Can Nick Kyrgios Win a Grand Slam?

Italian translation at settesei.it

Today’s breaking news? Former Wimbledon finalist Mark Philippoussis thinks that Nick Kyrgios can win the Australian Open. Hey, it’s almost the offseason. We take our news wherever we can get it.

Still, it’s an interesting question. Is it possible for such a volatile, one-dimensional player to string together seven wins on one of the biggest stages in the sport? Philippoussis–not the most versatile of players himself–reached two Slam finals. A big serve can take you far.

Last year, I published a post investigating the “minimum viable return game,” the level of return success that a player would need to maintain in order to reach the highest echelon of men’s tennis. It’s rare to finish a season in the top ten without winning at least 38% of return points, though a few players, including Milos Raonic, have managed it. When I wrote that article, Kyrgios’s average for the previous 52 weeks was a measly 31.7%, almost in the territory of John Isner and Ivo Karlovic.

Kyrgios has improved since then. In 2016, he won 35.4% of return points, almost equal to Raonic’s 35.9%–and most would agree that Milos had an excellent year. Philippoussis’s career mark was only 34.9%, though Kyrgios would be lucky to play as many tournaments on grass and carpet as Philippoussis did. Still, a sub-36% rate of return points won isn’t usually good enough in today’s game: Raonic was only the third player since 1991 (along with Pete Sampras and Goran Ivanisevic) to finish a season in the top five with such a low rate.

Then again, Philippoussis didn’t say anything about finishing in the top five. The “minimum viable Slam-winning return game” might be different. Looking at all Grand Slam champions back to 1991, here are the lowest single-tournament rates of return points won:

Year  Slam             Player               RPW%                     
2001  Wimbledon        Goran Ivanisevic    31.1%  
1996  US Open          Pete Sampras        32.8%  
2009  Wimbledon        Roger Federer       33.7%  
2002  US Open          Pete Sampras        35.6%  
2000  Wimbledon        Pete Sampras        36.6%  
2010  Wimbledon        Rafael Nadal        36.8%  
2014  Australian Open  Stan Wawrinka       37.0%  
1998  Wimbledon        Pete Sampras        37.2%  
1991  Wimbledon        Michael Stich       37.4%  
2000  US Open          Marat Safin         37.5%

Wimbledon is well-represented here, as we might expect. Not so for Kyrgios’s home Slam: Stan Wawrinka‘s 2014 Australian Open title is the only time it appears in the top 20, even though it has played very fast in recent years. Every other Melbourne titlist won at least 39.5% of return points. As with year-end top-ten finishes, 38% is a reasonable rule of thumb for the minimum viable level, though on rare occasions, it is possible to come in below that.

The bar is set: Can Kyrgios clear it? 18 months ago, when Kyrgios’s 52-week return-points-won average was below 32%, the obvious answer would have been negative. His current mark above 35% makes the question a more interesting one. To win a Slam, he’ll probably need to return better, but only for seven matches.

The Australian has enjoyed one seven-match streak–in fact, a nine-match run–that would be more than good enough. Combining his title in Marseille and his semifinal showing in Dubai this Februrary, Kyrgios played almost nine matches (he retired with a back injury in the last one) while winning a whopping 41.5% of return points. At 42 of the last 104 Slams, the champion has won return points at a lower rate.

However, February was an aberration. To approximate Kyrgios’s success over the length of a Slam, I looked at his return points won over every possible streak of ten matches. (Most of his matches have been best-of-three, so ten matches is about the same number of points as a Slam title run.) Aside from the streaks involving Marseille and Dubai this year, he has never topped 37% for that length of time.

There’s always hope for improvement, especially for a mercurial 21-year-old in a sport dominated by older men. But the evidence is against him here, as well. Research by falstaff78 suggests that players do not substantially improve their return statistics as they mature. That may seem counterintuitive, since some players clearly do develop their skills. However, as players get better, they go deeper in tournaments and alter their schedules, changing the mix of opponents they face. Two years ago, Kyrgios faced seven top-20 players. This year he played 18. Raonic, who represents an optimistic career trajectory for Kyrgios, faced 26 this season.

Against the top 20–the sorts of Grand Slam opponents a player has to beat to get from the fourth round to the trophy ceremony–Kyrgios has won less than 30% of his career return points. Even Raonic, who has yet to win a Slam himself, has done better, and won 32.6% of return points against top-20 opponents this year.

