Category: Serve statistics

Ivo Karlovic and the Odds-On Tiebreak

Italian translation at settesei.it

Ivo Karlovic is on track to accomplish something that no player has ever done before. Over the course of his career, Karlovic, along with John Isner, has set a new standard for one-dimensional tennis playing. The big men win so many service points that they are almost impossible to break, making their own service-return limitations manageable. With a player on court who maximizes the likelihood of service holds, tiebreaks seem inevitable.

This season, Karlovic has taken tiebreak-playing to a new level. Through last night’s semi-final at the Calgary Challenger (final score: 7-6, 7-6), the 6-11 Croatian has played 42 matches, including 115 sets and 61 tiebreaks. In percentage terms, that’s a tiebreak in 53% of all sets. Among player-seasons with at least 30 matches across the ATP, ATP qualifying, and ATP Challenger levels since 1990, no one has ever before topped 50%.

Even approaching the 50% threshold marks someone as very unusual. Less than 20% of tour-level sets reach 6-6, and it’s rare for any single player to top 30%. This year, only Isner and Nick Kyrgios have joined Karlovic in the 30%-plus club. Even Reilly Opelka, the seven-foot American prospect, has tallied only 31 tiebreaks in 109 sets this season, good for a more modest rate of 28.4%.

Karlovic is in truly uncharted territory. Isner came very close in his breakthrough 2007 season on the Challenger tour, playing 51 tiebreaks in 102 sets. The rest of the all-time top ten list starts to get a little repetitive:

Rank  Year  Player        Sets  TBs    TB%  
1     2018  Ivo Karlovic   115   61  53.0%  
2     2007  John Isner     102   51  50.0%  
3     2005  Ivo Karlovic   118   56  47.5%  
4     2016  Ivo Karlovic   146   68  46.6%  
5     2017  Ivo Karlovic    91   42  46.2%  
6     2006  Ivo Karlovic   106   48  45.3%  
7     2015  Ivo Karlovic   168   76  45.2%  
8     2018  John Isner     149   65  43.6%  
9     2001  Ivo Karlovic    78   34  43.6%  
10    2004  Ivo Karlovic   140   61  43.6%

* Karlovic’s and Isner’s 2018 totals are through matches of October 20th. 

For more variety, here are the 15 different players with the highest single-season tiebreak rates:

Rank  Year  Player           Sets  TBs    TB%  
1     2018  Ivo Karlovic      115   61  53.0%  
2     2007  John Isner        102   51  50.0%  
3     2004  Amer Delic         95   37  38.9%  
4     2008  Michael Llodra    117   45  38.5%  
5     2008  Chris Guccione    173   65  37.6%  
6     2002  Alexander Waske   109   40  36.7%  
7     1993  Greg Rusedski      99   35  35.4%  
8     2017  Reilly Opelka     115   40  34.8%  
9     2005  Wayne Arthurs      95   33  34.7%  
10    2004  Dick Norman        97   33  34.0%  
11    2001  Ivan Ljubicic     148   50  33.8%  
12    2004  Max Mirnyi        137   46  33.6%  
13    2014  Samuel Groth      172   57  33.1%  
14    2005  Gregory Carraz     98   32  32.7%  
15    2007  Fritz Wolmarans    80   26  32.5%

Karlovic is truly in a class by himself. He’ll turn 40 next February, but age has had little impact on the effectiveness of his serve. While he reached his career peak ranking of No. 14 back in 2008, it was more recently that his serve was at its best. In 2015, he won more than three-quarters of his service points and held 95.5% of his serve games. Both of those marks were career highs. His recent serve stats have remained among his career bests, winning 73.5% of service points in 2018, though as his ranking has tumbled, these feats have come against weaker competition, in ATP qualifying and Challenger matches.

Age has taken its toll, however, and Ivo’s return game is the victim. From 2008-12, he broke serve in more than one out of ten chances, while in 2016-18, it has fallen below 8%. Neither mark is particularly impressive–Isner and Kyrgios are the only tour regulars to break in less than 17% of games this season–but the difference, from a peak of 12.0% in 2011 to a low of 7.1% this year, helps explain why the Croatian is playing more tiebreaks than ever.

Karlovic has long been one of the most unique players on tour, thanks to his height, his extreme statistical profile, and his willingness (or maybe his need) to approach the net. As he gets older and his game becomes even more one-dimensional, it’s only fitting that he breaks some of his own records, continuing past the age when most of his peers retire in order to hit even more aces and play even more tiebreaks.

How Fast Was the Laver Cup Court?

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Italian translation at settesei.it

Laver Cup has redefined what a tennis event can be, and so far, the new definition seems to involve fast courts. Last year, we saw nine tiebreaks out of eighteen traditional sets, plus a pair of match tiebreaks that went to 11-9. This year’s edition wasn’t quite so extreme, with five tiebreaks out of sixteen traditional sets, but it still featured more tight sets than the typical tour event, in which tiebreaks occur less than once every five frames.

As usual, teasing out surface speed comes with its share of obstacles. Yes, there were lots of tiebreaks and yes, there were plenty of aces, but the player field featured more than its share of big servers. John Isner, Nick Kyrgios, and Roger Federer each contested two matches each year, and in Chicago, Kevin Anderson represented one-quarter of Team World’s singles contribution. No matter what the surface, we’d expect these guys to give us more serve-dominated matches than the tour-wide average.

Let’s turn to the results of my surface speed metric, which compares tournaments by using ace rate, adjusted for the serve and returning tendencies of the players at each event. The table below shows raw ace rate (“Ace%”) and the speed rating (“Speed”) for ten events from the last 52 weeks: The four 2018 grand slams, the fastest and slowest tour stops (Metz and Estoril, respectively), the two Laver Cups, and the two events that rate closest to the Laver Cups (Antalya and New York).

Year  Event            Surface   Ace%  Speed  
2018  Metz             Hard     10.6%   1.57  
2018  Antalya          Grass     9.9%   1.28  
2017  Laver Cup        Hard     17.0%   1.26  
2018  Australian Open  Hard     11.7%   1.17  
2018  Wimbledon        Grass    12.9%   1.16  
2018  Laver Cup        Hard     13.3%   1.09  
2018  New York         Hard     15.7%   1.09  
2018  US Open          Hard     10.8%   1.02  
2018  Roland Garros    Clay      7.7%   0.74  
2018  Estoril          Clay      5.2%   0.55

The speed rating metric ranges from about 0.5 for the slowest surfaces to 1.5 for the fastest, meaning that the stickiest clay results in about half as many aces as the same players would tally on a neutral surface, while the quickest grass or plexipave would give the same guys about half again as many aces as a neutral court would.

Last year’s Laver Cup, despite a whopping 17% ace rate, was barely among the top ten fastest courts out of the 67 tour stops I was able to rate. The surface in Chicago was on the edge of the top third, behind the speedy clay of Quito and considerably slower than the Australian Open.

These conclusions come with the usual share of caveats. First, surface speed is about more than ace rate. I’ve stuck with my ace-based metric because it’s one of the few stats we have for every tour-level event, and because despite its simplicity, it tracks closely with intuition, other forms of measurement, and player comments. Second, we’re not exactly overloaded with observations from either edition of the Laver Cup. Last year’s event featured nine singles matches, and this year there were eight. It’s even worse than that, because third sets are swapped out for match tiebreaks, leaving us even less data. That said, while we don’t have many matches to work with, we know a lot about the players involved, which isn’t as true of, say, Newport or Shenzhen, where a larger number of matches are contested by players who don’t make many appearances on tour.

