Match length – Heavy Topspin

What Happens to the Pace of Play Without Fans, Challenges, or Towelkids?

The COVID-19 pandemic has forced some experimentation on the US Open ahead of schedule. After just a couple of years at marginal events such as the NextGen Finals, Hawkeye’s live line-calling system is taking over (on most courts) for human line judges. Another NextGen-tested innovation, requiring players to fetch their own towels, has also arrived for social distancing reasons.

Automated line-calling and towel-fetching pale in comparison to the biggest change for the bubble slam: no fans. The biggest stars now get to experience what has long been de rigueur for qualifiers and challengers: high-stakes competition with no one in the stands watching.

All of these changes come not long after the US Open (and a few other tournaments) finally adopted a serve clock. I’ve written ad nauseam* about the effect of the serve clock, which is nominally designed to speed up play, but in practice has slowed it down. The problem is that chair umpires start the clock when they announce the score, which is not always immediately after the preceding point. The bigger the crowd, the more serious the discrepancy, as noisy fans tend to delay announcements from the chair.

* Incidentally, this is also the Latin term for a long game with many deuces.

Therefore, the pace of play should be faster with no fans, right? Use of the Hawkeye live system also eliminates challenges, which should speed things up a little more. The counteracting force is the time it takes players to fetch their towels. It would be nice to evaluate each of these effects in isolation*, but most of the data we have comes from matches with all of these changes at once.

* No pun intended.

The net effect

The most straightforward measurement of pace of play is seconds per point, where we simply take the official match time and divide by the total number of points. It’s an approximate measure, because official match time includes changeovers, medical timeouts, and all sorts of other delays which have nothing to do with how long it takes for players to get themselves to the line and hit a serve. It also captures a bit of first serve percentage (second serve points take more time) and rally length (longer rallies take more time), although these factors mostly wash out, especially when comparing pace of play at the same tournament from one year to the next.

The following graph shows seconds per point for all Cincinnati (and “Cincinnati”) main draw men’s singles matches each year since 2000:

(I’m looking only at pace of play for men’s matches because I don’t have match time for women before 2016. Lame, I know.)

Over the 21-year span, the average time per point is just under 40 seconds, and before 2020, the yearly average exceeded 42 seconds only once. This year, Cinci clocked in at a whopping 44.6 seconds per point, more than three standard deviations above the 2000-2017 (that is, pre-serve clock) average. The pace has gradually slowed down over the years for reasons unrelated to the serve clock, so it’s probably overstating things a bit to say that the effect of the bubble is 3 SD, but it’s clear that 2020 was slow.

But wait, what about

All four of this year’s men’s semi-finalists are rather deliberate, so you might think that the slow average pace is due in part to the mix of players who won a lot of matches. That’s what I thought too, but it’s not so. (It helps to remember that more than half of a tournament’s matches are in the first two rounds, even with some first-round byes, so we’re guaranteed a decent mix of players for calculations like this, no matter who advances.)

First, I re-did the seconds-per-point calculations above, but excluded all matches with Novak Djokovic or Rafael Nadal, two guys who win a lot of matches and are known to play slowly. It didn’t really matter. I won’t bother to print a second graph, because it looks essentially the same as the one above.

Another approach is to consider the average pace of play for each player in the draw, and compare his seconds per point in Cincinnati to his seconds per point at other events. If every man played at the same speed in Cincinnati that he did on average in 2019, the average seconds per point at the 2020 Cinci event would have been 41.3. That’s just barely above the 2019 Cinci figure of 41.0, and of course it is far below the actual rate of 44.6 seconds per point. The mix of players can’t account for 2020’s glacial pace.

But why?

I hope you’re with me thus far that the pace of play in the 2020 Cincinnati men’s event was very slow. It seems reasonable to assume that the US Open will be the same, because the conditions and rules are identical.

The simplest explanation is that players are spending extra time fetching their own towels.*

* No, you’re a towel.

It’s true–walking to and from the towel takes time. But it’s not the whole story. At the typical non-bubble rate of 40 seconds per point (again, including changeovers and other delays), there are plenty of points where the umpire delays calling the score and the server ends up taking longer than the rulebook-permitted 25 seconds without getting called for a time violation. So if the average is now pushing 45 seconds, there must be a lot of points like that.

Anecdotally, there definitely are such points. In the Cincinnati semi-final, I noticed one instance in which Roberto Bautista Agut used more than 40 seconds before serving. He’s not the only offender: All four men’s semi-finalists (among many others) occasionally used more than 25 seconds. My impression was that, ironically, Djokovic was the speediest of the four.

Chair umpires are using their discretion to act as if there are fans making noise. After long points, they often wait to call the score, and even when they announce the score immediately, they hold off several more seconds before starting the clock. In one glaring instance in the Lexington final, the umpire waited a full 17 seconds after the previous point ended before the clock showed 0:25. The broadcast camera angles at the National Tennis Center made it hard to measure the same thing for Cincinnati matches, but given the length of time between points and the dearth of time violation penalties, there must have been other delays in the range of 15 to 20 seconds.

With no fans delaying play, and no tactical challenges to force a delay, a slow pace is something that the umpire can control. Yes, towel-fetching takes time, but if the 25-second clock starts immediately and it is enforced, players will make it back to the line in time–matches at the NextGen Finals were generally brisk. But apparently, enforcing the rulebook-standard pace is not something that the officials are willing to do. We’re two years into the great tennis serve-clock experiment, and the game just keeps getting slower.