There’s little doubt that Kyrgios has the serve to win Grand Slams. And once the Big Four retire, I suppose someone will have to win the majors. But even in weak eras, you need to break serve, and at Slams, you typically need to do so many times, and against very high-quality opponents. The evidence we have so far strongly implies that Kyrgios, like Philippoussis before him, will struggle to triumph at a Slam.

The Speed of Every Surface, 2016 Edition

More than five years after I first started trying to use ATP match stats to estimate surface speed, the issue remains a contentious one. Most commentators agree that surface speeds have converged and generally gotten slower. The ATP has begun to release a trickle of court speed data, but it raises more questions than answers.

It’s been three years since I’ve published surface speed numbers, so we’re due for an update. Before we do that, it’s important to understand what exactly these figures mean, as well as their limitations.

Court surfaces–and, more broadly, the environments in which pro matches are played–have a variety of characteristics. Some courts are faster or slower and some cause higher or lower bounces. Tournaments use different balls, are played at a range of elevations, and take place in all sorts of weather conditions. All of these factors, and more, affect how matches are played.

Due to the limits of available tennis data, however, we can’t isolate those different factors. It would be great to know which surfaces allowed for the most effective slice approaches or the deadliest drop shots, but we don’t have the data to even begin trying to answer those questions. The Match Charting Project is a step in the right direction, but with only a few hundred men’s matches per year, there isn’t quite enough to compare surfaces while controlling for different players and playing styles.

So we work with what we have. Faster surfaces are more favorable to the server, which shows up in ace counts and service breaks. The ATP publishes those basic stats for every match, so that’s what we’ll use. When I first researched this issue, I discovered that there isn’t much difference between counting aces and counting service breaks, except that there’s a wider variation in ace rates between faster and slower surfaces, so the resulting numbers are easier to understand.

At the risk of repeating myself: Measuring surface speed by ace rate ignores a lot of court characteristics. It is far from complete and certainly imperfect. It does, however, give us an idea of how tournaments compare in one important regard.

Aces, adjusted

That said, simply counting aces–for example, 6.8% of points in Buenos Aires this year and 11.2% of points in Los Cabos–isn’t good enough. Players make scheduling choices based on their strengths and preferences, so the guys who show up for clay court events tend, on average, to be weaker servers than those who play on hard and grass courts. To take an extreme example, Gilles Muller managed to play only two matches on clay this season. As it turns out, the courts in Buenos Aires and Los Cabos had almost identical effects on ace rates–the difference is entirely due to the mix of players in each draw.

So we adjust for the makeup of the field. For every player with at least three tour-level matches on clay and another three on hard or grass, I calculated their season average ace rates on clay and hard/grass,which I then weighted (one-third clay, two-thirds hard/grass) so that the numbers give us idea of what their ace rate would’ve been had they played an “average” (that is, unbiased by scheduling preferences) season. I’ve lumped hard and grass together here, not because they are the same–of course they’re not–but because the small number of grass court events makes it difficult to treat on its own.

With player averages in hand, we can go through every match of the season (between players who meet our minimums) and, using their ace rates and the rates at which players hit aces against them, calculate a “predicted” ace rate for the match, given a neutral surface. Then, by comparing the match’s actual ace rate to the neutral prediction, we get one data point regarding the surface’s effect on aces. If the actual ace rate is greater than the prediction, it suggests the surface is faster than average. If the prediction is greater than the ace rate, it implies the surface is slower than average.

No single match can tell us about a court’s tendency, but by aggregating all the matches at an event, we get a fairly good idea. With that final step, we get a single number per event. A neutral surface rates at 1, faster surfaces are greater than 1, and slower surfaces are less than 1. For instance, this algorithm rates the 2016 Paris Masters as 1.18, meaning that there were 18% more aces than we would expect on a neutral surface, rating Bercy as faster than all but 10 other events this season.

Whew! Here are the ace-based surface ratings for the last three seasons of every current tour-level event listed from fastest to slowest:

Tournament            Surface  2016 Ace%  2016  2015  2014  
Shenzhen                 Hard      12.9%  1.54  1.20  1.49  
Quito                    Clay      11.9%  1.50  0.89        
Metz                     Hard      12.6%  1.43  1.28  1.37  
Marseille                Hard      15.3%  1.38  1.28  1.26  
Stuttgart               Grass      13.3%  1.38  1.32  0.89  
Chengdu                  Hard      11.7%  1.27              
Australian Open          Hard      12.3%  1.25  1.19  1.12  
Queen's Club            Grass      14.3%  1.25  1.27  1.26  
Washington               Hard      19.5%  1.24  1.12  1.25  
Cincinnati Masters       Hard      14.2%  1.18  1.04  1.17  
Paris Masters            Hard      13.7%  1.18  1.03  1.03  
Brisbane                 Hard      12.2%  1.16  1.20  1.23  
Canada Masters           Hard      12.6%  1.16  1.08  1.00  
Halle                   Grass      12.2%  1.16  1.12  1.31  
Nottingham              Grass      12.0%  1.15  1.21        
Gstaad                   Clay      10.1%  1.12  0.84  0.77  
Basel                    Hard      10.1%  1.12  1.01  1.20  
Tokyo                    Hard      11.5%  1.12  1.00  1.06  
Chennai                  Hard      10.3%  1.12  0.91  0.65  
Auckland                 Hard      12.9%  1.11  1.21  1.01  
                                                            
Tournament            Surface  2016 Ace%  2016  2015  2014  
Doha                     Hard       8.8%  1.11  1.06  0.83  
Sydney                   Hard      10.5%  1.11  1.32  1.27  
Montpellier              Hard       9.7%  1.10  1.29  1.29  
Shanghai Masters         Hard      10.7%  1.10  1.05  1.34  
Kitzbuhel                Clay       6.9%  1.09  0.85  0.81  
s-Hertogenbosch         Grass      13.2%  1.08  1.06  1.05  
Winston-Salem            Hard      10.4%  1.07  1.33  1.10  
Newport                 Grass      11.0%  1.07  1.26  1.23  
Tour Finals              Hard       9.5%  1.06  0.99  0.89  
Wimbledon               Grass      11.8%  1.06  1.20  1.35  
Rotterdam                Hard       9.8%  1.04  1.19  1.08  
Vienna                   Hard      11.8%  1.02  1.39  1.26  
Memphis                  Hard       8.7%  1.00  1.19  0.94  
Miami Masters            Hard      10.0%  1.00  0.86  1.04  
Sofia                    Hard       8.4%  1.00              
Beijing                  Hard       9.4%  0.99  1.05  0.81  
Atlanta                  Hard      15.5%  0.97  1.35  0.90  
St.Petersburg            Hard       8.1%  0.97  0.98        
Marrakech                Clay       8.5%  0.95              
Olympics                 Hard       7.1%  0.95              
                                                            
Tournament            Surface  2016 Ace%  2016  2015  2014  
Moscow                   Hard       6.6%  0.94  1.08  1.12  
Antwerp                  Hard       8.6%  0.93              
Delray Beach             Hard       9.2%  0.92  0.88  0.93  
US Open                  Hard       8.9%  0.91  1.10  1.10  
Dubai                    Hard       9.4%  0.88  0.93  0.81  
Madrid Masters           Clay       8.6%  0.86  0.85  0.94  
Los Cabos                Hard      11.2%  0.85              
Buenos Aires             Clay       6.8%  0.85  0.78  0.64  
Houston                  Clay      11.5%  0.84  0.76  0.70  
Sao Paulo                Clay       7.1%  0.83  1.03  1.20  
Acapulco                 Hard      10.5%  0.83  0.67  0.98  
Indian Wells Masters     Hard       8.2%  0.83  0.99  0.90  
Stockholm                Hard       7.6%  0.82  1.13  1.15  
Rio de Janeiro           Clay       7.4%  0.81  0.80  0.77  
Estoril                  Clay       7.4%  0.80  0.63  0.62  
Nice                     Clay       6.3%  0.79  0.64  0.74  
Geneva                   Clay       8.3%  0.77  0.78        
Umag                     Clay       5.4%  0.77  0.67  0.76  
Roland Garros            Clay       7.6%  0.77  0.72  0.71  
Rome Masters             Clay       7.2%  0.76  0.94  0.74  
Bucharest                Clay       5.9%  0.71  0.59  0.51  
Munich                   Clay       6.3%  0.71  1.01  0.87  
Monte Carlo Masters      Clay       6.2%  0.70  0.63  0.64  
Istanbul                 Clay       5.7%  0.67  0.83        
Barcelona                Clay       5.4%  0.65  0.70  0.72  
Bastad                   Clay       5.3%  0.65  0.64  1.07  
Hamburg                  Clay       5.7%  0.60  0.62  0.79

As usual, we have an interesting mix of usual suspects and surprises. The top of the list is primarily indoor hard and grass courts, along with the high-altitude clay in Quito and Gstaad. However, in both of the latter cases, those tournaments had lower-than-expected ace rates in 2015. The surface ratings for 250s are particularly volatile because, in addition to the small number of matches, many of these matches must be discarded because one or both of the players didn’t meet our minimums. For the 2015 Quito event, we have only 11 matches to work with.