The two Laver Cup surfaces rate as speedy, but not out of line with other indoor hard courts on the ATP tour. There will be tiebreaks and plenty of aces wherever Isner and Anderson go, no matter what the conditions.

The Right Amount of Serve-and-Volley

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Italian translation at settesei.it

In modern tennis, players approach the net at their own peril, especially behind their serve. Technological advances in both strings and rackets have made passing shots faster and more accurate, giving an added edge to the returner. It’s hard to imagine the game changing so that serve-and-volleying would once again become a dominant tactic.

Yet pundits and commentators often suggest that players should approach the net more often, sometimes advocating for more frequent serve-and-volleying. In a recent article at FiveThirtyEight, Amy Lundy brought some numbers to the discussion, pointing out that at the US Open this year, women have won 76% of their serve-and-volley points and men have won 66%. She also provides year-by-year numbers from the women’s Wimbledon draw showing that for more than a decade, the serve-and-volley success rate has hovered around the mid-sixties.

Sounds good, right? Well… not so fast. Through the quarter-finals in New York, men had won roughly 72% of their first-serve points. Most serve-and-volley attempts come on first serves, so a 66% success rate when charging the net doesn’t make for much of a recommendation. The women’s number of 76% is more encouraging, as the overall first-serve win rate in the women’s draw is about 64%. But as we’ll see, WTA players are usually much less successful.

Net game theory

When evaluating a tactic, we have to start by recognizing that players and coaches generally know what they’re doing. Sure, they make mistakes, and they can fall into suboptimal patterns. But it would be a big surprise to find that they’ve left hundreds of points on the table by ignoring a well-known option. If more frequent serve-and-volleying was such a slam dunk, wouldn’t players be doing so?

I dug into Match Charting Project data to get a better idea of how often players are using the serve-and-volley, how successful it has been. and, just as important, how successful they’ve been when they aren’t using it. The results are considerably more mixed than the serve-and-volley cheerleaders would have it.

Let’s start with the women. In close to 2,000 charted matches from 2010 to the present, I found 429 player-matches with at least one serve-and-volley attempt. After excluding aces, regardless of whether the server was intending to approach, those 429 players combined for 1,191 serve-and-volley attempts–95% of them on first serves–of which they won 747. Had those players not serve-and-volleyed on those 1,191 points and won at the same rate as their first- and second-serve baseline points in the same matches, they would have won 725 points. In other words, serve-and-volleying resulted in a winning percentage of 62.7%, and staying back was good for 60.9%. Just to be clear, this is a direct comparison of success rates for the same players against the same opponents, controlling for the differences between first and second serves.

A difference of nearly two percentage points is nothing to sneeze at, but it’s a far cry from the more than ten percent gap we’ve seen on the women’s side at the US Open this year. And it might not be enough of a benefit for many players to overcome their own discomfort or lack of familiarity with the tactic.

When we apply the same analysis to the men, the results are downright baffling. We have more data to work with here: In nearly 1,500 charted matches from 2010 to the present, more than half of the possible player-matches (1,631) tried at least one serve-and-volley. About four in five–once again excluding aces–were first serves. The tour-wide success rate was similar to what we’ve seen at the Open this year, at 66.8%.

Controlling for first and second serves, the same servers, at the same tournaments, facing the same opponents, won points at a 72.2% rate when they weren’t serve-and-volleying. That’s a five percentage point gap* that says men, on average, and serve-and-volleying too much.

* Technical note: These overall rates simply tally all the serve-and-volley attempts and successes for all players. Thus, they may give too much weight to frequent netrushers. I ran the same calculation in two other ways: giving equal weight to each player-match, and weighting each player-match by ln(a+1), where a is the number of serve-and-volley attempts. In both cases the gap shrunk a bit, to four percentage points, which doesn’t change the conclusion.

I was shocked to see this result, and I’m not sure what to make of it. It’s roughly the same for men who serve-and-volley frequently as for those who don’t, so it isn’t just an artifact of, say, the odd points that an Ivo Karlovic or Dustin Brown plays from baseline, or the low-leverage status of the occasional point when a baseliner decides to serve-and-volley. Since I don’t have a good explanation for this, I’m going to settle for a much weaker claim that I can make with more confidence: The evidence doesn’t suggest that men, in general, should serve-and-volley more.

Data from the women’s game is more encouraging for those who would like to see more serve-and-volleying, but it is still rather modest. Certainly, the 76% success rate in Flushing this year is a misleading indicator of what WTA players can expect to reap from the tactic on a regular basis. It’s possible that some women should come in behind their serves more often. But the overall evidence from a couple thousand matches suggests sticking to the baseline is just as good of a bet–if not better.

Two Servebots and Zero Tiebreaks

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Isner had energy to burn since he never needed to count to seven.

Italian translation at settesei.it

There have been plenty of upsets at this year’s US Open, but they all pale in comparison with the surprise that John Isner and Milos Raonic delivered Sunday night in their fourth round match. Isner won, 3-6 6-3 6-4 3-6 6-2, failing to hold twice and breaking Raonic’s serve four times. Rarely has a tiebreak seemed so assured, and the two big men didn’t even get close.

In five previous meetings, Isner and Raonic have been more likely to deliver two tiebreaks than only one, and most of their matches were best-of-three, not the grand slam best-of-five format. In 13 previous sets, they had played 9 tiebreaks. In the last year, 45% of Isner’s sets have reached 6-6, while nearly a quarter of the Canadian’s have. One or the other of these guys is responsible for the longest match in history, the longest ever major semi-final, and the longest match in Olympics history. They are really, really good at holding serve, and really not-so-good at breaking.

Great expectations

The likelihood that Isner and Raonic would play a tiebreak depends on some basic assumptions. If Raonic served like he has for the last 52 weeks, that’s a service-point won percentage (SPW) of 72.8%, which is equivalent to holding 93% of the time. If we use Isner’s actual SPW from the match of 74.3%, that translates to a hold rate of 94.4%. If we choose Isner’s SPW from his previous meetings with Raonic of a whopping 76.5%, that gives us an implied hold rate of 96%. Those all sound high but, as we’ll see, the difference between them ends up affecting the probability quite a bit.

I’m going to run the numbers using three sets of assumptions:

  1. The head-to-head. In five matches (four of them on hard courts, the fifth at Wimbledon this year), Isner won 76.5% of service points, while Raonic won 71.4%. That’s equivalent to hold rates of 96.0% and 91.7%, respectively.
  2. The last 52 weeks (adjusted). Across all surfaces, going back to last year’s US Open, Isner has won 73.6% of service points, against Raonic’s 72.8%. Those numbers, however, are against average opponents. Both players, and especially Isner, have below-par return games. If we adjust each SPWs for the other player’s rate of return points won (RPW), we get 75.5% for Isner and 78.5% for Raonic. In game-level terms, those are hold rates of 95.3% and 97.1%.
  3. The match itself. On Sunday night, Isner won 74.3% of service points and Raonic won 68.8%. Using these numbers doesn’t give us a true prediction, since we couldn’t have known them ahead of time. But maybe, if we used every scrap of information available to us and put them all together in a really smart way, we could have gotten close to the true number. Those rates translate to hold percentages of 94.4% for Isner and 88.5% for Raonic.

