“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.

]]>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-tiebreak****s**

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.

It’s unusual for a player to face two (or more) different #1-ranked opponents in the same season. Since 1985, it has happened 136 times on the WTA tour and 148 times on the ATP tour. That’s less than five times per season per tour.

Of course, it’s much less common to *upset *multiple #1-ranked opponents, as Svitolina did. This was only the 16th time a woman did so (again, since 1985), while it has happened on the men’s side 18 times.

Here is a full list of WTA player-seasons that featured defeats of more than one top-ranked player:

Year Player Upsets 2016 Elina Svitolina Kerber; Serena 2010 Samantha Stosur Serena; Wozniacki 2009 Venus Williams Serena; Safina 2008 Dinara Safina Henin; Sharapova; Jankovic 2006 Justine Henin Davenport; Mauresmo 2003 Justine Henin Serena; Clijsters 2002 Kim Clijsters Serena; Venus 2002 Serena Williams Capriati; Venus 2001 Lindsay Davenport Capriati; Hingis 1999 Amelie Mauresmo Hingis; Davenport 1999 Venus Williams Davenport; Hingis 1997 Amanda Coetzer Hingis; Graf 1996 Jana Novotna Graf; Seles 1996 Kimiko Date Krumm Graf; Seles 1991 Martina Navratilova Graf; Seles 1991 Gabriela Sabatini Graf; Seles

It’s quite an accomplished list. As we might expect, there’s a lot of overlap between the players who achieved these upsets and past and future #1-ranked players. The real standouts here are Justine Henin and Venus Williams, who managed the feat twice, and Dinara Safina, who faced three different #1s in 2008, going undefeated against them.

Here are the men who beat multiple #1s in the same season:

Year Player Upsets 2013 Juan Martin Del Potro Nadal; Djokovic 2012 Andy Murray Federer; Djokovic 2011 David Ferrer Nadal; Djokovic 2011 Jo Wilfried Tsonga Nadal; Djokovic 2010 Marcos Baghdatis Nadal; Federer 2009 Juan Martin Del Potro Nadal; Federer 2008 Andy Murray Nadal; Federer 2008 Gilles Simon Nadal; Federer 2003 Rainer Schuettler Roddick; Agassi 2003 Fernando Gonzalez Hewitt; Agassi 2001 Greg Rusedski Safin; Kuerten 2001 Max Mirnyi Safin; Kuerten 1995 Michael Chang Agassi; Sampras 1992 Richard Krajicek Courier; Edberg 1991 Guy Forget Edberg; Becker 1991 Andrei Cherkasov Edberg; Becker 1990 Boris Becker Lendl; Edberg 1988 Boris Becker Wilander; Lendl

This list isn’t quite as impressive, though it does capture several very good players at their best. It also highlights the world-beating potential of Max Mirnyi, who–despite never reaching the top 15 himself–finished the 2001 season with a 3-1 record against ATP #1s.

The rarity of facing multiple #1s in the same season–let alone beating them–stops us from drawing any meaningful conclusions about what Svitolina’s feat indicates for her future. At the very least, however, it reminds us of the Ukrainian’s potential as a future star, and puts her among some very good historical company.

]]>We need some context to appreciate just what an outlier that is. Of 50 tour-level WTA tournaments this year, no other titlist has spent more than about 11 hours and 35 minutes on court–and that includes Grand Slam winners, who play two more matches than McHale did! Before Christina’s marathon effort last week, the champion who spent the most time on court in a 32-draw event was Dominika Cibulkova, who needed “only” 9 hours and 20 minutes to win in Eastbourne.

There’s no complete source for historical WTA match-time data, so we can’t determine just how rare 13-hour efforts were in years past. We can, however, hunt for tournaments in which the winner needed to play so many sets.

Going back to 1991–encompassing almost 1,500 events–McHale’s effort marks only the second time a player has won a tournament while playing 15 sets in five matches. The only previous instance was Anastasia Pavlyuchenkova‘s Paris title run in 2014. Serena Williams played five three-setters en route to the Roland Garros title last year, but of course, she played two other matches as well. Three other players–none since 2003–received first-round byes and then won tournaments by playing three sets in each of their four matches.