The sample size problem doesn’t apply to larger events, however, so we can have a fair amount of confidence in the ratings for the Australian Open, showing up here as the fastest of the Grand Slams–considerably faster than Wimbledon, which is only a few ticks above neutral.

Ace ratings and Court Pace Index

Last month, TennisTV released some data on court speed for this season’s Masters events. Court Pace Index (CPI) is a commonly-accepted measure of the speed of the surface itself–that is, the physical makeup of the court. As I’ve said, that’s far from the only factor affecting how a court plays, but it is an important one.

cpi2

Here’s how my surface ratings compare to CPI:

Tournament            Surface  TA Rating   CPI  
Cincinnati Masters       Hard       1.18  35.1  
Paris Masters            Hard       1.18  39.1  
Canada Masters           Hard       1.16  35.2  
Shanghai Masters         Hard       1.10  44.1  
Tour Finals              Hard       1.06  40.6  
Miami Masters            Hard       1.00  33.1  
Madrid Masters           Clay       0.86  22.5  
Indian Wells Masters     Hard       0.83  30.0  
Rome Masters             Clay       0.76  24.0  
Monte Carlo Masters      Clay       0.70  23.7

It’s noteworthy that Madrid is, by my measure, the most ace-friendly of the three clay-court Masters, while its CPI is the lowest. Altitude could account for the difference.

The biggest mismatch, though, is the Tour Finals. The O2 Arena has one of the highest CPIs, but it doesn’t rate very far above average in aces. The Tour Finals has always been a bit problematic, as there is an unusually small number of matches, and the level of returning is very, very high. My algorithm takes into account how well each player prevents aces, but perhaps that issue is more complex when our view is limited to only the very best players.

TennisTV also showed CPI for the last several years of Tour Finals:

cpi1

Compared to my ratings:

Year  TA Rating   CPI  
2016       1.06  40.6  
2015       0.99  34.0  
2014       0.89  33.6  
2013       0.90  32.8  
2012       1.18  33.9

If the table cut off after 2013, it would look like a relatively good fit. As it is, the relationship between CPI and my rating for 2012 wouldn’t be out of place in the previous table, which included a 35.1 CPI for Cincinnati to go with an ace-based rating of 1.18.

I hope that this is a sign of more data to come. If so, we can move beyond approximations based on ace rate to get a better sense of what factors influence play at the ATP level. More data won’t settle the age-old surface speed debates, but it will make them a whole lot more interesting.

Andy Murray and the Longest Break-Per-Match Streaks

Italian translation at settesei.it

Among Andy Murray’s many accomplishments in 2016, he achieved an impressive–though obscure–feat. In each one of his 87 matches, he broke serve at least once. He has broken at least once per match since failing to do so against Roger Federer in the 2015 Cincinnati semifinals, for an active streak of 107 matches.

Where does that place him among the greats of men’s tennis? Just how unusual is it to break serve in every match for an entire season? As is the case with too many tennis statistics, we don’t know. Someone finds an impressive-sounding stat, and that’s the end of the story. We can’t always fix that, but in this case, we can add some context to Murray’s accomplishment.

Full break-per-match seasons

I’ve collected break stats for matches back to 1991, though we need to keep in mind that there are some mistakes in the 1990s data. Further, Davis Cup presents a problem, as it is excluded entirely. Sometimes we can tell from the scoreline that a player broke serve–as with all of Murray’s Davis Cup matches this year–but often we cannot. I’ll have more to say about that in specific cases below.

Since 1991, there have been at least 14, and perhaps as many as 20 instances in which a player broke serve in every match of a season. (Minimum 40 tour-level matches, and I’ve excluded retirements when calculating both minimums and the streaks themselves.) I say “instances” because several players–Andre Agassi, Lleyton Hewitt, Rafael Nadal, and Nikolay Davydenko–pulled it off more than once. Hewitt’s 2001 season had the most matches–95–of any of them, followed by Murray’s 2016 and Nadal’s 2005, at 87 each.