Not enough tiebreaks

Apparently, the betting odds for at least one tiebreak in the match set the probability around 95%. That turns out to be in line with my predictions, though the specific assumptions affect the result quite a bit.

I’ve calculated a few likelihoods using each set of assumptions. The first, “p(No brk),” is the probability that the two men would simply hold serve for 12 games. It’s not the only way to reach a tiebreak, but it accounts for most of the possibilities. Next, “p(TB)” is the result of a Monte Carlo simulation to show the odds that any given set would result in a tiebreak. “eTB” is the expected number of tiebreaks if we knew that Isner and Raonic would play five sets. Finally, “p(1+ TB)” is the chance that the match would have at least one tiebreak in five sets.

Model   JI Hld  MR Hld  p(No brk)   p(TB)   eTB  p(1+ TB)  
H2H      96.0%   91.7%      46.5%   51.3%   2.6     97.3%  
Last52   95.3%   97.1%      62.8%   65.3%   3.3     99.5%  
Match    94.4%   88.5%      34.0%   41.2%   2.1     93.0%

Given how the big men played on Sunday, it isn’t unthinkable that they never got to 6-6. In large part because Isner’s return game brought Raonic’s SPW under 70%, each set had “only” a 41.2% chance of going to a tiebreak, and there was a 7% chance that a five-setter would have none. The other two sets of assumptions, though, point to the sort of tiebreak certainty reflected in the betting market … and just about anyone who has ever seen these two guys play tennis.

Perhaps the strangest aspect of all of this is that, in six previous matches at this year’s Open, Isner and Raonic combined for seven tiebreaks–at least one in five of their six matches–before their anticlimactic encounter. Knowing Isner, this is a blip, not a trend, and he’s sure to give us a breaker or two in his quarter-final against Juan Martin del Potro. His tournament record will likely show one or two tiebreaks in every match … except for the one against his fellow servebot. This must be why we stick with tennis: Every match has the potential to surprise us, even if we never really wanted to watch it.

The Victims of Tiebreak Pressure

The conventional wisdom is that tiebreaks are all about two things: serves and mental strength. Despite my previous efforts, pundits continue to promote the idea that big servers have an edge in the first-to-seven shootout. Less contestably, experts remind us that a lot is at stake in a tiebreak, and the player who can withstand the pressure will prevail.

Back in 2012, I wrote a few articles about tiebreaks, using a year’s worth of data from men’s matches at grand slams to discover that servers hold less of an advantage during shootouts. On average, more points go the direction of the returner. I also found that very few players exceeded expectations in tiebreaks–that is, a player’s performance in non-tiebreak situations did a very good job of predicting his chances of winning tiebreaks. Last, I determined that big servers were not any more likely than their weaker-serving peers to be among the small group of players who boasted stronger-than-expected results in shootouts.

I’ve dug into a much larger dataset to revisit the first of these conclusions. My collection of sequential point-by-point data allows us to look at over 15,000 tiebreaks from the ATP tour alone, compared to fewer than 400 that I used in my earlier study. The broader and deeper sample will allow us go beyond general statements about serve or return advantages and look at how particular players fare in the jeu décisif.

Serving under pressure

First, the basics. In these 15,000 tour-level breakers, servers won 3.4% fewer points than they did in non-tiebreak situations. This is an apples-to-apples comparison: For each player in each match, I used his rate of service points won (SPW) on non-tiebreak points and his SPW on tiebreak points. To get the aggregate figure, I calculated the average of all player-matches, weighted by the number of tiebreaks in the match.*

* Initially, I weighted by the number of tiebreak points, thinking that, say, a 16-point tiebreak should be weighted more than an 8-point breaker. That gave me results that pointed to a huge improvement in SPW in tiebreaks … because of selection bias. When a tiebreak goes beyond 12 points, it often means that both players are serving well. Thus, when two servers are hot, they must play more points, increasing their weight in this calculation. It’s always possible that an extra-long tiebreak results from a lot of return points won, but in the serve-leaning men’s game, it is the much less likely scenario.

The 3.4% decrease in serve points won means that, for instance, a server who wins 65% on his own deal in the twelve games before the tiebreak will fall to 62.8% in the breaker. Fortunately for him, his opponent probably suffers the same drop. Benefits only accrue to those players who either maintain or increase their SPW after the twelfth game of the set.

It makes sense that servers suffer a bit under the pressure. In the men’s game, at least, the returner has little to lose. Since tiebreaks are thought to be serve-dominated, every return point won seems like a lucky break. Perhaps if players knew the real numbers, the mental game would shift back in their favor. They wouldn’t have to focus on becoming superhuman, unbreakable servers; they would need only to maintain the level that got them into the tiebreak in the first place.

The less-breakables

When we split things up by player, the dataset conveniently spits out 50 players with at least 100 tiebreaks. (Well, 49, but Nicolas Mahut was next on the list, so we’ll include him also.) The guys who play the most tiebreaks are either good, lucky, or both, because they’ve managed to stick around and play so many tour matches, so the average player on this list is a little better than the average player in general.

Here are the top and bottom ten in our group of the 50 most prolific tiebreak players. The first stat, “SPW Ratio,” is the ratio between tiebreak SPW and non-tiebreak SPW, so a higher number means that the player wins more serve points in tiebreaks than otherwise. Because that stat awkwardly centers on 0.966 (the 3.4% decrease), I’ve shown another stat, called here “Ratio+,” with all numbers normalized so the average is 1.0. Again, a higher number means more serve points won in tiebreaks. The 1.09 held by John Isner at the top of the list means that the big man wins 9% more breakers than expected, where “expected” is defined as the tour-average 3.4% drop.

Player               TBs  SPW Ratio  Ratio+  
Andy Murray          141       1.05    1.09  
John Isner           368       1.05    1.09  
Nick Kyrgios         109       1.05    1.08  
David Ferrer         132       1.01    1.05  
Alexandr Dolgopolov  116       1.01    1.05  
Lukas Rosol          100       1.01    1.05  
Jo-Wilfried Tsonga   188       1.01    1.04  
Roger Federer        175       1.01    1.04  
Nicolas Mahut         94       1.01    1.04  
Benoit Paire         139       1.00    1.04  
…                                            
Denis Istomin        120       0.94    0.98  
Viktor Troicki       104       0.94    0.97  
Tomas Berdych        181       0.93    0.96  
Nicolas Almagro      118       0.93    0.96  
Fernando Verdasco    156       0.93    0.96  
Robin Haase          123       0.93    0.96  
Adrian Mannarino     101       0.91    0.95  
Jiri Vesely          105       0.90    0.93  
Ryan Harrison        100       0.89    0.92  
Pablo Cuevas         100       0.87    0.90

Most of the big names who aren’t shown above (Rafael Nadal, Novak Djokovic, Juan Martin del Potro, Milos Raonic) are a bit better than average, with a Ratio+ stat around 1.02. I’m not surprised to see Isner or Roger Federer near the top, as those two have traditionally won more tiebreaks than expected. Less predictable is the chart-topping Andy Murray, who apparently manages to raise his serve game in breakers as well as anyone else.