Let Bernie Keep His Money

Italian translation at settesei.it

On Tuesday, Bernard Tomic lost his first-round match at Wimbledon to Jo-Wilfried Tsonga. No surprise there: My forecast gave Tsonga a 64% chance of advancing, and that didn’t even take into account Tomic’s shaky health, which has caused him to retire from matches twice in the last six weeks.

Tomic-Tsonga immediately made the news, and for the wrong reasons. The Australian lost, winning only seven games. Ignominiously, the match lasted only 58 minutes, the shortest at Wimbledon since Roger Federer needed only 54 minutes to thump Alejandro Falla back in 2004.

The All England Club responded this morning, announcing that Tomic would lose his prize money. Officially, he “did not perform to the required professional standard.”

Fast and insufficiently furious

I don’t know whether Tomic performed to the required professional standard, because there’s no exact definition of “professional standard.” I suspect it’s some combination of the following:

The player lost badly
The player has a reputation for tanking
The match got a lot of attention so we have to be seen doing something about it

What I do know is that Wimbledon officials are looking at the wrong number. Yes, 58 minutes is an extremely fast three-set match. But Tomic–even when he’s fully engaged and playing his best–is probably the quickest player on tour, often serving as soon as a ballkid gets him the ball. Tsonga also plays fast. Neither player is a good returner, and the Frenchman is a devastating server on a fast surface, so the points were always going to be short.

The more appropriate metric, then, is points played. Tomic and Tsonga contested 125, which is considerably less headline-grabbing than the time on the clock.

Fines all around!

Suddenly, Tomic-Tsonga doesn’t stand out as much. Since 2000, there have been 77 other men’s grand slam matches that required 125 points or less. That’s almost exactly one per slam. The list includes two quarter-finals, three semi-finals, and the 2003 Australian Open title match, in which Andre Agassi dispatched Rainer Schuettler in 76 minutes, needing only 123 points. If we expand our view to matches with fewer than 130 points, we’re looking at another 45 matches, including both of this year’s Australian Open semi-finals.

Simply put: It is not unusual for a men’s slam match to be decided with 125 points. Really good players sometimes lose that fast. It just doesn’t usually attract so much attention, because on average, 125 points takes an hour and 21 minutes to play.

Of course, there are plenty of one-sided contests in the women’s draw, as well. 125 points is about 42 per set, so the “Tomic line” is at 83 or 84 points for a best-of-three match. Since 2003, there have been 235 women’s singles matches of 83 points or less, including five at this year’s French Open alone. (Ironically, Anna Tatishvili’s loss to Maria Sakkari, which triggered its own unprecedented fine, lasted 93 points and 28 minutes per set.)

Reactionary

All of this isn’t to say that Tomic tried his hardest on Tuesday, or that he “deserves” £45,000 in an ethical sense. If tournament referees made it a practice to review video of every first-round match and dock the prize money of the one player who competed most lackadaisically, then sure, the Australian is probably that guy at Wimbledon this year.

But that’s not how it works. The “professional standard” clause is almost never invoked. Had Tomic frittered away more time between points in order to push this match over the one-hour mark, or the offender had been a player with a less checkered past, we wouldn’t be talking about it now.

If the All England Club were focused on the right metric–the amount of tennis played, not how long it took–Bernie’s speedy, casual style of play wouldn’t be in the headlines. After all, there’s another casual, mercurial Australian with a poor return game who deserves more of our attention today.

Another Slam, Another Pointless Serve Clock

Italian translation at settesei.it

The 25-second serve clock has quickly become a regular feature on the ATP and WTA tours. After a few trials, it made a debut in the run-up to last year’s US Open, and has become broadly accepted since. The US Open and Australian Open both used the countdown timer, and the WTA will employ the devices at 2019 Premier events, with an eye toward the full slate of tournaments in 2020.

As I understand it, the goal of the serve clock is twofold: First, to keep matches shorter by holding players to a standard time limit between points; and second, to enforce that time limit fairly. Tennis and broadcasting execs are always looking for ways to make matches shorter (or, at least, more predictable in length), so the first goal fits in with broader aims. The second is more specific. Many of the players best known for using a long time between points are big stars, and umpires were thought to be reluctant to penalize them. In theory, a standardized serve clock should make enforcement more transparent and ensure fairness.

The success of the second goal is difficult to assess. In one regard, it seems to be working, because we haven’t heard many players complaining about the system. Progress toward the first goal is much easier to judge, and I’ve done so three times: Once after the 2018 Rogers Cup, once after the joint event in Cincinnati, and a third time following the US Open. Each time, the conclusion was clear: The serve clock did not speed up play, and in many cases, it coincided with slower matches.

Count down under

The simplest way to measure the speed of a tennis match is to use the official match time and number of points played, then calculate the number of seconds per point. It’s a crude technique, since the official match time includes time spent playing, pauses between points, changeovers, heat breaks, medical time outs, challenges, and short rain delays. It’s imperfect. But the time spent on changeovers and the like is usually fairly consistent, making comparisons possible.

Here is the average seconds per point for men and women at the 2018 and 2019 Australian Open, reflecting the pace of play both before and after the introduction of the serve clock:

Year  Men Sec/Pt  Women Sec/Pt  
2018        40.2          40.4  
2019        41.0          40.3

This doesn’t exactly constitute a ringing endorsement of the serve clock. On average, matches were a bit slower in 2019 than in 2018. On the other hand, it’s a better result than the 2018 US Open, which was about 2.5 seconds slower than the 2017 pre-serve clock edition.