In general, we might expect a player who goes the distance in every round to struggle in the final. First of all, we would expect her to be tired–especially if, as is almost always the case, her opponent hasn’t spent as much time on court. Second, we might deduce that, if a player needed three-sets to win early rounds, she’s in relatively weak form, compared to the typical tour-level finalist.

Sure enough, the last 25 years of WTA history give us 16 players who reached a final by playing three sets in every round. Of the 16, only four–McHale, Pavlyuchenkova, and two others who didn’t require three sets in the final–won the title. The other 12 couldn’t retain their three-set magic and lost in the final.

While 16 players don’t make up much of a sample, we get a similar result if we broaden our view to those who played three-setters in exactly three of their four matches before the final. Excluding those who faced opponents who also played so many three-setters, we’re left with 134 players, only 48 (35.8%) of whom won the title match. A simple ranking-based forecast indicates that 58 (43.3%) of those players should have won, suggesting that while these players are indeed weaker than their more-dominant opponents, their underperformance may be due partly to fatigue.

McHale spent over 10 hours on court simply reaching the Tokyo final, far more than the six-plus hours required by her opponent, Katerina Siniakova. Even when a player doesn’t spend the record-setting amount of time on court that the American did this week, competitors tend to underperform after playing so many three-setters. The fact that McHale didn’t, and that she triumphed in yet another marathon match, makes her achievement all the more impressive.

]]>With stats of 0-10 in ATP quarterfinals, he is still pretty far away from Teymuraz Gabashvili‘s streak of 0-16. Despite having lost six more quarterfinals before winning his first QF this January against a retiring Bernard Tomic, Teymuraz climbed only to a ranking of 50. Still, we could argue that the QF losing-streak of Teymuraz is not really over after having won against a possibly injured player.

Running the numbers can answer questions such as *“Who could climb up highest in the rankings without having won an ATP quarterfinal?”* Doing so will put Andrey’s number 42 into perspective and will possibly reveal some other statistical trivia.

Player Rank Date On Andrei Chesnokov 30 1986.11.03 1 Yen Hsun Lu 33 2010.11.01 1 Nick Kyrgios 34 2015.04.06 1 Adrian Voinea 36 1996.04.15 1 Paul Haarhuis 36 1990.07.09 1 Jaime Yzaga 40 1986.03.03 1 Antonio Zugarelli 41 1973.08.23 1 Bernard Tomic 41 2011.11.07 1 Omar Camporese 41 1989.10.09 1 Wayne Ferreira 41 1991.12.02 1 Andrey Kuznetsov 42 2016.08.22 0 David Goffin 42 2012.10.29 1 Mischa Zverev 45 2009.06.08 1 Alexandr Dolgopolov 46 2010.06.07 1 Andrew Sznajder 46 1989.09.25 1 Lukas Rosol 46 2013.04.08 1 Ulf Stenlund 46 1986.07.07 1 Dominic Thiem 47 2014.07.21 1 Janko Tipsarevic 47 2007.07.16 1 Paul Annacone 47 1985.04.08 1 Renzo Furlan 47 1991.06.17 1 Mike Fishbach 47 1978.01.16 0 Oscar Hernandez 48 2007.10.08 1 Ronald Agenor 48 1985.11.25 1 Gary Donnelly 48 1986.11.10 0 Francisco Gonzalez 49 1978.07.12 1 Paolo Lorenzi 49 2013.03.04 1 Boris Becker 50 1985.05.06 1 Brett Steven 50 1993.02.15 1 Dominik Hrbaty 50 1997.05.19 1 Mike Leach 50 1985.02.18 1 Patrik Kuhnen 50 1988.08.01 1 Teymuraz Gabashvili 50 2015.07.20 1 Blaine Willenborg 50 1984.09.10 0

The table shows career highs (up until #50) for players *before* they won their first ATP QF. A 0 in the last column indicates that the player can still climb up in this table, because he did not win a QF, yet. There may also be retired players being denoted with a 0, because they never managed to get past a QF during their career.

