likely to win a short return point than a long one.  While other players need a few shots to negate the advantage conferred by serving, Djokovic is most effective early in service points.

This graph shows the percentage of second-serve-return points won by Djokovic, by rally length, in four matches I’ve charted (US Open vs Stanislas Wawrinka and Rafael Nadal; Tour Finals vs Wawrinka and Juan Martin del Potro), compared to the the same percentage for other top-ten players (excluding Rafael Nadal) in 19 other matches I’ve charted from the US Open and Tour Finals this year:

novak1

When the return lands in play, Djokovic wins almost 53% of return points, while the pack manages less than 44%.  (All of these matches are between top-ten opponents, so the averages are much lower than season numbers, which are affected by matches against lesser opponents.)  The difference stays about the same when we take out 2- and 3-shot rallies.

When we limit our view to points that reach six shots, Novak still has a substantial edge, roughly 48% to 42%.  But in points longer than seven shots, there’s virtually no difference.

Djokovic’s return is so good that if his opponent misses his first serve, the point has turned into a Novak service point.  Opponents are forced to fight their way into their own service points!

This was particularly true in the Djokovic-Nadal US Open final.  (Follow the link, then click the ‘Serve Influence’ tab for a shot-by-shot winning percentage breakdown.)  Nadal won barely half of his second-serve points when Djokovic got his return in play, but once the rally reached five shots (or six, or seven, and so on), Nadal had the edge, winning 60% of points.  From the five-shot mark, Rafa’s advantage only increased.

Of course, Nadal won that match.  It’s not quite so useful to convert return points into service against an opponent whose own return of serve is so effective.  To win today, Novak needs to do more than just attack Rafa’s second serve.  He must either do so even more effectively than he did in New York, or put himself in a better position to win longer return points after the effect of his return has worn off.

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Filed under Match charting, Serve statistics, World Tour Finals

Juan Martin del Potro and Return of Serve Gaps (+Updated WTForecast)

While Juan Martin del Potro isn’t known for his return of serve, it isn’t a major hole in his game.  This year, he has won 38.5% of return points, worse than most of the top 10, but better than Stanislas Wawrinka, Jo Wilfried Tsonga, and about 30 other members of the ATP top 50.

Where del Potro underwhelms is more specific.  Despite effectively returning second serves, he’s far worse than average against first serves.  In 2013, his 28.4% of first-serve-return points won ranked him 36th among the top 50, only 0.1% above Milos Raonic and far behind every other member of the top 10.  Yet Delpo is in the top ten when it comes to second-serve-return points.

Even for a big server like del Potro, it’s difficult to reach the top five without an effective return game.  While he breaks serve less often than any other World Tour Finals qualifier this year, he’s within a percentage point of Wawrinka, Tomas Berdych, and Roger Federer, so it’s clear that statistically, the Argentine is far from being a John Isner-style one-trick pony.

What sets him apart, then, is the enormous gap between first- and second-serve-return effectiveness.  To illustrate the difference, I calculated the ratio of second-serve-return points to first-serve-return points for all eight men in London this week, plus Andy Murray.  Delpo is third among all players with 40 or more tour-level matches this year, while the bottom five names on this list are all in the opposite third of ATP regulars.

Player                  v1W%   v2W%  v2/v1  
Juan Martin Del Potro  28.4%  53.4%   1.88  
Tomas Berdych          30.6%  54.6%   1.79  
Richard Gasquet        30.5%  54.2%   1.78  
Stanislas Wawrinka     30.7%  50.3%   1.64  
David Ferrer           34.5%  56.4%   1.63  
Andy Murray            33.7%  54.7%   1.62  
Roger Federer          32.9%  51.6%   1.57  
Novak Djokovic         35.5%  55.4%   1.56  
Rafael Nadal           35.0%  54.6%   1.56

An aspect–or perhaps a cause–of del Potro’s first-serve-return woes is his knack for letting aces sail by him.  In 2013, 10.5% of his opponents’ first serves were aces, more than any other member of the top 50.  Controlling for opponent serve quality (he did play Isner twice this year), he “improves” to third-worst, ahead of Dmitry Tursunov and Feliciano Lopez.  After this adjustment, we discover that Delpo allowed 22% more aces than an average player would have against the same set of opponents.