Here is the complete list:

Player                  Season  Matches  (Unsure)  
Andy Murray               2016       87         0  
Juan Monaco               2014       41         0  
Novak Djokovic            2013       83         0  
Rafael Nadal              2010       79         0  
Nikolay Davydenko         2008       73         0  
Nikolay Davydenko         2007       82         0  
Lleyton Hewitt            2006       46         0  
Rafael Nadal              2005       87         0  
David Nalbandian          2005       63         0  
Andre Agassi              2003       55         0  
Lleyton Hewitt            2001       95         0  
Lleyton Hewitt            2000       76         1  
Hernan Gumy               1997       53         1  
Alex Corretja             1997       67         0  
Andre Agassi              1995       81         0  
Magnus Gustafsson         1994       40         0  
Carlos Costa              1992       60         0  
Guillermo Perez Roldan    1991       40         2  
Ivan Lendl                1991       72         0  
Boris Becker              1991       61         2

(The “Unsure” column indicates how many matches are missing stats and may not have included a break of serve.)

Several more players came close. Federer broke serve in all but one match in three separate seasons. Agassi, Novak Djokovic, David Ferrer, and Thomas Muster all did so twice.

We shouldn’t be surprised that so many players–especially the greats–have broken so often. It’s very rare to win a match without breaking serve: Of the 2,570 ATP tour-level matches from this season for which I have match stats, the winner broke serve in all but 30 of them. Even losers break serve in more than two out of every three matches: In 2016, the loser broke serve in 1,843 of the 2,570 matches, 72% of the time.

Still, there are enough dominant servers on tour that it is difficult to last an entire season without being shut out of the break column. In 1995, Muster broke serve in 99 matches, but failed to do so when he drew the big-serving (and completely unheralded) qualifier TJ Middleton on the carpet in St. Petersburg. Murray’s current streak is all the more impressive because, in his 107 matches, he has faced Milos Raonic six times, John Isner four times, Kevin Anderson and Nick Kyrgios twice each, and Ivo Karlovic once. Given the chance, he probably would’ve broken TJ Middleton as well.

Break-per-match streaks

For Murray to surpass the longest streaks in this category, it will take several more months of high-quality returning. As we saw above, Davydenko and Hewitt may have gone two full years breaking serve in every match they played. In both cases, the lack of ITF data makes their records unclear, but regardless of those details, Davydenko has set an extremely high bar.

Here are all the break-per-match streaks of 100 or more matches since 2000:

Player             Start   End  Streak  Possible  
Nikolay Davydenko   2006  2009     159       182  
Rafael Nadal        2004  2006     156            
Rafael Nadal        2009  2011     146            
Andre Agassi        2002  2004     143            
Novak Djokovic      2012  2014     127            
Lleyton Hewitt      1999  2002     124       230  
Andy Murray         2015  2016     107         ∞  
David Nalbandian    2004  2006     104

This season, Murray didn’t play his 53rd match until August at the Olympics; he’ll need to break serve at least once in that many matches to reach the top of this list.

The exact length of Davydenko’s streak hinges on his 2008 Davis Cup semifinal match against Juan Martin del Potro, which he lost in straight sets. If he broke serve in that match, his streak stretched into early 2009, spanning 182 matches.

(Edit: Thanks to Andrew Moss, we now know that Davydenko did break serve in that match, according to this contemporaneous report.)

Hewitt’s best streak is even more unclear. I don’t have break stats for his 6-3 6-3 loss to Max Mirnyi at the 2000 Olympics. If he didn’t break Mirnyi–a definite possibility, given The Beast’s serving prowess–the streak is “only” 124 matches. If he did, the streak is at least 187, and the exact length depends on more unknowns, including both of his singles matches in the 1999 Davis Cup final against France.

(Edit #2! Thanks to Carl, we know that Hewitt broke Mirnyi, so his streak is at least 187 matches. The next issue is his last match of the 1999 season, a dead rubber against Sebastian Grosjean in that year’s Davis Cup final. Hewitt lost 6-4 6-3, but Grosjean was hardly an overpowering server. Hewitt lost his previous Davis Cup match in straight sets as well, a live rubber against Cedric Pioline, and a match report establishes that Hewitt broke serve. If he broke Grosjean, the streak stretches back to April 1999, and numbers the full 230 matches.)

In any case, Murray has already earned himself a place among the greatest returners in modern tennis. In 2017, we’ll see just how far he can climb this list.

Why Novak Djokovic is Still Number One

Italian translation at settesei.it

Two weeks ago, Andy Murray took over the ATP #1 ranking from Novak Djokovic. Yesterday, he defeated Djokovic in their first meeting since June, securing his place at the top of the year-end ranking table. Murray has been outstanding in the second half of this season, winning all but three of his matches since the Roland Garros final, and he capped the year in style, beating four top-five players to claim the title at the World Tour Finals.