I wonder, who had Andrei Chesnokov on the radar for this? Before winning his first ATP QF he pushed his ranking as far as 30. He later went on to have a career high of 9. Nick Kyrgios could also improve his ranking quickly without the need to go as deep as a SF. His Wimbledon 2014 QF, Roland Garros 2015 R32, and Australian Open 2015 QF runs helped him to get up until #34 without a single win at an ATP QF. Also, I particularly would like to highlight Alexandr Dolgopolov who reached #46 before having even played a single QF.

Looking only at players who are still active *and* able to up their ranking without an ATP SF we get the following picture:

Player Rank Date Andrey Kuznetsov 42 2016.08.22 Rui Machado 59 2011.10.03 Tatsuma Ito 60 2012.10.22 Matthew Ebden 61 2012.10.01 Kenny De Schepper 62 2014.04.07 Pere Riba 65 2011.05.16 Tim Smyczek 68 2015.04.06 Blaz Kavcic 68 2012.08.06 Alejandro Gonzalez 70 2014.06.09

Andrey seems to be relatively alone with Rui Machado being second in the list having reached his highest ranking already about five years ago. Skimming through the remainder of the table, we would be surprised if anyone soon would be able to come close to Andrey’s 42, which doesn’t mean that a sudden unexpected streak of an upcoming player would render this scenario impossible.

So what practical implications does this give us for analyzing tennis? Hardly any, I am afraid. Still, we can infer that it is possible to get well within the top-50 without winning more than two matches at a single tournament over a duration that can even range over a player’s whole career. Of course it would be interesting to see how long such players can stay in these ranking areas, guaranteeing direct acceptance into ATP tournaments and, hence, a more or less regular income from R32, R16, and QF prize money. Moreover, as the case of 2015-ish Nick Kyrgios shows, the question arises how one’s ranking points are composed: Performing well at the big stage of Masters or Grand Slams can be enough for a decent ranking while showing poor performance at ATP 250s. On the other hand, are there players whose ATP points breakdown reveals that they are willing to go for easier points at ATP 250s while never having deep runs at Masters or Grand Slams? These are questions which I would like to answer in a future post.

—

This is a guest article by me, Peter Wetz. I am a computer scientist interested in racket sports and data analytics based in Vienna, Austria. I would like to thank Jeff for being open-minded and allowing me to post these surface-scratching lines here.

]]>As is often the case with new metrics, no one seems to be asking whether these new stats mean anything. Thanks to IBM (you never thought I’d write *that*, did you?), we have more than merely anecdotal data to play with, and we can start to answer that question.

At Roland Garros and Wimbledon this year, distance run during each point was tracked for players on several main courts. From those two Slams, we have point-by-point distance numbers for 103 of the 254 men’s singles matches. A substantial group of women’s matches is available as well, and I’ll look at those in a future post.

Let’s start by getting a feel for the range of these numbers. Of the available non-retirement matches, the shortest distance run was in Rafael Nadal’s first-round match in Paris against Sam Groth. Nadal ran 960 meters against Groth’s 923–the only match in the dataset with a total distance run under two kilometers.

At the other extreme, Novak Djokovic ran 4.3 km in his fourth-round Roland Garros match against Roberto Bautista Agut, who himself tallied a whopping 4.6 km. Novak’s French Open final against Andy Murray is also near the top of the list. The two players totaled 6.7 km, with Djokovic’s 3.4 km edging out Murray’s 3.3 km. Murray is a familiar face in these marathon matches, figuring in four of the top ten. (Thanks to his recent success, he’s also wildly overepresented in our sample, appearing 14 times.)

Between these extremes, the *average* match features a combined 4.4 km of running, or just over 20 meters per point. If we limit our view to points of five shots or longer (a very approximate way of separating rallies from points in which the serve largely determines the outcome), the average distance per point is 42 meters.

Naturally, on the Paris clay, points are longer and players do more running. In the average Roland Garros match, the competitors combined for 4.8 km per match, compared to 4.1 km at Wimbledon. (The dataset consists of about twice as many Wimbledon matches, so the overall numbers are skewed in that direction.) Measured by the point, that’s 47 meters per point on clay and 37 meters per point on grass.