When aces are removed from the calculation, del Potro still stands out in comparison to other top players, but he is no longer quite so extreme.  His ratio of second-serve-return points won to first-serve-return points won ignoring aces is 1.55, just a bit higher than Berdych’s 1.53, Richard Gasquet‘s 1.52, and David Ferrer‘s 1.51.

If Delpo gets a racquet on the ball, then, he’s not that much less effective against first offerings than his London competitors.  But he doesn’t get his racquet on as many balls, and however we might manipulate the numbers for fun and profit, the Argentine doesn’t have the option to ignore aces.

So, how much does a poor first-serve return matter?  As with Murray’s infamous second serve, it’s tough to say.  In both cases, the weakness doesn’t keep its possessor from winning big matches against the game’s best, but it might be what is preventing him from ascending from the very top of the rankings.

Were del Potro to improve his first-serve return to the level of the next-worst London participant, Gasquet, it would mean a jump this year from 28.3% of first-serve-return points won to 30.5%.  That would bump up his overall return points won to just short of 40%, and improve his break percentage from its current middle-of-the-pack 23.8% to a nearly-top-ten 26.0%, in the neighborhood of Berdych and Federer.

An improvement of that nature would make Delpo a much bigger factor at the very top of the men’s game.  But like Murray’s second serve, it isn’t that easy.  There’s more than one route to the top–del Potro’s game isn’t so unbalanced to keep him from beating the best players in the world, so perhaps he could more easily improve, say, his second serve than his first-serve return.  It’s tough to tell from the sideline or, especially, the statsheet.

In the meantime, if you’re supporting del Potro tomorrow against Novak Djokovic, you might consider becoming one of those boorish fans that cheers every first-serve miss off of Novak’s racquet.  Lots of Djokovic second serves might be Delpo’s best path to victory.

London forecast: With Berdych’s win today, all eight players remain in contention.  A lot hinges on Friday’s match between Wawrinka and Ferrer, while we won’t gain much clarity on Group B until tomorrow.

Player     3-0  2-1  1-2  0-3       SF      F      W  
Nadal      70%  30%   0%   0%    98.4%  57.0%  34.1%  
Djokovic   42%  46%  11%   0%    88.3%  54.9%  30.9%  
Ferrer      0%   0%  54%  46%    14.8%   5.5%   2.0%  
Del Potro  22%  50%  28%   0%    71.6%  36.3%  16.4%  
Federer     0%  30%  51%  20%    29.9%  13.1%   5.9%  
Berdych     0%  30%  70%   0%    36.0%  12.4%   4.0%  
Wawrinka    0%  46%  54%   0%    50.9%  17.4%   5.6%  
Gasquet     0%  10%  44%  45%    10.1%   3.2%   1.0%

For the pre-tournament forecast, click here.

Berdych d. Ferrer: Click here for detailed serve, return, and shot-by-shot stats for today’s evening match.

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Filed under Serve statistics, World Tour Finals

Avoiding Double Faults When It Matters

The more gut-wrenching the moment, the more likely it is to stick in memory.  We easily recall our favorite player double-faulting away an important game; we quickly forget the double fault at 30-0 in the middle of the previous set.  Which one is more common? The mega-choke or the irrelevancy?

There are three main factors that contribute to double faults:

  1. Aggressiveness on second serve. Go for too much, you’ll hit more double faults.  Go for too little, your opponent will hit better returns.
  2. Weakness under pressure. If you miss this one, you lose the point. The bigger the point, the more pressure to deliver.
  3. Chance. No server is perfect, and every once in a while, a second serve will go wrong for no good reason.  (Also, wind shifts, distractions, broken strings, and so on.)

In this post, I’ll introduce a method to help us measure how much each of those factors influences double faults on the ATP tour. We’ll soon have some answers.

In-game volatility

At 30-40, there’s more at stake than at 0-0 or 30-0.  If you believe double faults are largely a function of server weakness under pressure, you would expect more double faults at 30-40 than at lower-pressure moments.  To properly address the question, we need to attach some numbers to the concepts of “high pressure” and “low pressure.”

That’s where volatility comes in.  It quantifies how much a point matters by considering several win probabilities.  An average server on the ATP tour starts a game with an 81.2% chance of holding serve.  If he wins the first point, his chances of winning the game increase to 89.4%. If he loses, the odds fall to 66.7%.  The volatility of that first point is defined as the difference between those two outcomes: 89.4% – 66.7% = 22.7%.