Warning: Negative result ahead

Murray, Isner, and Federer have consistently served well in tiebreaks over the last seven years, the time span of this dataset. But even they have had seasons where they just barely edged out the tour average: Murray was 9% better than his peers in 2013 and 10% better in 2016, serving better in tiebreaks than non-tiebreaks by a 5% and 6% margin, resepectively, but in between, he was merely average. Isner, who was at least 10% better than tour average in each season from 2012 to 2015, served slightly worse in tiebreaks than in non-tiebreaks in 2016, and is just barely better than average in his first fifty shootouts of 2018.

These are small margins, and most players do not sustain positive or negative trends from year to year. To take another example, from 2014 to 2017, Raonic recorded single-season Ratio+ numbers of 1.11, 0.92, 1.00, and 0.98. I wouldn’t recommend putting any money on Milos’s full-season 2018 figure, let alone his tiebreak serve success in 2019.

Despite the evocative appearance of Isner, Federer, and Murray at the top of the list and some players considered to be mentally weaker near the bottom, there is no evidence that this is a skill, something that players will predictably repeat, rather than luck. As I did in my match point study earlier this week, I divided each player’s tiebreaks randomly into two groups. If tiebreak serve prowess were a skill, a player’s SPW Ratio in one random group would be reasonably predictive of his corresponding number in the other group. It is not to be: No matter where we set the minimum number of tiebreaks for inclusion, there is no correlation between the two groups.

If you’ve gone through many of my posts, you’ve read something like this before. Handling the pressure and serving well in tiebreaks seems like something that certain players will do well and others will not. This overall finding isn’t sufficient proof to say that no players have tendencies in either direction–most tour pros simply don’t contest enough tiebreaks over their entire careers to know that for sure. But with possible exceptions like Isner, Murray, Federer, and the unfortunate Pablo Cuevas, players converge around the tour average, which means their service game becomes a little less effective in breakers. If someone posts a particularly high or low SPW Ratio for a season, it probably means luck figured heavily in their results. If you’re going to bet on something using these numbers, the smart money suggests that most players will revert to the mean.

The Cost of a Double Fault

We all know that double faults aren’t good, but it’s less clear just how bad they are. Over the course of an entire match, a single point here or there doesn’t seem to matter too much, especially when a double fault creeps in at a harmless moment, like 40-love. Yet many missed second serves are far more costly. Let’s try to quantify the impact of tennis’s most enervating outcome.

To do this, we need to think in terms of win probability. In each match, a player wins a certain percentage of service points and a certain percentage of return points. If those rates are sufficiently dominating–say, Mihaela Buzarnescu’s 65% of service points won and 59% of return points won in last week’s San Jose final–the player’s chance of winning the match is 100%. No matter how unlucky or unclutch she was, those percentages result in a win. But in a close contest, in which both players win about 50% of points (often referred to as “lottery matches”), the result is heavily influenced by clutch play and luck. In Buzarnescu’s tour de force, flipping the result of a single point would be meaningless. But in a tight match, like the Wimbledon semifinal between John Isner and Kevin Anderson, a single point could mean the difference between a spot in the championship match and an early flight home.

My aim, then, is to measure the average win probability impact of a double fault. To take another example, consider last week’s Washington quarter-final between Andrea Petkovic and Belinda Bencic. Bencic won nearly 51% of total points–59% of her service points and 42% on return–but lost in a third-set tiebreak. Those serve and return components were enough to give her a 56.3% chance of winning the match: claiming more than half of total points usually results in victory, but so close to 50%, there’s plenty of room for things to go the other way.

I refer to this match because double faults played a huge role. Bencic tallied 12 double faults in 105 service points, a rate of 11.4%, more than double the WTA tour average of 5.1%. Had she avoided those 12 double faults and won those points at the same rate as her other 93 service points, she would have ended up with a much more impressive service-points-won rate of 67%. Combined with her 42% rate of return points won, that implies an 87% chance of winning the match–more than 30 percentage points higher than her actual figure! Roughly speaking, each of her 12 double faults cost her a 2.5% chance (30% divided by 12) of winning the match.

A double fault rate above 10% is unusual, but a cost of 2.5% per offense is not. When we run this algorithm across the breadth of the ATP and WTA tours, we find that the cost of double faults adds up fast.

Tour averages

Using the method I’ve described above–replacing double faults with average non-double-fault service points–and taking the average of all tour-level matches in 2017 and 2018 through last week’s tournaments, we find that the average WTA double fault costs a player 1.83% of a win. Put another way, every 55 additional double faults subtracts one match from the win column and adds one to the loss column.

In the men’s game, the equivalent number is 1.99% of a win. The slightly bigger figure is due to the fact that men, on average, win more service points, so the difference between a double fault and a successful service offering is greater.

There is, however, an alternative way we could approach this. By comparing double faults to all other service points, we’re trading a lot of the double faults for first serve outcomes. We might be more interested in knowing how a player would fare if his or her second serve were bulletproof–still eliminating double faults, but replacing them specifically with second serves instead of a generic mix of service points.

In that case, the algorithm remains very similar. Instead of replacing double faults with non-double-fault serve points, we replace them with non-double-fault second serve points. Then the cost of a double fault is a little bit less, because second serve points result in fewer points won than service points overall. The second-serve numbers are 1.61% per double fault in the women’s game and 1.70% per double fault in the men’s game. For the remainder of this post, I’ll stick with the generic service points, but one approach is not necessarily better than the other; they simply measure different things.

Building a player-specific stat

Odious as double faults are, they are not completely avoidable. Very few players are able to sustain a double fault rate below 2%, and tour averages are around twice that. Since the beginning of 2017, the ATP average has been about 3.9%, and the WTA average roughly 5.1%, as we saw above.

We can measure players by considering their match-by-match double fault rates compared to tour average. In Bencic’s unfortunate case, her 12 double faults were 6.7 more than a typical player would’ve committed in the same number of service points. In contrast, in the same match, Petkovic recorded only 3 double faults in 102 service points, 2.2 double faults fewer than an average player would have.

We know that each WTA double fault affects a player’s chances of winning the match by 1.83%, so compared to an average service performance, Bencic’s excessive service errors cost her about a 17% chance of winning (6.7 times 1.83%), while Petkovic’s stinginess increased her own odds by about 6.6% (2.2 times 1.83%).

Repeat the process for every one of a player’s matches, and you can assemble a longer-term statistic. Let’s start with the WTA players who, since the start of last season, have cost themselves the most matches (“DF Cost”–negative numbers are bad), along with those who have most improved their lot by avoiding double faults:

Player                   DF%  DF Cost  
Kristina Mladenovic     7.7%    -3.84  
Daria Gavrilova         7.9%    -3.77  
Jelena Ostapenko        7.7%    -3.58  
Petra Kvitova           8.1%    -3.01  
Camila Giorgi           8.3%    -2.63  
Oceane Dodin           10.2%    -2.51  
Donna Vekic             7.0%    -1.91  
Venus Williams          6.7%    -1.71  
Coco Vandeweghe         6.4%    -1.60  
Aliaksandra Sasnovich   6.7%    -1.55  
…                                      
Agnieszka Radwanska     2.3%     1.27  
Sloane Stephens         2.1%     1.43  
Caroline Wozniacki      3.2%     1.43  
Barbora Strycova        3.5%     1.47  
Elina Svitolina         3.9%     1.48  
Simona Halep            3.5%     1.53  
Qiang Wang              2.6%     1.54  
Anastasija Sevastova    3.1%     1.57  
Carla Suarez Navarro    2.1%     1.67  
Caroline Garcia         3.6%     1.82