More precision, still rather slow

As I said, this is a crude way of measuring match speed. For most tournaments, it’s the best we can do without access to proprietary data that the ATP and WTA (presumably) possess. But at the majors, more detailed information is available. At the US Open, and at the Australian Open until 2017, that was the IBM “Slamtracker” data. The Australian Open no longer works with IBM, but it displays similar point-by-point data on its website.

Armed with better data, we can offer more precise estimates of how often players have exceeded the 25-second limit, both before and after the introduction of the serve clock. (Before the timer, the official limit at slams was 20 seconds, but I don’t think that a single time violation was assessed before at least 25 seconds–or more–had elapsed.) After the US Open last year, I found the number of times that players exceeded 25 seconds increased dramatically, as did the frequency that they went over 30 seconds. If you’re interested, went into more methodological detail in that article.

Again, the Australian Open fares better than its American counterpart, but that doesn’t exactly mean the clock is working, just that it isn’t dramatically slowing things down. Here are some figures from the 2017 and 2019 Australian Opens (I didn’t collect the relevant data last year), showing how often players violated the time limit both before and after the introduction of the timer:

Time Between   2017   2019  Change (%)  
under 20s     77.6%  75.9%       -2.2%  
under 25s     91.6%  91.8%        0.2%  
over 25s       8.4%   8.2%       -1.7%  
over 30s       2.8%   2.1%      -25.2%

The last row of this table is the first point I’ve seen that indicates the serve clock is working. Players are exceeding 30 seconds between points far less often than they did two years ago. On the other hand, there’s almost no difference in how often they cross the 25-second mark. And another negative: The “improved” figure of 2.1% of points over 30 seconds is considerably worse than the same rate in New York last year, which was a mere 0.8%. The clock has eliminated some of the most egregious offenses in Melbourne, but a lot more remain.

Carpenters, not tools

The main problem continues to be the way the serve clock is used. The countdown begins when the score is called, and umpires generally wait until crowd noise has subsided before making their announcement. Thus, after exciting shots or long rallies–the very points after which players have historically taken a long time to serve–the time limit is effectively extended. There’s simply no reason for this. Start the timer when the point is over, and if the crowd is still going wild 20 or 25 seconds later, make the appropriate adjustments. But many servers are already playing “to” the serve clock, using all the time they are allotted. The longer the umpire waits to start the clock, the longer all of us must wait until play resumes.

My primary complaint with delayed clock-starting, though, is a different one. Yes, I’d like matches to move along faster. But as with just about every line in the rulebook, the time limit ends up being extended for stars more than it is for journeymen. On a stadium court like Rod Laver Arena, a modest ovation follows nearly every point played, especially those won by a big name like Federer, Nadal, or Serena. Out on Court 20, Johanna Larsson can play a bruising rally and earn nothing more than a polite golf clap. The more anonymous the player, the less recovery time. After a couple of matches, that adds up. A rule designed to increase fairness and transparency shouldn’t work against unknowns, but in this case, at majors, it appears to do just that.

Eventually, I may stop writing about the serve clock. But as long as the tours are pushing an innovation that fails to meet its stated goals, I’ll keep auditing the results. Given a few more years, maybe they’ll get it right.

The Effect of the US Open Serve Clock

Embed from Getty Images

Italian translation at settesei.it

This year’s US Open was the first grand slam to use a countdown clock before each serve. The time between points was set at 25 seconds, up from the official grand slam time limit of 20 seconds, partly to acknowledge the reality that 20 seconds was never going to happen, and to compromise with the ATP and WTA, whose limits have long been 25 seconds. The clock was tested at several North American events this summer, and I’ve already measured the effect of the clock on match times: once at The Economist’s Game Theory blog, and a second time here at Heavy Topspin.

In those two articles, I found that the serve clock seemed to make the sport slower. Using the limited data at hand–the number of points in each match and its overall time–it turned out that at every event using the clock in 2018, matches were slower by between 0.3 and 2.0 seconds per point. That doesn’t sound like much, but it adds up to a few minutes per match, and this is an innovation that was designed to hurry up play, not hold it back.

The US Open gives us a larger set of matches to study as well as more detailed data to work with. Before we attempt a less ham-handed approach to the problem, let’s see how the matches in New York measured up by the simple standard of seconds per point. Here is that calculation for all main draw singles matches in 2017 (without the clock, and a nominal 20-second time limit) and 2018 (with a 25-second clock):

Draw   2017  2018  
Men    40.0  43.4  
Women  40.7  42.3

Those are some awfully slow matches. Of the other summer events I analyzed, only the 2018 men’s draw in Washington exceeded 42 seconds per point.

However, the excessive heat probably played a part in some of the glacial play. The US Open heat policy certainly slowed down matches, as it allowed for a 10-minute break after the first two sets of women’s matches and the first three sets of men’s matches when the conditions were particularly bad. Those breaks are included in the official match times, so we need to account for them somehow.

Let’s skip some extra work and avoid the heat policy entirely by comparing only straight-set matches from 2017 and 2018, none of which were eligible for a heat break. That still leaves us with half of the original data points:

Draw   2017 Straight-Sets  2018 Straight-Sets  
Men                  39.2                43.4  
Women                39.8                41.3

That was not what I expected. The straight-set matches this year were almost the same speed as the longer ones, even without the possibility of a 10-minute heat break. Maybe players don’t dally as much during straight-set matches because so many of them are lopsided. Or perhaps the mix of players is a bit different. Whatever the reason, this apples-to-apples comparison shows that this year’s apples were quite a bit slower than last year’s.