Despite all that, Murray is not the best player in the world. That title still belongs to Djokovic. Since June, Murray has closed the gap, establishing himself as part of what we might call the “Big Two,” but he hasn’t quite ousted his rival. There’s no question that over this period, Murray has played better–that sort of thing is occasionally debatable, but this season it’s just historical fact–but identifying the best player implies something more predictive, and it’s much more difficult to determine by simply looking over a list of recent results.

The ATP rankings generally do a good job of telling us which players are better than others. But the official system has two major problems: It ignores opponent quality, and it artificially limits its scope to the last 52 weeks. Pundits and fans tend to have different problems: They often give too much credit to opponent quality (“He beat Djokovic, so now he’s number one!”) and exhibit an even more extreme recency bias (“He’s looked unbeatable this week!”).

Two systems that avoid these issues–Elo and Jrank–both place Djokovic comfortably ahead of Murray. These algorithms handle the details of recent matches and opponent quality differently from each other, but what they share in common is more important: They consider opponent quality and they don’t use an arbitrary time cutoff like the ATP ranking system does.

Here’s how the three methods would forecast a Djokovic-Murray match, were it held today:

  • ATP: Murray favored, 51.6% chance of winning
  • Elo: Djokovic favored, 61.6% chance of winning
  • Jrank: Djokovic favored, 57.0% chance of winning

Betting markets favored Djokovic by a margin of slightly more than 60/40 yesterday, though bettors probably gave him some of that edge because they thought Murray would be fatigued after his marathon match on Saturday.

As I wrote last week, Elo doesn’t deny that Murray has had a tremendous half-season. Instead, it gives him less credit than the official algorithm does for victories over lesser opponents (such as John Isner in the Paris Masters final), and it recognizes that he started his current run of form at an enormous disadvantage. With his title in London, Murray reached a new peak Elo rating, but it still isn’t enough to overtake Djokovic.

Even though Elo still prefers Novak by a healthy margin, it reflects how much the situation at the top of the ranking list has changed. At the beginning of 2016, Elo gave Djokovic a 76.5% chance of winning a head-to-head against Murray, and that probability rose as high as 81% in April. It fell below 70% after the Olympics, and the gap is now the smallest it has been since February 2011.

Last week illustrates how difficult it will be for Murray take over the #1 Elo ranking place. The pre-tournament Elo difference of 91 points between the two players has shrunk by only 8%, to 84 points. Murray’s win yesterday was worth a bit more than a measly seven points, but Djokovic had several opportunities to nudge his rating upwards in his first four matches, as well. Despite some of Novak’s head-scratching losses this fall, he still wins most of his matches–some of them against very good players–slowing the decline of his Elo rating.

Of course, Elo is just a measuring stick–like any ranking system, it doesn’t tell us what’s really happening on court. It’s possible that Murray has made a significant (and semi-permanent) leap forward or that Djokovic has taken a major step back. On the other hand, streaks happen even without such leaps, and they always end. The smart money is usually on small, gradual changes to the status quo, and Elo gives us a way to measure those changes.

For Elo to rate Murray ahead of Djokovic, it will probably require several more months of these gradual changes. The only faster alternative is for Djokovic to start losing more matches to the likes of Jiri Vesely and Sam Querrey. When faced with dramatic evidence, Elo makes more dramatic changes. While Djokovic has occasionally provided that evidence this season, he has usually offered enough proof–like four wins at the World Tour Finals–to comfortably maintain his position at the top.

Factchecking the History of the ATP Number One With Elo

Italian translation at settesei.it

As I wrote at The Economist this week, Andy Murray might sit atop the ATP rankings, but he probably isn’t the best player in tennis right now. That honor still belongs to Novak Djokovic, who comes in higher on the Elo ranking list, which uses an algorithm that is more predictive of match outcomes than the ATP table.

This isn’t the first time Elo has disagreed with the official rankings over the name at the top. Of the 26 men to have reached the ATP number one ranking, only 18 also became number one on the Elo list. A 19th player, Guillermo Coria, was briefly Elo #1 despite never achieving the same feat on the ATP rankings.

Four of the remaining eight players–Murray, Patrick Rafter, Marcelo Rios, and John Newcombe–climbed as high as #2 in the Elo rankings, while the last four–Thomas Muster, Carlos Moya, Marat Safin, and Yevgeny Kafelnikov–only got as high as #3. Moya and Kafelnikov are extreme cases of the rankings mismatch, as neither player spent even a single full season inside the Elo top five.