And the same for the men:

Player                  DF%  DF Cost  
Benoit Paire           6.2%    -4.51  
Ivo Karlovic           5.8%    -3.63  
Fabio Fognini          5.0%    -2.38  
Denis Shapovalov       6.3%    -2.26  
Grigor Dimitrov        5.1%    -2.25  
Gael Monfils           5.0%    -2.22  
David Ferrer           5.2%    -2.06  
Jeremy Chardy          5.3%    -2.00  
Fernando Verdasco      4.8%    -1.94  
Jack Sock              4.8%    -1.73  
…                                     
Roger Federer          2.1%     0.88  
Tomas Berdych          2.9%     0.89  
Juan Martin del Potro  2.8%     0.93  
Albert Ramos           3.1%     0.97  
Pablo Carreno Busta    2.2%     1.07  
Richard Gasquet        2.6%     1.12  
John Isner             2.6%     1.23  
Dusan Lajovic          1.9%     1.23  
Denis Istomin          1.9%     1.23  
Philipp Kohlschreiber  2.5%     1.24

Situational double faults

These aggregate numbers have the potential to hide a lot of information. They consider only two things about each match: how many double faults a player committed, and how close the match was. This statistic would treat Bencic the same whether she hit nine of her double faults at 40-love, or nine of her double faults in the third-set tiebreak. Yet the latter would have a colossally greater impact.

While this is an important limitation to keep in mind, it appears that double faults are distributed relatively randomly. That is, most players do not hit a majority of their double faults in particularly high- or low-leverage situations. The player lists displayed above show both the most basic stat–double fault percentage–along with my more complex approach. For players with at least 20 matches since the beginning of last season, double fault rate is very highly correlated with the match-denominated cost of double faults. (For men, r^2 = 0.752, and for women, r^2 = 0.789.) In other words, most of the variance in double fault cost can be explained by the number of double faults, leaving little room for other factors, such as the importance of the situation when double faults are committed.

That said, there’s plenty of room for additional analysis into those specific sitations. Instead of taking a match-level look at win probability, as I have here, one could identify the point score of every single one of a player’s double faults, and see how each event affected the win probability of that match. I suspect that, for most players, that would amount to a whole lot of extra complexity for not a lot of added insight, but perhaps there are some players who are uniquely able to land their second serve when it matters most, or particularly prone to double faults at key moments. This match-level look has made it clear how costly double faults can be, and it’s possible that for some players, missed serves are even more damaging than that.

How Servers Respond To Double Faults

Italian translation at settesei.it

In the professional game, double faults are quite rare. They sometimes reflect a momentary lapse in concentration, and can negatively impact a server’s confidence. Players are sometimes particularly careful after losing a point to a double fault, taking some speed off their next delivery, or aiming closer to the middle of the box.

Let’s dig into some data from last year’s grand slams to see what players do–and how it affects their results–immediately after double faults. IBM’s Slamtracker provided point-by-point data for most 2017 grand slam singles matches, including serve speed and direction, and the available matches give us about 5,000 double faults to work with. (I’ve organized the data and made it freely available here.)

For each server in each match, I’ve tallied their results on points immediately following double faults. (That means that we exclude after-double-fault points when the double fault ended the game.) Then, for each player, I compared those results with match-long averages. Because double faults are so unusual, and because we only have this data for the majors, the sample isn’t adequate to tell us much about individual players. But for tour-wide analyses, it’s more than enough.

Serve points won: As we’ll see in a moment, men and women have different overall tendencies on the point following a double fault. But by the most important measure of simply winning the next point, gender plays little part. Men, who in this sample win 65.1% of service points, fall just over one percentage point to 64.0% on the point following a double fault. Women, who average 57.8% of service points won, drop even more, to 56.1% after a double.

First serve percentage: I expected that servers become more conservative immediately after a double fault. For women, that hypothesis is correct: In these matches, they land 63.3% of their first serves, while after a double fault, that number jumps to 65.4%. On the other hand, men don’t seem to change their approach very much. On average, they make 62.3% of their first offerings, a number that barely changes, to 62.5%, after double faults.

First serve points won: Here is additional evidence that women become more conservative after double faults, while men do not. In general, women win 63.7% of their first serve points, but just after a double fault, that number drops to 62.9%. For men, there is a decrease in first serve points won, but it is almost as small as their difference in first serve percentage: 72.7% overall, 72.4% after a double fault.

First serve speed: With serve speed, we run into a limitation of the Slamtracker data, which gives us speed only for those serves that go in. So when we look at the average speed of first serves, we’re excluding attempts that miss the box. Even with that caveat, the data keeps pointing in the same direction. Contrary to my “conservative” hypothesis, men serve a bit faster than usual after a double fault–183.3 km/h following doubles, versus 182.8 km/h in general. Women do seem to change their tactics, dropping from an average speed of 155.5 km/h to a post-double-fault pace of 152.2 km/h.

First serve direction: Slamtracker divides serve direction into five categories: wide, body-wide, body, body-center, and center. After a double fault, men are less likely than usual to hit a wide serve (24.1% to 25.8%), and those serves get split roughly evenly between the body and center categories. The difference in body serves is most striking: They account for only 3.5% of first serves overall, but 4.4% of post-double first serves. This may be the one way in which men opt for the conservative path, by maintaining speed but giving themselves a wider margin of error.

Women move many of their after-double-fault serves toward the middle of the box. On average, over 44% of serves are classified as either “wide” or “center,” but immediately after a double fault, that number drops below 41%. It’s not a huge difference, but like all of the other tendencies we’ve seen in the women’s game, it suggests that for many players, caution creeps in immediately after missing a second serve.

Tactics

As usual, it’s difficult to move from these sorts of findings to any sort of tactical advice. Even the first data point, that both men and women win fewer service points than usual right after they’ve double faulted, can be interpreted in multiple ways. By one reading, players may be serving too conservatively, missing out of the benefits of big first serves. On the other hand, if confidence is an issue, perhaps serving more aggressively would just result in more misses.

When in doubt, we have to trust that the players and coaches know what they’re doing–they’ve honed these tradeoffs through decades of experience and thousands of hours of match play. For fans, these numbers add to our understanding of the conclusions that players have reached. For the pros, perhaps a more detailed look at what happens after a double fault would help tweak their own strategies, both bouncing back from their own double faults and taking advantage of the lapses in concentration of their opponents.

Measuring the Impact of the Serve in Men’s Tennis

By just about any measure, the serve is the most important shot in tennis. In men’s professional tennis, with its powerful deliveries and short points, the serve is all the more crucial. It is the one shot guaranteed to occur in every rally, and in many points, it is the only shot.

Yet we don’t have a good way of measuring exactly how important it is. It’s easy to determine which players have the best serves–they tend to show up at the top of the leaderboards for aces and service points won–but the available statistics are very limited if we want a more precise picture. The ace stat counts only a subset of those points decided by the serve, and the tally of service points won (or 1st serve points won, or 2nd serve points won) combines the effect of the serve with all of the other shots in a player’s arsenal.

Aces are not the only points in which the serve is decisive, and some service points won are decided long after the serve ceases to have any relevance to the point. What we need is a method to estimate how much impact the serve has on points of various lengths.