Again, with better data

The heat policy issue illustrated the problem with using overall match time: It includes set breaks, changeovers, challenges, lets, and every other random type of delay you can imagine. In the long run, all the delays will even out, but in the long run, we’ll all be dead. So far, we’ve seen only a few hundred matches on each tour using the serve clock.

The US Open Slamtracker includes timestamps for the beginning of every point of most singles matches. That’s still not perfect–it doesn’t tell us when points end, for one thing–but with a bit of care and handling, it’s something we can work with. First, I took the Slamtracker data and identified every first-serve point that didn’t end the service game. I filtered out second serves because players use such wildly differing times between first and second serves, and that’s not something addressed by the serve clock. And I filtered out game-ending points because the pause after those points would be longer, involving switching servers and often changing sides.

That left about 16,000 points, a healthy amount of data to work with. From there, I tried to figure out how time was spent actually playing tennis. You know, serving, returning, hitting a bunch of slices, that sort of thing. It turns out that each additional shot adds roughly two seconds to the time between the start of that point and the start of the next. A portion of that might be additional fatigue, resulting in a longer between-points break, but I’ll give the players the benefit of the doubt and assume it’s all time spent playing tennis. I’ll also be generous and say that the first shot–the length of an ace or unreturned serve–is five seconds, to allow for some of the more elaborate service motions.

Put it all together, and we have 16,000 points for which we can estimate the length of the break after the point. If the timestamps for point 1 and point 2 are 35 seconds apart and point 1 was a five-stroke rally–5 seconds for the first shot, 8 seconds for the ensuing shots, for a total of 13 seconds–we can conclude that it took 22 seconds for the server to towel off, choose between various amounts of tennis-ball fuzz, and get ready to serve again.

One last step, again in the spirit of generosity: I eliminated the longest 5% of between-point breaks in each match. Some of those are probably challenges, or let serves, or other disruptions not reflected in the data. I’ve probably filtered out some legimate cases in which the server was really, really slow, but I want to do what I can to give us results that are uncontaminated by too many external issues.

Enough methodology, here are the results. The table shows the number of between-point pauses that were under 20 seconds, under 25 seconds, over 25 seconds, and over 30 seconds. Remember that these times, and the resulting rates, are built on a series of player- and official-friendly assumptions. I’m fairly confident that if we took a stopwatch to 16,000 points and audited the process in person, we would be much more likely to come up with equal or longer times between points than shorter ones.

Time Between Points   2017   2018  Change (%)  
Under 20s            86.5%  78.6%       -9.2%  
Under 25s            97.0%  95.1%       -2.0%  
Over 25s              3.0%   4.9%       63.1%  
Over 30s              0.4%   0.8%       91.0%

The number of excessively long breaks was not very high–less than one point in 20 this year–but the figures skyrocketed in comparison with last year. We could attribute this to the rule change from 20 seconds between points in 2017 to 25 this year, but as we’ve seen, matches with the 20 second limit last year were about as fast (on a match-time per point basis) as those with the 25 second time limit. So I think that’s a non-starter.

The heat, of course, remains a factor, even when heat policy breaks are taken out of the equation. Hotter, more humid conditions will tire players out more quickly, and that will show up in the amount of time they spend recovering between points. Maybe that accounts for the near-doubling of 30-second-or-longer pauses since last year.

Still, there are plenty of questions left to be answered about the serve clock and the way umpires are using it. The rate of 30-second or longer breaks, 0.8%, sounds tiny, but across 16,000 points, it’s over 100 cases. My study was able to include only about half of the points in Slamtracker-covered matches, which itself represents perhaps three-quarters of singles rubbers. Thus, we could be talking about over 300 instances of a player taking more than 30 seconds before serving over the course of the tournament. (And remember, we excluded the longest 5% of between-point pauses.) The number of 25-second-or-longer breaks is even more damning: By the same reasoning, there may have been nearly 2,000 times when a player exceeded the 25-second limit. A few time violations were called, sure, but only a tiny fraction of these probable offenses.

As I noted in my previous article here, a big part of the problem stems from officials waiting until after the crowd has settled down to start the clock. Thus, in an exciting, well-attended match, the time limit effectively becomes 35 seconds or more. This may be what umpires are instructed to do, but it is a sure-fire way to slow matches down. There’s no reason not to start the clock immediately and pause it later for the rare instances when the crowd is making too much noise 25 seconds later.

The simple approach to evaluating the effect of the serve clock, outlined at the beginning of this article, continues to suggest that the serve clock has made matches slower. The more sophisticated tack, made possible by the more detailed data available for most grand slams, supports the same argument, and shows us just how often players are still able to take extra time between points. Let’s hope the serve clock is a work in progress, because changes are necessary if it’s going to contribute to a speedier sport.

What Cincinnati Taught Us About the Serve Clock

Italian translation at settesei.it

So far, the serve clock has not made matches faster. In my article for The Economist earlier this week, I showed that in the handful of tournaments played with the new technology thus far, players took longer to play each point than they did at the same events last year.

That article included data from San Jose, Washington, Toronto, and Montreal. Last week, the combined Masters/Premier event in Cincinnati gave us another several dozen matches, with a slightly different mix of players, to further test how the serve clock is affecting the speed of play. Given another week of experience with the visible timers, the pace of play remains slower than it was one year ago.