(Of course, any number of things can tweak the odds. A big server, a fast surface, or a crappy returner will increase the hold percentages. These are all averages.)

The least volatile point is 40-0, when the volatility is 3.1%. If the server wins, he wins the game (after which, his probability of winning the game is, well, 100%). If he loses, he falls to 40-15, where the heavy server bias of the men’s game means he still has a 96.9% chance of holding serve.

The most volatile point is 30-40 (or ad-out, which is logically equivalent), when the volatility is 76.0%.  If the server wins, he gets back to deuce, which is strongly in his favor. If he loses, he’s been broken.

Mixing in double faults

Using point-by-point data from 2012 Grand Slam tournaments, we can group double faults by game score.  At 40-0, the server double faulted 3.0% of points; at 30-0, 4.2%; at ad-out, 2.8%.

At any of the nine least volatile scores, servers double faulted 3.0% of points. At the nine most volatile scores, the rate was only 2.7%.

(At the end of this post, you can find more complete results.)

To be a little more sophisticated about it, we can measure the correlation between double-fault rate and volatility.  The relationship is obviously negative, with an r-squared of .367.  Given the relative rarity of double faults and the possibility that a player will simply lose concentration for a moment at any time, that’s a reasonably meaningful relationship.

And in fact, we can do better.  Scores like 30-0 and 40-0 are dominated by better servers, while weaker servers are more likely to end up at 30-40. To control for the slightly different populations, we can use “adjusted double faults” by estimating how many DFs we’d expect from these different populations.  For instance, we find that at 30-0, servers double fault 26.7% more than their season average, while at 30-40, they double fault 28.6% less than average.

Running the numbers with adjusted double fault rate instead of actual double faults, we get an r-squared of .444.  To a moderate extent, servers limit their double faults as the pressure builds against them.

More pressure on pressure

At any pivotal moment, one where a single point could decide the game, set, or match, servers double fault less than their seasonal average.  On break point, 19.1% less than average. With set point on their racket, 22.2% less. Facing set point, a whopping 45.2% less.

The numbers are equally dramatic on match point, though the limited sample means we can only read so much into them.  On match point, servers double faulted only 4 times in 296 opportunities (1.4%), while facing match point, they double faulted only 4 times in 191 chances (2.2%).

Better concentration or just backing off?

By now, it’s clear that double faults are less frequent on important points.  Idle psychologizing might lead us to conclude that players lose concentration on unimportant points, leading to double faults at 40-0. Or that they buckle down and focus on the big points.

While there is surely some truth in the psychologizing–after all, Ernests Gulbis is in our sample–it is more likely that players manage their double fault rates by changing their second-serve approach.  With a better than 9-in-10 chance of winning a game, why carefully spin it in when you can hit a flashy topspin gem into the corner?  At break point, there’s no thought of gems, just fighting on to play another point.

And here, the numbers back us up, at least a little bit.  If players are avoiding double faults by hitting more conservative second serves on important points, we would expect them to lose a few more second serve points when the serve lands in play.

It’s a weak relationship, but at least the data suggests that it points in the expected direction.  The correlation between in-game volatility and percentage of second serve points won is negative (r = -0.282, r-squared = 0.08).  Complicating the results may be the returner’s conservative approach on such points, when his initial goal is simply to keep the ball in play, as well.

Clearly, chance plays a substantial role in double faults, as we expected from the beginning.  It’s also clear that there’s more to it.  Some players do succumb to the pressure and double fault some of the time, but those moments represent the minority.  Servers demonstrate the ability to limit double faults, and do so as the importance of the point increases.

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The Unlikeliness of Inducing Double Faults

Some players are much better returners than others.  Many players are such good returners that everyone knows it, agrees upon it, and changes their game accordingly.  This much, I suspect, we can all agree on.

How far does that go? When players are altering their service tactics and changing their risk calculations based on the man on the other side of the net, does the effect show up in the numbers? Do players double fault more or less depending on their opponent?

Put it another way: Do some players consistently induce more double faults than others?

The conventional wisdom, to the extent the issue is raised , is yes.  When a server faces a strong returner, like Andy Murray or Gilles Simon, it’s not unusual to hear a commentator explain that the server is under more pressure, and when a second serve misses the box, the returner often gets the credit.