**Not a key to the match**

All that running may be necessary, but covering more distance than your opponent doesn’t seem to have anything to do with winning the match. Of the 104 matches, almost exactly half (53) were won by the player who ran farther.

It’s possible that running more or less is a benefit for certain players. Surprisingly, Murray ran less than his opponent in 10 of his 14 matches, including his French Open contests against Ivo Karlovic and John Isner. (Big servers, immobile as they tend to be, may induce even less running in their opponents, since so many of their shots are all-or-nothing. On the other hand, Murray outran another big server, Nick Kyrgios, at Wimbledon.)

We think of physical players like Murray and Djokovic as the ones covering the entire court, and by doing so, they simultaneously force their opponents to do the same–or more. In Novak’s ten Roland Garros and Wimbledon matches, he ran farther than his opponent only twice–in the Paris final against Murray, and in the second round of Wimbledon against Adrian Mannarino. In general, running fewer meters doesn’t appear to be a leading indicator of victory, but for certain players in the Murray-Djokovic mold, it may be.

In the same vein, *combined *distance run may turn out to be a worthwhile metric. For men who earn their money in long, physical rallies, total distance run could serve as a proxy for their success in forcing a certain kind of match.

It’s also possible that aggregate numbers will never be more than curiosities. In the average match, there was only a 125 meter difference between the distances covered by the two players. In percentage terms, that means one player outran the other by only 5.5%. And as we’ll see in a moment, a difference of that magnitude could happen simply because one player racked up more points on serve.

**Point-level characteristics**

In the majority of points, the returner does a lot more running than the server does. The server usually forces his opponent to start running first, and in today’s men’s game, the server rarely needs to scramble too much to hit his next shot.

On average, the returner must run just over 10% further. When the first serve is put in play, that difference jumps to 12%. On second-serve points, it drops to 7%.

By extension, we would expect that the player who runs further would, more often than not, lose the point. That’s not because running more is necessarily bad, but because of the inherent server’s advantage, which has the side effect of showing up in the distance run stats as well. That hypothesis turns out to be correct: The player who runs farther in a single point loses the point 56% of the time.

When we narrow our view to only those points with five shots or more, we see that running more is still associated with losing. In these longer rallies, the player who covered more distance loses 58% of the points.

Some of the “extra” running in shorter points can be attributed to returning serve–and thus, we can assume that players are losing points because of the disadvantage of returning, not necessarily because they ran so much. But even in very long rallies of 10 shots or more, the player who runs farther is more likely to lose the point. Even at the level of a single point, my suggestion above, that physical players succeed by forcing opponents to work even harder than they do, seems valid.

With barely 100 matches of data–and a somewhat biased sample, no less–there are only so many conclusions we can draw about distance run stats. Two Grand Slams worth of show court matches is just enough to give us a general context for understanding these numbers and to hint at some interesting findings about the best players. Let’s hope that IBM continues to collect these stats, and that the ATP and WTA follow suit.

]]>- every men’s Wimbledon and US Open final all the way back to 1980;
- every men’s Slam final since 1989 Wimbledon;
- every women’s Slam final back to 2001, with a single exception.

The Match Charting Project gathers and standardizes data that, for many of these matches, simply didn’t exist before. These recaps give us shot-by-shot breakdowns of historically important matches, allowing us to quantify how the game has changed–at least at the very highest level–over the last 35 years. A couple of months ago, I did one small project using this data to approximate surface speed changes–that’s just the tip of the iceberg in terms of what you can do with this data. (The dataset is also publicly available, so have fun!)

We’ve got about 30 Slam finals left to chart, and you might be able to help. As always, we are actively looking for new contributors to the project to chart matches (here’s how to get started, and why you should, and you don’t have to chart Slam finals!), but right now, I have a different request.

We’ve scoured the internet, from YouTube to Youku to torrent trackers, to find video for all of these matches. While I don’t expect any of you to have the 1980 Teacher-Warwick Australian Open final sitting around on your hard drive, I’ve got higher hopes for some of the more recent matches we’re missing.

If you have full (or nearly full) video for any of these matches, or you know of a (preferably free) source where we can find them, please–please, please!–drop me a line. Once we have the video, Edo or I will do the rest, and the project will become even more valuable.