In the Cincinnati men’s event, players used 41.2 seconds per point this year, compared to 39.8 seconds per point last year. In the women’s draw, it was 40.8 seconds per point this year, up from 40.2 seconds per point last year. Both increases are roughly the average change that we saw in the tournaments of the two previous weeks. Here is a breakdown of the time per point at each event, where “S/P” means seconds per point. Also shown are tour and overall averages, weighted by the number of matches at each event:

M/W      Tournament  2017 S/P  2018 S/P  Change  
Men      Cincinnati      39.8      41.2    +1.4  
Men      Canada          40.2      41.4    +1.2  
Men      Washington      40.3      42.2    +1.9 
 
Women    Cincinnati      40.2      40.8    +0.6  
Women    Canada          40.7      41.8    +1.1  
Women    Washington      40.2      41.6    +1.4  
Women    San Jose        40.3      40.7    +0.4  
                                                 
Men      Average         40.1      41.6    +1.5  
Women    Average         40.4      41.2    +0.8  
Overall  Average         40.2      41.4    +1.2

* alert readers might notice small discrepancies between these figures and those cited in the Economist, which are due to rounding errors.

Several readers have commented on the imprecision of this measurement. (I did too, in the original post.) Short of taking a stopwatch to every single match, there’s no way of auditing umpires by collecting the exact length of time between each pair of points. The exact mix of players in any given draw can affect the overall measurements–I experimented with a simple model to control for players, but it presented more problems than it solved. I agree, this is far from the final word on the serve clock, even apart from the fact that the way that umpires use it will probably evolve.

Still, these numbers point in only one direction. A similar survey of unaffected tournaments confirms that 2018 is not slower in general: For instance, of the men’s and women’s draws in Indian Wells, Miami, and Madrid this year, four of the six brackets decreased in average time per point, and one of the others increased by only 0.1 seconds per point.

Also, it’s important to remember that one presumed goal of the clock is to speed up play, not simply keep it steady. If time per point were staying roughly the same as last year, that itself would indicate that the new technology isn’t living up to its billing. That seven out of seven events have all gotten slower allows us to make an even stronger claim.

Fortunately for the tours, there is plenty of room for the use of the clock to evolve. The most glaring example is the umpiring practice of waiting until crowd noise dies down to start the clock. Yes, players can’t be expected to serve in a noisy stadium, but the cheering usually stops after ten seconds or so. Rather than add that ten seconds to the time allotment between points, umpires should start the clock immediately and then, on the rare occasions when the crowd remains disruptive, pause as necessary.

Its unlikely that matches will still be slower when the serve-clock dust has settled. But the goalposts have moved: At this stage of the process, it would be progress if matches with visible timers were simply the same speed as the ones that came before.

The Negative Impact of Time of Court

Italian translation at settesei.it

With 96 men’s matches in the books so far at Roland Garros this year, we’ve seen only one go to the absolute limit, past 6-6 in the fifth set. Still, we’ve had our share of lengthy, brutal five-set fights, including three matches in the first round that exceeded the four-hour mark. The three winners of those battles–Victor Estrella, David Ferrer, and Rogerio Dutra Silva–all fell to their second-round opponent.

A few years ago, I identified a “hangover effect” after Grand Slam marathons, defined as those matches that reach 6-6 in the fifth. Players who emerge victorious from such lengthy struggles would often already be considered underdogs in their next matches–after all, elite players rarely need to work so hard to advance–but marathon winners underperform even when we take their underdog status into account. (Earlier this week, I showed that women suffer little or no hangover effect after marathon third sets.)

A number of readers suggested I take a broader look at the effect of match length. After all, there are plenty of slugfests that fall just short of the marathon threshold, and some of those, like Ferrer’s loss yesterday to Feliciano Lopez, 6-4 in the final set, are more physically testing than some of those that reach 6-6. Match time still isn’t a perfect metric for potential fatigue–a four-hour match against Ferrer is qualitatively different from four hours on court with Ivo Karlovic–but it’s the best proxy we have for a very large sample of matches.

What happens next?

I took over 7,200 completed men’s singles matches from Grand Slams back to 2001 and separated them into groups by match time: one hour to 1:29, 1:30 to 2:00, and so on, up to a final category of 4:30 and above. Then I looked at how the winners of all those matches fared against their next opponents:

Prev Length   Matches  Wins  Win %  
1:00 to 1:29      448   275  61.4%  
1:30 to 1:59     1918  1107  57.7%  
2:00 to 2:29     1734   875  50.5%  
2:30 to 2:59     1384   632  45.7%  
3:00 to 3:29      976   430  44.1%  
3:30 to 3:59      539   232  43.0%  
4:00 to 4:29      188    64  34.0%  
4:30 and up        72    23  31.9%

The trend couldn’t be any clearer. If the only thing you know about a Slam matchup is how long the players spent on court in their previous match, you’d bet on the guy who recorded his last win in the shortest amount of time.

Of course, we know a lot more about the players than that. Andy Murray spent 3:34 on court yesterday, but even with his clay-court struggles this year, we would favor him in the third round against most of the men in the draw. As I’ve done in previous studies, let’s account for overall player skill by estimating the probability of each player winning each of these 7,200+ matches. Here are the same match-length categories, with “expected wins” (based on surface-specific Elo, or sElo) shown as well:

Prev Length   Wins  Exp Wins  Exp Win %  Ratio  
1:00 to 1:29   275       258      57.5%   1.07  
1:30 to 1:59  1107      1058      55.2%   1.05  
2:00 to 2:29   875       881      50.8%   0.99  
2:30 to 2:59   632       657      47.5%   0.96  
3:00 to 3:29   430       445      45.6%   0.97  
3:30 to 3:59   232       244      45.3%   0.95  
4:00 to 4:29    64        77      41.2%   0.83  
4:30 and up     23        30      42.1%   0.76

Again, there’s not much ambiguity in the trend here. Better players spend less time on court, so if you know someone beat their previous opponent in 1:14, you can infer that he’s a very good player. Often that assumption is wrong, but in the aggregate, it holds up.