It seems like a fair assumption that if a server hits a winner on his second shot, the serve itself deserves some of the credit, even if the returner got it back in play. In any particular instance, the serve might be really important–imagine Roger Federer swatting away a weak return from the service line–or downright counterproductive–think of Rafael Nadal lunging to defend against a good return and hitting a miraculous down-the-line winner. With the wide variety of paths a tennis point can follow, though, all we can do is generalize. And in the aggregate, the serve probably has a lot to do with a 3-shot rally. At the other extreme, a 25-shot rally may start with a great serve or a mediocre one, but by the time by the point is decided, the effect of the serve has been canceled out.

With data from the Match Charting Project, we can quantify the effect. Using about 1,200 tour-level men’s matches from 2000 to the present, I looked at each of the server’s shots grouped by the stage of the rally–that is, his second shot, his third shot, and so on–and calculated how frequently it ended the point. A player’s underlying skills shouldn’t change during a point–his forehand is as good at the end as it is at the beginning, unless fatigue strikes–so if the serve had no effect on the success of subsequent shots, players would end the point equally often with every shot.

Of course, the serve does have an effect, so points won by the server end much more frequently on the few shots just after the serve than they do later on. This graph illustrates how the “point ending rate” changes:

On first serve points (the blue line), if the server has a “makeable” second shot (the third shot of the rally, “3” on the horizontal axis, where “makeable” is defined as a shot that results in an unforced error or is put back in play), there is a 28.1% chance it ends the point in the server’s favor, either with a winner or by inducing an error on the next shot. On the following shot, the rate falls to 25.6%, then 21.8%, and then down into what we’ll call the “base rate” range between 18% and 20%.

The base rate tells us how often players are able to end points in their favor after the serve ceases to provide an advantage. Since the point ending rate stabilizes beginning with the fifth shot (after first serves), we can pinpoint that stage of the rally as the moment–for the average player, anyway–when the serve is no longer an advantage.

As the graph shows, second serve points (shown with a red line) are a very different story. It appears that the serve has no impact once the returner gets the ball back in play. Even that slight blip with the server’s third shot (“5” on the horizontal axis, for the rally’s fifth shot) is no higher than the point ending rate on the 15th shot of first-serve rallies. This tallies with the conclusions of some other research I did six years ago, and it has the added benefit of agreeing with common sense, since ATP servers win only about half of their second serve points.

Of course, some players get plenty of positive after-effects from their second serves: When John Isner hits a second shot on a second-serve point, he finishes the point in his favor 30% of the time, a number that falls to 22% by his fourth shot. His second serve has effects that mirror those of an average player’s first serve.

Removing unforced errors

I wanted to build this metric without resorting to the vagaries of differentiating forced and unforced errors, but it wasn’t to be. The “point-ending” rates shown above include points that ended when the server’s opponent made an unforced error. We can argue about whether, or how much, such errors should be credited to the server, but for our purposes today, the important thing is that unforced errors aren’t affected that much by the stage of the rally.

If we want to isolate the effect of the serve, then, we should remove unforced errors. When we do so, we discover an even sharper effect. The rate at which the server hits winners (or induces forced errors) depends heavily on the stage of the rally. Here’s the same graph as above, only with opponent unforced errors removed:

The two graphs look very similar. Again, the first serve loses its effect around the 9th shot in the rally, and the second serve confers no advantage on later shots in the point. The important difference to notice is the ratio between the peak winner rate and the base rate, which is now just above 10%. When we counted unforced errors, the ratio between peak and base rate was about 3:2. With unforced errors removed, the ratio is close to 2:1, suggesting that when the server hits a winner on his second shot, the serve and the winner contributed roughly equally to the outcome of the point. It seems more appropriate to skip opponent unforced errors when measuring the effect of the serve, and the resulting 2:1 ratio jibes better with my intuition.

Making a metric

Now for the fun part. To narrow our focus, let’s zero in on one particular question: What percentage of service points won can be attributed to the serve? To answer that question, I want to consider only the server’s own efforts. For unreturned serves and unforced errors, we might be tempted to give negative credit to the other player. But for today’s purposes, I want to divvy up the credit among the server’s assets–his serve and his other shots–like separating the contributions of a baseball team’s pitching from its defense.

For unreturned serves, that’s easy. 100% of the credit belongs to the serve.

For second serve points in which the return was put in play, 0% of the credit goes to the serve. As we’ve seen, for the average player, once the return comes back, the server no longer has an advantage.

For first-serve points in which the return was put in play and the server won by his fourth shot, the serve gets some credit, but not all, and the amount of credit depends on how quickly the point ended. The following table shows the exact rates at which players hit winners on each shot, in the “Winner %” column:

Server's…  Winner %  W%/Base  Shot credit  Serve credit  
2nd shot      21.2%     1.96        51.0%         49.0%  
3rd shot      18.1%     1.68        59.6%         40.4%  
4th shot      13.3%     1.23        81.0%         19.0%  
5th+          10.8%     1.00       100.0%          0.0%

Compared to a base rate of 10.8% winners per shot opportunity, we can calculate the approximate value of the serve in points that end on the server’s 2nd, 3rd, and 4th shots. The resulting numbers come out close to round figures, so because these are hardly laws of nature (and the sample of charted matches has its biases), we’ll go with round numbers. We’ll give the serve 50% of the credit when the server needed only two shots, 40% when he needed three shots, and 20% when he needed four shots. After that, the advantage conferred by the serve is usually canceled out, so in longer rallies, the serve gets 0% of the credit.

Tour averages

Finally, we can begin the answer the question, What percentage of service points won can be attributed to the serve? This, I believe, is a good proxy for the slipperier query I started with, How important is the serve?

To do that, we take the same subset of 1,200 or so charted matches, tally the number of unreturned serves and first-serve points that ended with various numbers of shots, and assign credit to the serve based on the multipliers above. Adding up all the credit due to the serve gives us a raw number of “points” that the player won thanks to his serve. When we divide that number by the actual number of service points won, we find out how much of his service success was due to the serve itself. Let’s call the resulting number Serve Impact, or SvI.

Here are the aggregates for the entire tour, as well as for each major surface:

         1st SvI  2nd SvI  Total SvI  
Overall    63.4%    31.0%      53.6%  
Hard       64.6%    31.5%      54.4%  
Clay       56.9%    27.0%      47.8%  
Grass      70.8%    37.3%      61.5%

Bottom line, it appears that just over half of service points won are attributable to the serve itself. As expected, that number is lower on clay and higher on grass.

Since about two-thirds of the points that men win come on their own serves, we can go even one step further: roughly one-third of the points won by a men’s tennis player are due to his serve.

Player by player

These are averages, and the most interesting players rarely hew to the mean. Using the 50/40/20 multipliers, Isner’s SvI is a whopping 70.8% and Diego Schwartzman‘s is a mere 37.7%. As far from the middle as those are, they understate the uniqueness of these players. I hinted above that the same multipliers are not appropriate for everyone; the average player reaps no positive after-effects of his second serve, but Isner certainly does. The standard formula we’ve used so far credits Isner with an outrageous SvI, even without giving him credit for the “second serve plus one” points he racks up.

In other words, to get player-specific results, we need player-specific multipliers. To do that, we start by finding a player-specific base rate, for which we’ll use the winner (and induced forced error) rate for all shots starting with the server’s fifth shot on first-serve points and shots starting with the server’s fourth on second-serve points. Then we check the winner rate on the server’s 2nd, 3rd, and 4th shots on first-serve points and his 2nd and 3rd shots on second-serve points, and if the rate is at least 20% higher than the base rate, we give the player’s serve the corresponding amount of credit.