By any measure, though, Murray has spent a lot of time close to the top spot. What makes his current ascent to the #1 spot so odd is that in the past, Elo thought he was much closer. Despite his outstanding play over the last several months, there is still a 100-point Elo gap between him and Djokovic. That’s a lot of space: Most of the field at the WTA Finals in Singapore this year was within a little more than a 100-point range.

January 2010 was the Brit’s best shot. At the end of 2009, Murray, Djokovic, and Roger Federer were tightly packed at the top of the Elo leaderboard. In December, Murray was #3, but he trailed Fed–and the #1 position–by only 25 points. In January, Novak took over the top spot, and Murray closed to within 16 points–a small enough margin that one big upset could make the difference. Altogether, Murray has spent 63 weeks within 100 points of the Elo top spot, none of those since August 2013.

For most of the intervening three-plus years, Djokovic has been steadily setting himself apart from the pack. He reached his career Elo peak in April of this season, opening up a lead of almost 200 points over Federer, who was then #2, and 250 points over Murray. Since Roland Garros, Murray has closed the gap somewhat, but his lack of opportunities against highly-rated players has slowed his climb.

If Murray defeats Djokovic in the final this week in London, it will make the debate more interesting, not to mention secure the year-end ATP #1 ranking for the Brit. But it won’t affect the Elo standings. When two players have such lengthy track records, one match doesn’t come close to eliminating a 100-point gap. Novak will end the season as Elo #1, and he is well-positioned to maintain that position well into 2017.

Dominic Thiem and the Best Deciding-Sets Seasons in ATP History

Italian translation at settesei.it

Yesterday at the ATP World Tour Finals, Dominic Thiem won a three-set match against Gael Monfils, his 22nd deciding-set victory of 2016. Despite losing to Novak Djokovic in three sets on Sunday, Thiem is enjoying one of the best deciding-set seasons in ATP history.

The loss to Djokovic was only Thiem’s third in 25 deciding sets this year. He began the season with 14 consecutive deciding-set wins, including back-to-back third-set tiebreaks in Buenos Aires against Rafael Nadal and Nicolas Almagro. He strung together another seven straight between May and September, including a grass-court upset of Roger Federer in Stuttgart.

Among players who contested at least 20 deciding sets in a season, Thiem’s winning percentage of 88% is the fifth-best record in the ATP’s modern era. Not every player reaches the 20-decider threshold–some, like Djokovic, avoid it by winning most of their matches in straight sets–but it’s no statistical oddity. There have been nearly 1,000 player-seasons with at least 20 deciders since the 1970s, including Andy Murray’s 17-6 record in 2016.

Outstanding single-season deciding-set records don’t guarantee long-term success. Thiem appears on this list amid a mix of famous and lesser-known names, from Federer to Onny Parun:

Player           Year  Deciders  Wins  Win Perc  
Mario Ancic      2006        24    22     91.7%  
Ilie Nastase     1971        23    21     91.3%  
Tom Okker        1974        20    18     90.0%  
Roger Federer    2006        20    18     90.0%  
Dominic Thiem    2016        25    22     88.0%  
Kei Nishikori    2014        24    21     87.5%  
Stan Smith       1972        22    19     86.4%  
Joakim Nystrom   1984        22    19     86.4%  
Guillermo Vilas  1977        29    25     86.2%  
Onny Parun       1975        34    29     85.3%

Parun’s 1975 season is particularly notable, as no other player has won so many deciding sets in a single year. In 1996, Yevgeny Kafelnikov came close, winning 28. One gets the idea he was trying: He played 105 matches that year, 40 of which went the distance. In more recent years, big names have played more limited schedules, and Thiem is the only active player to win at least 22 deciding sets in a single season. Dmitry Tursunov gave it a shot in 2006, playing 37 deciders, but he won only 20.

Like so many tennis stats, this one can be fluky. For every Kei Nishikori–who has won an incredible 77% of deciding sets at tour level, including some record-setting streaks--there is a Grigor Dimitrov, who won 18 of 22 deciding sets in 2014, then barely broke even the following year, claiming only 11 of 21. Of the 27 players who have posted a 20-decider, 80% winning percentage season, not a single one managed an 80% winning percentage the following year.

For all of his talents, Thiem probably won’t follow in Nishikori’s footsteps. The Austrian won only half of his 40 deciding sets before this season. But a more modest record in these matches is hardly insurmountable. In 1996, Pete Sampras put together his best deciding-sets record, winning 83% of his 24 deciders. The following year, his record fell to a pedestrian 56%, which didn’t keep him from winning two Grand Slams and finishing the season at the top of the rankings.