The “Ratio” column shows the relationship between actual winning percentage (from the first table) and expected winning percentage. If previous match time had no effect, we’d expect to see ratios randomly hovering around 1. Instead, we see a steady decline from 1.07 at the top–meaning that players coming off of short matches win 7% more often than their skill level would otherwise lead us to forecast–to 0.76 at the bottom, indicating that competitors tend to underperform following a battle of 4:30 or longer.

It’s difficult to know whether we’re seeing a direct effect of time of court or a proxy for form. As good as surface-specific Elo ratings are, they don’t capture everything that could possibly predict the outcome of a match, especially micro-level considerations like a player’s comfort on a specific type of surface or at a certain tournament. sElo also needs a little time to catch up with players making fast improvements, particularly when they are very young. All this is to say that our correction for overall skill level will never be perfect.

Thus, a 75-minute win may improve a player’s chances by keeping him fresh for the next round … or it might tell us that–for whatever reason–he’s a stronger competitor right now than our model gives him credit for. One point in favor of the latter is that, at the most extreme, less time on court doesn’t help: Players don’t appear to benefit from advancing via walkover. That isn’t a slam-dunk argument–some commentators believe that walkovers could be detrimental due to the long resulting layoff at a Slam–but it does show us that less time on court isn’t always a positive.

Whatever the underlying cause, we can tweak our projections accordingly. Murray could be a little weaker than usual tomorrow after his length battle yesterday with Martin Klizan. Albert Ramos, the only man to complete a second-rounder in less than 90 minutes, might be playing a bit better than his rating suggest. It’s certainly evident that match time has something to tell us even when players aren’t stretched to the breaking point of a marathon fifth set.

Best of Five and Marin Cilic’s Improbable Collapse

Italian translation at settesei.it

Leading up to the final two rubbers of this year’s Davis Cup final in Croatia, the hosts were heavily favored. They held a 2-1 advantage, and both of the remaining singles matches would pit a Croatian against a lower-ranked Argentine. To win the Cup, they only needed to win one of those matches.

When Marin Cilic built a two-set lead over Juan Martin del Potro, Croatian fans could be forgiven for thinking it was in the bag. Instead, Delpo fought back to win in five sets, and Federico Delbonis upset a flat Ivo Karlovic to seal Argentina’s first-ever Davis Cup title. Some people will point to the Cilic-Delpo match time of 4:53 as another reason to switch to best-of-three. The rest of us will see it as yet another reminder of why best-of-five must retain its role on tennis’s biggest stages.

In a best-of-three format, Cilic would’ve claimed the Cup for Croatia after two hours of play. Instead, he merely came very close. My Elo singles ratings gave Cilic a 36.3% chance of beating Delpo and Karlovic a 75.8% chance of defeating Delbonis. Taken together, that’s a likelihood of 84.6% that Croatia would claim the trophy. After Cilic won the first two sets, his odds increased to about 81%, pushing Croatia’s chances over the 95% mark. In fourteen previous tries, del Potro had never recovered from an 0-2 deficit.

And then Argentina came back. Comebacks from two sets down tend to stick in our memory, so it’s easy to forget just how rare they are. Yesterday’s match was only the 28th such comeback in 2016. That’s out of a pool of 656 best-of-five contests, including 431 in which one player built a 2-0 lead. This year isn’t unusual: Going back to 2000, the number of wins from a 0-2 deficit has never exceeded 32.

Comebacks from 0-2 are even rarer in Davis Cup. At the World Group level this year, including play-offs, Delpo was the 61st player to fall into a 0-2 hole, but he was only the second to recover and win the match. The other was Jack Sock, whose July comeback (over Cilic–more on that in a bit) wasn’t enough to move his USA squad into the semifinals. Since 2000, 5.8% of 2-0 leads turn into comeback victories, but only 4.3% of World Group 2-0 leads do the same.

Cilic’s season has defied the numbers. In addition to his 2-0 collapses against Sock and del Potro, he held a 2-0 advantage before losing to Roger Federer in the Wimbledon quarterfinals. His 2016 is only the third time in ATP history that a player lost three or more matches after winning the first two sets. The previous two–Viktor Troicki’s 2015 season and Jan Siemerink’s 1997–are unlikely to make Cilic feel any better.

Still, even Cilic’s record indicates the rarity of victories from an 0-2 disadvantage. Before the Wimbledon quarterfinal, the Croatian had never lost a match after taking the first two sets, for a record of 60-0. Even now, his Davis Cup record after going up two sets to love is a respectable 11-2. His overall career mark of 95.7% (66-3) is better than average.

Unless Cilic crumbles under certain spotlights (but not others, as evidenced by his five-set win over Delbonis on Friday), his series of unfortunate collapses may just be a fluke. In addition to that 60-0 streak, he has never had a problem converting one-set leads in best-of-three matches. This year, he won 29 out of 33 best-of-threes after winning the first set, an above-average rate of 88%. (And one of the losses was against Dominic Thiem, so he never had a chance.)

The longer the match format, the more likely that the better player emerges triumphant. That’s why there are fewer upsets in best-of-five than in best-of-three, and why tiebreaks are often little better than flips of a coin. Usually that works in favor of a top-tenner such as Cilic: In most matchups he is the superior player. But in two of his three collapses this season, he’s fallen victim to a favorite who uses the longer format to overcome an early run of poor form.