Here are the resulting multipliers for a quartet of players you might find interesting, with plenty of surprises already:

                   1st serve              2nd serve       
                    2nd shot  3rd  4th     2nd shot  3rd  
Roger Federer            55%  50%  30%           0%   0%  
Rafael Nadal             31%   0%   0%           0%   0%  
John Isner               46%  41%   0%          34%   0%  
Diego Schwartzman        20%  35%   0%           0%  25%  
Average                  50%  30%  20%           0%   0%

Roger Federer gets more positive after-effects from his first serve than average, more even than Isner does. The big American is a tricky case, both because so few of his serves come back and because he is so aggressive at all times, meaning that his base winner rate is very high. At the other extreme, Schwartzman and Rafael Nadal get very little follow-on benefit from their serves. Schwartzman’s multipliers are particularly intriguing, since on both first and second serves, his winner rate on his third shot is higher than on his second shot. Serve plus two, anyone?

Using player-specific multipliers makes Isner’s and Schwartzman’s SvI numbers more extreme. Isner’s ticks up a bit to 72.4% (just behind Ivo Karlovic), while Schwartzman’s drops to 35.0%, the lowest of anyone I’ve looked at. I’ve calculated multipliers and SvI for all 33 players with at least 1,000 tour-level service points in the Match Charting Project database:

Player                 1st SvI  2nd SvI  Total SvI  
Ivo Karlovic             79.2%    56.1%      73.3%  
John Isner               78.3%    54.3%      72.4%  
Andy Roddick             77.8%    51.0%      71.1%  
Feliciano Lopez          83.3%    37.1%      68.9%  
Kevin Anderson           77.7%    42.5%      68.4%  
Milos Raonic             77.4%    36.0%      66.0%  
Marin Cilic              77.1%    34.1%      63.3%  
Nick Kyrgios             70.6%    41.0%      62.5%  
Alexandr Dolgopolov      74.0%    37.8%      61.3%  
Gael Monfils             69.8%    37.7%      60.8%  
Roger Federer            70.6%    32.0%      58.8%  
                                                    
Player                 1st SvI  2nd SvI  Total SvI  
Bernard Tomic            67.6%    28.7%      58.5%  
Tomas Berdych            71.6%    27.0%      57.2%  
Alexander Zverev         65.4%    30.2%      54.9%  
Fernando Verdasco        61.6%    32.9%      54.3%  
Stan Wawrinka            65.4%    33.7%      54.2%  
Lleyton Hewitt           66.7%    32.1%      53.4%  
Juan Martin Del Potro    63.1%    28.2%      53.4%  
Grigor Dimitrov          62.9%    28.6%      53.3%  
Jo Wilfried Tsonga       65.3%    25.9%      52.7%  
Marat Safin              68.4%    22.7%      52.3%  
Andy Murray              63.4%    27.5%      52.0%  
                                                    
Player                 1st SvI  2nd SvI  Total SvI  
Dominic Thiem            60.6%    28.9%      50.8%  
Roberto Bautista Agut    55.9%    32.5%      49.5%  
Pablo Cuevas             57.9%    28.9%      47.8%  
Richard Gasquet          56.0%    29.0%      47.5%  
Novak Djokovic           56.0%    26.8%      47.3%  
Andre Agassi             54.3%    31.4%      47.1%  
Gilles Simon             55.7%    28.4%      46.7%  
Kei Nishikori            52.2%    30.8%      45.2%  
David Ferrer             46.9%    28.2%      41.0%  
Rafael Nadal             42.8%    27.1%      38.8%  
Diego Schwartzman        39.5%    25.8%      35.0%

At the risk of belaboring the point, this table shows just how massive the difference is between the biggest servers and their opposites. Karlovic’s serve accounts for nearly three-quarters of his success on service points, while Schwartzman’s can be credited with barely one-third. Even those numbers don’t tell the whole story: Because Ivo’s game relies so much more on service games than Diego’s does, it means that 54% of Karlovic’s total points won–serve and return–are due to his serve, while only 20% of Schwartzman’s are.

We didn’t need a lengthy analysis to show us that the serve is important in men’s tennis, or that it represents a much bigger chunk of some players’ success than others. But now, instead of asserting a vague truism–the serve is a big deal–we can begin to understand just how much it influences results, and how much weak-serving players need to compensate just to stay even with their more powerful peers.

How Much Does Height Matter in Men’s Tennis?

Italian translation at settesei.it

Clearly, height matters. On average, tall players can serve faster and more effectively than can shorter players. And usually, short players who succeed on tour do so by returning and moving better than their taller colleagues. The conventional wisdom is that height is an advantage, but only up to a point. An inch or two above six feet (a range between 185 and 190 cm) is good, but much more than that is too much. No player above 6’4″ (193 cm, Marat Safin) has ever reached No. 1 in the ATP rankings.

While 5’7″ (170 cm) Diego Schwartzman‘s surprise run to the US Open quarterfinals has brought this issue to the forefront, pundits and fans talk about it all the time. This is a topic crying out for some basic data analysis, yet as is too often the case in tennis, some really simple work is missing from the conversation. Let’s try to fix that.

When I say “basic,” I really mean it. We all know that tall men hit more aces than short men. But how many? How strong is the relationship between height and, say, first serve points won? In this post, I’ll show the relationship between height and each of nine different stats, from overall records to serve- and return-specific numbers.

For my dataset, I took age-25 seasons from 1998 to 2017 in which the player completed at least 30 tour-level matches. (I used only one season per player so that the best players with the longest careers wouldn’t be weighted too heavily.) That gives us 156 player-seasons, from Hicham Arazi and Greg Rusedski in 1998 up to Schwartzman and Jack Sock in 2017. There aren’t very many players at the extremes, so I lumped together everyone 5’8″ (173 cm) and below and did the same with everyone 6’5″ (196 cm) and above. I also grouped players standing 5’10” with those at 5’9″, because there were only four 5’10” guys in the dataset.

That gives us nine “height levels”: one per inch from 5’8″ to 6’5″ with the exception of 5’10”. (The ATP website displays heights in meters, but its database must record and/or store them in inches, because every height translates to something close to an integer height in inches. For example, no player is listed at 174 cm, or 5’8.5″.) Some individual heights are certainly exaggerated, as male athletes and their organizations tend to do, but we have to make do with the information available, and we may assume that the exaggerations are fairly consistent.

Let’s start with the most basic building block of tennis, the match win. There is a reasonably strong relationship here, although the group of players at 6’1″ is nearly as good as the tallest subset. In each of these graphs, height is given on the horizontal axis in centimeters, from 173 (the 5’8″ and below group) up to 196 (the 6’5″ and higher group).

There is a similar, albeit slightly weaker, relationship when we look at the level of single points. Since a small difference in points results in a larger difference in matches won (at the extreme, winning 55% of points translates to nearly a 100% chance of winning the match) this isn’t a surprise. At the match level, r^2 = 0.38, and at the point level, below, r^2 = 0.27:

(If you’re wondering how all of the averages are above 50%, it’s because the sample is limited to player-seasons with at least 30 matches. A fair number of those matches are against players who aren’t tour regulars, and the regulars–the guys in this sample–win a hefty proportion of those matches.)