- 2007 Wimbledon, Venus Williams vs Marion Bartoli
- 2000 US Open, Venus Williams vs Lindsay Davenport
- 1998 US Open, Lindsay Davenport vs Martina Hingis
- 1989 or 1995 Roland Garros, and 1994 US Open, Steffi Graf vs Arantxa Sanchez Vicario
- 1990 Wimbledon, Martina Navratilova vs Zina Garrison
- 1989 Roland Garros, Stefan Edberg vs Michael Chang
- 1987 Australian Open, Stefan Edberg vs Pat Cash
- 1985 or 1987 Roland Garros, Ivan Lendl vs Mats Wilander

There are several more finals from the 1980s that we’re still looking for. Here’s the complete list.

Thanks for your help!

]]>Aside from the traditional break point stats, which have plenty of limitations, we don’t have a good way to measure clutch performance in tennis. There’s a lot more to this issue than counting break points won and lost, and it turns out that a lot of the work necessary to quantify clutchness is already done.

I’ve written many times about *win probability* in tennis. At any given point score, we can calculate the likelihood that each player will go on to win the match. Back in 2010, I borrowed a page from baseball analysts and introduced the concept of *volatility*, as well. (Click the link to see a visual representation of both metrics for an entire match.) Volatility, or *leverage*, measures the importance of each point–the difference in win probability between a player winning it or losing it.

To put it simply, the higher the leverage of a point, the more valuable it is to win. “High leverage point” is just a more technical way of saying “big point.” To be considered clutch, a player should be winning more high-leverage points than low-leverage points. You don’t have to win a disproportionate number of high-leverage points to be a very *good* player–Roger Federer’s break point record is proof of that–but high-leverage points are key to being a *clutch* player.

(I’m not the only person to think about these issues. Stephanie wrote about this topic in December and calculated a full-year clutch metric for the 2015 ATP season.)

To make this more concrete, I calculated win probability and leverage (LEV) for every point in the Wimbledon semifinal between Federer and Milos Raonic. For the first point of the match, LEV = 2.2%. Raonic could boost his match odds to 50.7% by winning it or drop to 48.5% by losing it. The highest leverage in the match was a whopping 32.8%, when Federer (twice) had game point at 1-2 in the fifth set. The lowest leverage of the match was a mere 0.03%, when Raonic served at 40-0, down a break in the third set. The average LEV in the match was 5.7%, a rather high figure befitting such a tight match.

On average, the 166 points that Raonic won were slightly more important, with LEV = 5.85%, than Federer’s 160, at LEV = 5.62%. Without doing a lot more work with match-level leverage figures, I don’t know whether that’s a terribly meaningful difference. What *is* clear, though, is that certain parts of Federer’s game fell apart when he needed them most.

By Wimbledon’s official count, Federer committed nine unforced errors, not counting his five double faults, which we’ll get to in a minute. (The Match Charting Project log says Fed had 15, but that’s a discussion for another day.) There were 180 points in the match where the return was put in play, with an average LEV = 6.0%. Federer’s unforced errors, by contrast, had an average LEV nearly twice as high, at 11.0%! The typical leverage of Raonic’s unforced errors was a much less noteworthy 6.8%.

Fed’s double fault timing was even worse. Those of us who watched the fourth set don’t need a fancy metric to tell us that, but I’ll do it anyway. His five double faults had an average LEV of 13.7%. Raonic double faulted more than twice as often, but the average LEV of those points, 4.0%, means that his 11 doubles had less of an impact on the outcome of the match than Roger’s five.

Even the famous Federer forehand looks like less of a weapon when we add leverage to the mix. Fed hit 26 forehand winners, in points with average LEV = 5.1%. Raonic’s 23 forehand winners occurred during points with average LEV = 7.0%.

Taking these three stats together, it seems like Federer saved his greatness for the points that didn’t matter as much.

**The bigger picture**

When we look at a handful of stats from a single match, we’re not improving much on a commentator who vaguely summarizes a performance by saying that a player didn’t win enough of the big points. While it’s nice to attach concrete numbers to these things, the numbers are only worth so much without more context.