The debate over best-of-five will surely continue, despite this weekend’s Davis Cup tie adding another unforgettable five-set epic to an already long list. But after Delpo’s performance yesterday, you’ll have a harder time finding someone to campaign for shorter matches–especially in Argentina.

The Pointlessness of Playing the Lets

Italian translation at settesei.it

Some people always want tennis matches to be shorter. Among the many recurring proposals to accomplish that, one that has been implemented in some places is eliminating service lets. In other words, serves are treated the same way as any other shot: If the serve clips the net and lands in the box, it’s in play.

“No-let” rules have been adopted by World Team Tennis and American university tennis. In the latter case, eliminating lets has more to do with ensuring fair play in the absence of an umpire. In 2013, the ATP experimented with no lets on the Challenger tour for the first three months of the year.

With an umpire on every professional court and machines that detect service lets at tour-level events, fairness (or avoiding cheating) is not the issue here. The reason we’re talking about this is that service lets take time, and apparently time is the enemy.

How much time?

The Match Charting Project has tracked lets in most of the 2,500-plus matches it has logged. Thus, we have some real-life data on the frequency of service lets. For today, I’ve limited our view to matches since 2010, which still gives us more than 2,000 matches to work with.

The average men’s match in the database, which consists of 151 total points, had six first-serve lets and fewer than one (0.875) second-serve let. Women’s matches are similar: Of the typical 139 points, there were 4.5 first-serve lets and 0.8 second-serve lets.

Let’s estimate the extra time all those lets are taking. After a first-serve let, most players restart their preparations, so let’s say a first-serve let is an extra 20 seconds. When the second serve is a let, most players are quicker to try again, so call that 10 seconds.

For the average men’s match in the database, that’s an extra 128 seconds–just over two minutes. For women, that’s 99 extra seconds per match. In both cases, the time consumed by service lets is less than one second per point. Just about any other rule change aimed at speeding up the game would be more effective than that.

Even at the extremes, it’s tough to argue that service lets are taking too much time. Of all the matches in the charting database, none had more than 24 service lets, and that was in the 2012 London Olympics marathon between Roger Federer and Juan Martin Del Potro. Using the estimates I gave above, those 20 first-serve and four second-serve lets accounted for just over seven minutes of the total match time of 4:26.

Only one of the 1,000 women’s matches in the database featured more than 17 service lets or more than five let-attributable minutes: Petra Cetkovska‘s three-set upset of Angelique Kerber at the 2014 Italian Open. That outlier included 22 lets, which we would estimate at a cost of just under seven minutes.

Playing service lets wouldn’t destroy the very fabric of tennis as we know it, but it also wouldn’t substantially shorten matches. By changing the let rule, tennis executives would needlessly annoy players and fans for no noticeable benefit.

What Would Happen If the WTA Switched to Super-Tiebreaks?

Italian translation at settesei.it

It’s in the news again: Some tennis execs think that matches are too long, fans’ attention spans are too short, and the traditional format of tennis matches needs to change. Since ATP and WTA doubles have already swapped a full third set for a 10-point super-tiebreak, something similar would make for a logical proposal to cap singles match length.

Let’s dig into the numbers and see just how much time would be saved if the WTA switched from a third set to a super-tiebreak. It is tempting to use match times from doubles, but there are two problems. First, match data on doubles is woefully sparse. Second, the factors that influence match length, such as average point length and time between points, are different in doubles and singles.

Using only WTA singles data, here’s what we need to do:

Determine how many matches would be affected by the switch
Figure out how much time is consumed by existed third sets
Estimate the length of singles super-tiebreaks
Calculate the impact (measured in time saved) of the change

The issue: three-setters

Through last week’s tournaments on the WTA tour this year, I have length (in minutes) for 1,915 completed singles matches. I’ve excluded Grand Slam events, since third sets at three of the four Slams can extend beyond 6-6, skewing the length of a “typical” third set.

The average length of a WTA singles match is about 97 minutes, with a range from 40 minutes up to 225 minutes. Here is a look at the distribution of match times this year:

The most common lengths are between 70 and 90 minutes. Some executives may wish to shorten all matches–switching to no-ad games (which I’ve considered here) or a more radically different format such as Fast4–but for now, I think it’s fair to assume that those 90-minute matches are safe from tinkering.

If there is a “problem” with long matches–both for fan engagement and scheduling–it arises mostly with three-setters. About one-third of WTA matches go to a third set, and these account for nearly all of the contests that last longer than two hours. 460 matches have passed the two-hour mark this season. Of those, all but 24 required a third set.

Here is the distribution of match lengths for WTA three-setters this season:

If we simply removed all third sets, nearly all matches would finish within two hours. Of course, if we did that, we’d be left with an awful lot of ties. Instead, we’re talking about replacing third sets with something shorter.

Goodbye, third set

Third sets are a tiny bit shorter than the first and second sets in three-setters. If we count sets that go to tiebreaks as 14 games, the average number of games in a third set is 9.5, while the typical number of games in the first and second sets of a three-setter is 9.7.

Those counts are close enough that we can estimate the length of each set very simply, as one-third the length of the match. There are other considerations, such as the frequency of toilet breaks before third sets and the number of medical timeouts in different sets, but even if we did want to explore those minor issues, there is very little available data to guide us in those areas.