Serve stats

Now we get to confirm our main assumptions. Taller players are better servers, and the gap is enormous, ranging from 60% of service points won for the shortest players up to nearly 70% for the tallest:

As strong as that relationship is (r^2 = 0.81), the relationship between height and ace rate is stronger still, at r^2 = 0.83:

Aces don’t tell the whole story–the stat with the strongest correlation to height is first serve points won (r^2 = 0.92) as you can see here:

But this is where things start to get interesting. Nearly every inch makes a player more effective on the first serve, but opponents are able to negotiate tall players’ second serves much more successfully. There remains a modest relationship with height (r^2 = 0.18), but it is the weakest of all the stats presented here:

It’s nice to be tall, as anyone who has seen John Isner casually spin a second-serve ace out of the reach of an unlucky opponent. But except in the tallest category, height doesn’t confer much of a second-serve advantage. Players standing 6’4″ (193 cm) win about as many second-serve points as do players at 5’9″ (175 cm). That doesn’t mean that the second serves of the shorter players are just as good–they probably aren’t–but that shorter players tend to possess other skills that they can leverage in second-serve points, which usually last longer. For the purposes of today’s overview, it doesn’t really matter why short players are able to negate the advantage of height on second serve points, just that they are clearly able to do so.

Return stats

We wouldn’t be having this conversation–and David Ferrer wouldn’t be headed to a likely place in the Hall of Fame–if the inverse relationship between height and return effectiveness weren’t nearly as strong as the positive one between height and serving prowess. “Nearly” is the key word here. The relationship between height and overall return points won is almost as strong (r^2 = 0.74) as that of height and overall service points won, but not quite:

Schwartzman is doing more than his part to hold up the left side of that trendline: He is both the shortest player in the top 50 and the best returner. On first serve points, however, there’s only so much the returner can do, so while shorter players still have an advantage, it is less substantial. The relationship here is a bit weaker, at r^2 = 0.63:

It follows, then, that the relationship between height and second-serve return points won must be stronger, at r^2 = 0.77:

The overall and first-serve return point graphs make clear just how much worse the tallest players are than the rest of the pack. The graphs exaggerate it a bit, because I’ve grouped players from 6’5″ all the way up to 6’11”, and the Isners of the sport are considerably less effective than players such as Marin Cilic. Still, we find plenty of confirmation for the conventional wisdom that a height of 6’2″ or 6’3″ (188 cm to 190 cm) allows for players to remain effective on both sides of the ball, while a small increase from there can be a disadvantage.

A note on selection bias

It’s easy to lapse into shorthand and say something like, “shorter players are better returners.” More precisely, what we mean is, “of the players who have become tour regulars, shorter players are better returners.” They have to be, because it is nearly impossible for them to be top-tier servers. If they’ve cracked the top 50, they must have developed a world-class return game. The shorter the player, the more likely this is true.

The same logic is considerably weaker if we descend a couple rungs lower on the ladder of tennis skill. In collegiate tennis, it’s still an advantage to be tall–as Isner can attest–but a player such as 5’10” Benjamin Becker can serve as well as nearly all the competition he will face at that level.

One more note on selection bias

My choice to use each player’s age-25 season might understate the ability of either short or tall players. It is possible that certain playing styles result in earlier or later peaks, meaning that while tall players could be better at age 25, shorter players may be superior at age 28. There are anecdotes that support the argument in both directions, so I don’t think it’s a major issue, but it is one worthy of additional study.

Further reading

A guest post on this blog earlier this year posed the question, Are Taller Players the Future of Tennis?

I didn’t mention serve speed in the above, but here’s a quick study of the fastest serves and their correlation with height.

Second-Strike Tennis: When Returners Dominate

Italian translation at settesei.it

On Wednesday, Diego Schwartzman scored a notable upset, knocking out 12th seed Roberto Bautista Agut in the second round of the Monte Carlo Masters. Even more unusual than Bautista Agut’s first-round exit was the way it happened. Both players won more than half of their return points: 61% for Schwartzman and 52% for Bautista Agut. There were 14 breaks of serve in 21 games.

Players like Schwartzman win more than half of return points fairly regularly. In the last 12 months, including both Challenger and tour-level matches, the Argentine–nicknamed El Peque for his diminutive stature–has done so more than 20 times. What is almost unheard of in the men’s game is for both players to return so well (or serve so poorly) that neither player wins at least half of his service points.

Since 1991–the first year for which ATP match stats are available–there have been fewer than 70 matches in which both players win more than half of their return points. (There are another 25 or so in which one player exceeded 50% and the other hit 50% exactly.) What’s more, these matches have become even less frequent over time: Wednesday’s result was the first instance on the ATP tour since 2014, and there have been fewer than 30 since 2000.

Here are the last 15 such matches, along with the both the winner’s (W RPW) and loser’s (L RPW) rates of return points won. Few of the players or surfaces come as a surprise:

Year  Event            Players                 W RPW  L RPW  
2017  Monte Carlo      Schwartzman d. RBA      61.4%  51.9%  
2014  Rio de Janeiro   Fognini d. Bedene       50.6%  50.6%  
2014  Houston          Hewitt d. Polansky      51.3%  51.5%  
2014  Estoril          Berlocq d. Berdych      51.5%  50.6%  
2013  Monte Carlo      Bautista Agut d. Simon  58.8%  50.6%  
2013  Estoril          Goffin d. P Sousa       55.2%  50.5%  
2011  Casablanca       Fognini d. Kavcic       51.0%  51.9%  
2011  Belgrade         Granollers d. Troicki   61.5%  50.8%  
2008  Barcelona        Chela d. Garcia Lopez   54.3%  50.5%  
2008  Costa Do Sauipe  Coria d. Aldi           58.5%  51.9%  
2007  Rome Masters     Ferrero d. Hrbaty       52.9%  51.7%  
2007  Hamburg          Ferrer d. Bjorkman      50.6%  50.6%  
2006  Monte Carlo      Coria d. Kiefer         53.2%  50.9%  
2006  Hamburg Masters  Gaudio d. A Martin      57.3%  51.1%  
2006  Australian Open  Coria d. Hanescu        53.4%  50.6%

All but 8 of the 69 total matches were on clay. One of the exceptions is at the bottom of this list, from the 2006 Australian Open, and before 2006, there were another five hard-court contests, along with two on grass courts. (The ATP database isn’t completely reliable, but in each of these cases, the high rate of return points won is partially verified by a similarly high number of reported breaks of serve.)

Bautista Agut, who won one of these matches four years ago in Monte Carlo, is one of several players who participated in multiple return-dominated clashes. Guillermo Coria played in five, winning four, and Fabrice Santoro took part in four, winning three. Coria won more than half of his return points in 75 tour-level matches over the course of his career.

Over course, both Schwartzman and Baustista Agut cleared the 50% bar with plenty of room to spare. The Spaniard won 51.9% of return points and Schwartzman comfortably exceeded 60%, putting them in an even more elite category. It was only the 22nd match since 1991 in which both players won at least 51.9% of return points.

As rare as these matches are, Schwartzman is doing everything he can to add to the list. With a ranking now in the top 40, he has entered just about every clay tournament on the schedule, so the most return-oriented competitor in the game is going to play a lot more top-level matches on slow surfaces. If anyone has a chance at equaling Coria’s mark of winning four of these return-dominated matches, my money’s on El Peque.