In order to gain a more meaningful understanding of this (or any) performance with leverage stats, there are many, many more questions we should be able to answer. Were Federer’s high-leverage performances typical? Does Milos often double fault on less important points? Do higher-leverage points usually result in more returns in play? How much can leverage explain the outcome of very close matches?

These questions (and dozens, if not hundreds more) signal to me that this is a fruitful field for further study. The smaller-scale numbers, like the average leverage of points ending with unforced errors, seem to have particular potential. For instance, it may be that Federer is less likely to go for a big forehand on a high-leverage point.

Despite the dangers of small samples, these metrics allow us to pinpoint what, exactly, players did at more crucial moments. Unlike some of the more simplistic stats that tennis fans are forced to rely on, leverage numbers could help us understand the situational tendencies of every player on tour, leading to a better grasp of each match as it happens.

]]>The official ATP and WTA rankings have always represented a collection of compromises, as they try to accomplish dual goals of rewarding certain behaviors (like showing up for high-profile events) and identifying the best players for entry in upcoming tournaments. Stripping the Olympics of ranking points altogether was an even weirder compromise than usual. Four years ago in London, some points were awarded and almost all the top players on both tours showed up, even though many of them could’ve won more points playing elsewhere.

For most players, the chance at Olympic gold was enough. The level of competition was quite high, so while the ATP and WTA tours treat the tournament in Rio as a mere exhibition, those of us who want to measure player ability and make forecasts must factor Olympics results into our calculations.

Elo, a rating system originally designed for chess that I’ve been using for tennis for the past year, is an excellent tool to use to integrate Rio results with the rest of this season’s wins and losses. Broadly speaking, it awards points to match winners and subtracts points from losers. Beating a top player is worth many more points than beating a lower-rated one. There is no penalty for not playing–for example, Stan Wawrinka‘s and Simona Halep‘s ratings are unchanged from a week ago.

Unlike the ATP and WTA ranking systems, which award points based on the level of tournament and round, Elo is context-neutral. Del Potro’s Elo rating improved quite a bit thanks to his first-round upset of Novak Djokovic–the same amount it would have increased if he had beaten Djokovic in, say, the Toronto final.

Many fans object to this, on the reasonable assumption that context matters. It certainly seems like the Wimbledon final should count for more than, say, a Monte Carlo quarterfinal, even if the same player defeats the same opponent in both matches.

However, results matter for ranking systems, too. A good rating system will do two things: predict winners correctly more often than other systems, and give more accurate degrees of confidence for those predictions. (For example, in a sample of 100 matches in which the system gives one player a 70% chance of winning, the favorite should win 70 times.) Elo, with its ignorance of context, predicts more winners and gives more accurate forecast certainties than any other system I’m aware of.

For one thing, it wipes the floor with the official rankings. While it’s possible that tweaking Elo with context-aware details would better the results even more, the improvement would likely be minor compared to the massive difference between Elo’s accuracy and that of the ATP and WTA algorithms.

Relying on a context-neutral system is perfect for tennis. Instead of altering the ranking system with every change in tournament format, we can always rate players the same way, using only their wins, losses, and opponents. In the case of the Olympics, it doesn’t matter which players participate, or what anyone thinks about the overall level of play. If you defeat a trio of top players, as Puig did, your rating skyrockets. Simple as that.

Two weeks ago, Puig was ranked 49th among WTA players by Elo–several places lower than her WTA ranking of 37. After beating Garbine Muguruza, Petra Kvitova, and Angelique Kerber, her Elo ranking jumped to 22nd. While it’s tough, intuitively, to know just how much weight to assign to such an outlier of a result, her Elo rating just outside the top 20 seems much more plausible than Puig’s effectively unchanged WTA ranking in the mid-30s.

Del Potro is another interesting test case, as his injury-riddled career presents difficulties for any rating system. According to the ATP algorithm, he is still outside the top 100 in the world–a common predicament for once-elite players who don’t immediately return to winning ways.

Elo has the opposite problem with players who miss a lot of time due to injury. When a player doesn’t compete, Elo assumes his level doesn’t change. That’s clearly wrong, and it has cast a lot of doubt over del Potro’s place in the Elo rankings this season. The more matches he plays, the more his rating will reflect his current ability, but his #10 position in the pre-Olympics Elo rankings seemed overly influenced by his former greatness.