The length of a super-tiebreak

The typical WTA three-setter involves about 189 individual points, so we can roughly estimate that foregoing the third set saves about 63 points. How many points are added back by playing a super-tiebreak?

The math gets rather involved here, so I’ll spare you most of the details. Using the typical rate of service and return points won by each player in three-setters (58% on serve and 46% on return for the better player that day), we can use my tiebreak probability model to determine the distribution of possible outcomes, such as a final score 10-7 or 12-10.

Long story short, the average super-tiebreak would require about 19 points, less than one-third the number needed by the average third-set.

That still doesn’t quite answer our question, though. We’re interested in time savings, not point reduction. The typical WTA third set takes about 44 minutes, or about 42 seconds per point. Would a super-tiebreak be played at the same pace?

Tiebreak speed

While 10-point breakers are largely uncharted territory in singles, 7-point tiebreaks are not, and we have plenty of data on the latter. It seems reasonable to extend conclusions about 7-pointers to their 10-point cousins, and they are played with similar rules–switch servers every two points, switch points every six–and under comparable levels of increased pressure.

Using IBM’s point-by-point data from this year’s Grand Slam women’s draws, we have timestamps on about 700 points from tiebreaks. Even though the 42-seconds-per-point estimate for full sets includes changeovers, tiebreaks are played even more slowly. Including mini-changeovers within tiebreaks, points take about 54 seconds each, almost 30% longer than the traditional-set average.

The bottom line impact of third-set super-tiebreaks

As we’ve seen, the average third-set takes about 44 minutes. A 19-point super-tiebreak, at 54 seconds per point, comes in at about 17 minutes, chopping off more than 60% off the length of the typical third set, or about 20% from the length of the entire match.

If we alter this year’s WTA singles match times accordingly, reducing the length of all three-setters by one-fifth, we get some results that certain tennis executives will love. The average match time falls from 97 minutes to 89 minutes, and more importantly, far fewer matches cross the two-hour threshold.

Of the 460 matches this season over two hours in length, we would expect third-set super-tiebreaks to eliminate more than two-thirds of them, knocking the total down to 147. Here is the revised match length distribution, based on the assumptions I’ve laid out in this post:

The biggest benefit to switching to a third-set super-tiebreak is probably related to scheduling. By massively cutting down the number of marathon matches, it’s less likely that players and fans will have to wait around for an 11:00 PM start.

Of the various proposals floating around to shorten matches–third-set super-tiebreaks, no-ad scoring, playing service lets, and Fast4–changing the third-set format strikes the best balance of shortening the longest matches without massively changing the nature of the sport.

Personally, I hope none of these changes are ever seen on a WTA or ATP singles court. After all, I like tennis and tend to rankle at proposals that result in less tennis. If something must be done, I’d prefer it involve finding new executives to replace the ones who can’t stop tinkering with the sport. But if some rule needs to be changed to shorten matches and make scheduling more TV-friendly, this is likely the easiest one to stomach.

At Slams, Do Shorter Matches Lead to Later Success?

Italian translation at settesei.it

Over the weekend, Tom Perrotta made the claim that grand slam champions such as Roger Federer and Serena Williams got that way, in part, by keeping early matches short. In his words: “They’re great at not being exhausted.”

This is intuitively appealing, especially after a third round in which Federer and Novak Djokovic barely broke a sweat, while Andy Murray, David Ferrer, and Tomas Berdych each dropped a set. (Even Juan Martin Del Potro was forced to a tiebreak by Leonardo Mayer.)

Before we get carried away, let’s find out what the numbers tell us. As we’ll see, slam champions usually are the men who spent fewer minutes on court getting to the final. It’s less clear, though, whether there is a causal link: After all, a better player should have an easier time of it in the early going.

The ATP has complete match-length numbers for our purposes going back to 2001. That gives us enough data to look at the last 47 slams.

In the last 47 grand slam finals, the favorite (defined simply as the guy with the better ATP ranking) won 33 times. In 6 of the 14 slam finals in which the underdog won, the underdog had spent less time on court in his previous six matches than the favorite did in his. Pretty good, huh?

One problem: Six other times, the favorite won the final despite having spent more time on court. So if you have to pick between the favorite and the better-rested player, there’s nothing in this sample to differentiate your choices.

A more positive takeaway occurs when the favorite has spent less time on court. There have been 35 such finals since 2001, and the better-rested favorite has gone 27-8. Most of the time, the favorite has reached the final expending less effort than his challenger did, and perhaps we can view that as a confirmation of his status as favorite.

(If you prefer games played to minutes on court, perhaps in deference to the Nadal and Djokovic speed of play, rest assured the numbers come out almost identical. There are a few cases where players spent less time on court but played more games–or vice versa–but if the analysis above replaced minutes with games, the results would be the same.)

All else equal, we’d bet on the finalist who has spent less time on court. But that doesn’t necessary imply that the better-rested player is more likely to win the final because he hasn’t spent as much time on court. That seems particularly true at slams, where players almost always get a day of rest between matches, and where top contenders almost never play doubles.

More likely is that one player spent less time on court because he is the favorite. Surely no one was surprised when Federer breezed past Verdasco, and few were surprised that Murray needed more time to put away Feliciano Lopez. Time on court is a clue that one man is playing better tennis, regardless of whether the extra rest aids him in later matches.

We can probably all agree on a safer claim: All else equal, the world’s best would certainly prefer to spend less time on court, even if it doesn’t boost his odds of winning the final. It might be gratifying to fight off an early challenge, but surely it’s more enjoyable to remind the rest of the field why you’re the favorite.