Credit where credit isn’t due

In the last 52 weeks, Jeremy Chardy‘s opponents have hit double faults on 4.3% of their service points, the highest rate of anyone in the top 50.  At the other extreme, Simon’s opponents doubled only 2.8% of the time, with Novak Djokovic and Rafael Nadal just ahead of him at 2.9% and 3.0%, respectively.

The conventional wisdom isn’t off to a good start.

But the simple numbers are misleading–as the simple numbers so often are.  Djokovic and Nadal, going deep into tournaments almost every week, play tougher opponents.  Djokovic’s median opponent over the last year was ranked 21st, while Chardy’s was outside the top 50.  While it isn’t always true that higher-ranked opponents hit fewer double faults, it’s certainly something worth taking into consideration.  So even though Chardy has certainly benefited from some poorly aimed second serves, it may not be accurate to say he has benefited the most–he might have simply faced a schedule full of would-be Fernando Verdascos.

Looking now at the most recent full season, 2012, it turns out that Djokovic did face those players least likely to double fault.  His opponents DF’d on 2.9% of points, while Filippo Volandri‘s did so on 3.9% of points.  While these are minor differences when compared to all points played, they are enormous when attempting to measure the returners impact on DF rate.  While Djokovic “induced” double faults on 3.0% of points and Volandri did so on 3.9% of points, you can see the importance of considering their opponents.  Despite the difference in rates, neither player had much effect on their opponents, as least as far as double faulting is concerned.

This approach allows to express opponent’s DF rate in a more efficient way, relative to “expected” DF rate.  Volandri benefited from 1% more doubles than expected, Chardy enjoyed a whopping 39% more than expected, and–to illustrate the other extreme–Simon received 31% fewer doubles than his opponents would be predicted to suffer through.

You can’t always get what you want

One thing is clear by now. Regardless of your method and its sophistication, some players got a lot more free return points in 2012 than others.  But is it a skill?

If it is a skill, we would expect the same players to top the leaderboard from one year to the next.  Or, at least, the same players would “induce” more double faults than expected from one year to the next.

They don’t.  I found 1405 consecutive pairs of “player-years” since 1991 with at least 30 matches against tour-level regulars in each season. Then I compared their adjusted opponents’ double fault rate in year one with the rate in year two.  The correlation is positive, but very weak: r = 0.13.

Nadal, one player who we would expect to have an effect on his opponents, makes for a good illustration.  In the last nine years, he has had six seasons in which he received fewer doubles than expected, three with more.  In 2011, it was 15% fewer than expected; last year, it was 9% more. Murray has fluctuated between -18% and +25%. Lots of noise, very little signal.

There may be a very small number of players who affect the rate of double faults (positively or negatively) consistently over the course of their career, but a much greater amount of the variation between players is attributable to luck.  Let’s hope Chardy hasn’t built a new game plan around his ability to induce double faults.

The value of negative results

Regular readers of the blog shouldn’t be surprised to plow through 600 words just to reach a conclusion of “nothing to see here.”  Sorry about that. Positive findings are always more fun. Plus, they give you more interesting things to talk about at cocktail parties.

Despite the lack of excitement, there are two reasons to persist in publishing (and, on your end, understanding) negative findings.

First, negative results indicate when journalists and commentators are selling us a bill of goods. We all like stories, and commentators make their living “explaining” causal connections.  Sometimes they’re just making things up as they go along. “That’s bad luck” is a common explanation when a would-be winner clips the net cord, but rarely otherwise.  However, there’s a lot more luck in sport than these obvious instances.  We’re smarter, more rational fans when we understand this.

(Though I don’t know if being smarter or rational helps us enjoy the sport more.  Sorry about that, too.)

Second, negative results can have predictive value. If a player has benefited or suffered from an extreme opponents’ double-fault rate (or tiebreak percentage) and we also know that there is little year-to-year correlation, we can expect that the stat will go back to normal next year. In Chardy’s case, we can predict he won’t get as many free return points, thus he won’t continue to win quite as many return points, thus his overall results might suffer.  Admittedly, in the case of this statistic, regression to the mean would have a tiny effect on something like winning percentage or ATP rank.

So at Heavy Topspin, negative results are here to stay. More importantly, we can all stop trying to figure out how Jeremy Chardy is inducing all those double faults.

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