(A more sophisticated Elo-based system, Glicko, was created in part to improve ratings for competitors with few recent results. I’ve tinkered with Glicko quite a bit in hopes of more accurately measuring the current levels of players like Delpo, but so far, the system as a whole hasn’t come close to matching Elo’s accuracy while also addressing the problem of long layoffs. For what it’s worth, Glicko ranked del Potro around #16 before the Olympics.)

Del Potro’s success in Rio boosted him three places in the Elo rankings, up to #7. While that still owes something to the lingering influence of his pre-injury results, it’s the first time his post-injury Elo rating comes close to passing the smell test.

You can see the full current lists elsewhere on the site: here are ATP Elo ratings and WTA Elo ratings.

Any rating system is only as good as the assumptions and data that go into it. The official ATP and WTA ranking systems have long suffered from improvised assumptions and conflicting goals. When an important event like the Olympics is excluded altogether, the data is incomplete as well. Now as much as ever, Elo shines as an alternative method. In addition to a more predictive algorithm, Elo can give Rio results the weight they deserve.

]]>One of the most frequent complaints was that I was looking at the wrong data–surface speed should really be quantified by rally length, spin rate, or any number of other things. As is so often the case with tennis analytics, we have only so much choice in the matter. At the time, I was using all the data that existed.

Thanks to the Match Charting Project–with a particular tip of the cap to Edo Salvati–a lot more data is available now. We have shot-by-shot stats for 223 Grand Slam finals, including over three-fourths of Slam finals back to 1980. While we’ll never be able to measure anything like ITF Court Pace Rating for surfaces thirty years in the past, this shot-by-shot data allows us to get closer to the truth of the matter.

Sure enough, when we take a look at a simple (but until recently, unavailable) metric such as rally length, we find that the sport’s major surfaces are playing a lot more similarly than they used to. The first graph shows a five-year rolling average* for the rally length in the men’s finals of each Grand Slam from 1985 to 2015:

** since some matches are missing, the five-year rolling averages each represent the mean of anywhere from two to five Slam finals.*

Over the last decade and a half, the hard-court and grass-court slams have crept steadily upward, with average rally lengths now similar to those at Roland Garros, traditionally the slowest of the four Grand Slam surfaces. The movement is most dramatic in the Wimbledon grass, which for many years saw an average rally length of a mere two shots.

For all the advantages of rally length and shot-by-shot data, there’s one massive limitation to this analysis: It doesn’t control for player. (My older analysis, with more limited data per match, but for many more matches, *was* able to control for player.) Pete Sampras contributed to 15 of our data points, but none on clay. Andres Gomez makes an appearance, but only at Roland Garros. Until we have shot-by-shot data on multiple surfaces for more of these players, there’s not much we can do to control for this severe case of selection bias.

So we’re left with something of a chicken-and-egg problem. Back in the early 90’s, when Roland Garros finals averaged almost six shots per point and Wimbledon finals averaged barely two shots per point, how much of the difference was due to the surface itself, and how much to the fact that certain players reached the final? The surface itself certainly doesn’t account for everything–in 1988, Mats Wilander and Ivan Lendl averaged over seven shots per point at the US Open, and in 2002, David Nalbandian and Lleyton Hewitt topped 5.5 shots per point at Wimbledon.

Still, outliers and selection bias aside, the rally length convergence we see in the graph above reflects a real phenomenon, even if it is amplified by the bias. After all, players who prefer short points win more matches on grass because grass lends itself to short points, and in an earlier era, “short points” meant something more extreme than it does today.

The same graph for women’s Grand Slam finals shows some convergence, though not as much:

Part of the reason that the convergence is more muted is that there’s less selection bias. The all-surface dominance of a few players–Chris Evert, Martina Navratilova, and Steffi Graf–means that, if only by historical accident, there is less bias than in men’s finals.

We still need a lot more data before we can make confident statements about surface speeds in 20th-century tennis. (You can help us get there by charting some matches!) But as we gather more information, we’re able to better illustrate how the surfaces have become less unique over the years.

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