If Thiem is to continue climbing the rankings, he’ll be better off taking Djokovic’s path, winning most of his deciding sets, but playing them much less frequently. In the last decade, Novak has played 20 deciding sets in a season only three times, and he has only gone the distance 10 times in 2016. Even Nishikori would have to agree: Djokovic’s method is working just fine.

Forecasting the 2016 ATP World Tour Finals

Italian translation at settesei.it

Andy Murray is the #1 seed this week in London, but as I wrote for The Economist, Novak Djokovic likely remains the best player in the world. According to my Elo ratings, he would have a 63% chance of winning a head-to-head match between the two. And with the added benefit of an easier round-robin draw, the math heavily favors Djokovic to win the tournament.

Here are the results of a Monte Carlo simulation of the draw:

Player        SF      F      W  
Djokovic   95.3%  73.9%  54.6%  
Murray     86.3%  58.3%  29.7%  
Nishikori  60.4%  24.9%   7.8%  
Raonic     50.9%  16.3%   3.3%  
Wawrinka   29.4%   7.8%   1.6%  
Monfils    33.2%   8.7%   1.4%  
Cilic      23.9%   5.8%   1.1%  
Thiem      20.7%   4.1%   0.5%

I don’t think I’ve ever seen a player favored so heavily to progress out of the group stage. Murray’s 86% chance of doing so is quite high in itself; Novak’s 95% is otherworldly. His head-to-heads against the other players in his group are backed up by major differences in Elo points–Dominic Thiem is a lowly 15th on the Elo list, given only a 7.4% chance of beating the Serb.

If Milos Raonic is unable to compete, Djokovic’s chances climb even higher. Here are the probabilities if David Goffin takes Raonic’s place in the bracket:

Player        SF      F      W  
Djokovic   96.8%  75.2%  55.4%  
Murray     86.2%  60.7%  30.6%  
Nishikori  60.7%  26.3%   8.1%  
Monfils    47.7%  12.4%   1.8%  
Wawrinka   29.3%   8.5%   1.7%  
Cilic      23.8%   6.2%   1.1%  
Thiem      29.5%   5.8%   0.7%  
Goffin     26.0%   4.9%   0.5%

The luck of the draw was on Novak’s side. I ran another simulation with Djokovic and Murray swapping groups. Here, Djokovic is still heavily favored to win the tournament, but Murray’s semifinal chances get a sizable boost:

Player        SF      F      W  
Djokovic   92.8%  75.1%  54.9%  
Murray     90.9%  58.1%  29.8%  
Nishikori  58.4%  26.9%   7.5%  
Raonic     52.3%  14.3%   3.3%  
Wawrinka   26.9%   8.4%   1.6%  
Monfils    35.3%   7.5%   1.4%  
Cilic      21.9%   6.2%   1.0%  
Thiem      21.6%   3.4%   0.5%

Elo rates Djokovic so highly that he is favored no matter what the draw. But the draw certainly helped.

Doubles!

I’ve finally put together a sufficient doubles dataset to generate Elo ratings and tournament forecasts for ATP doubles. While I’m not quite ready to go into detail, I can say that, by using the Elo algorithm and rating players individually, the resulting forecasts outperform the ATP rankings about as much as singles Elo ratings do.

Here is the forecast for the doubles event at the World Tour Finals:

Team               SF      F      W  
Herbert/Mahut   76.4%  49.5%  32.1%  
Bryan/Bryan     68.7%  36.8%  19.9%  
Kontinen/Peers  55.7%  29.1%  13.8%  
Dodig/Melo      58.4%  28.1%  13.2%  
Murray/Soares   48.3%  20.8%   8.6%  
Lopez/Lopez     37.7%  16.4%   6.2%  
Klaasen/Ram     30.2%  11.9%   4.0%  
Huey/Mirnyi     24.6%   7.3%   2.2%

This distribution is more like what round-robin forecasts usually look like, without a massive gap between the top of the field and the rest. Pierre-Hugues Herbert and Nicolas Mahut are the top rated team, followed closely by Bob Bryan and Mike Bryan. Max Mirnyi was, at his peak, one of the highest Elo-rated doubles players, but his pairing with Treat Huey is the weakest of the bunch.

The men’s doubles bracket has some legendary names, along with some players–like Herbert and Henri Kontinen–who may develop into all-time greats, but it has no competitors who loom over the rest of the field like Murray and Djokovic do in singles.

How To Keep Round Robin Matches Interesting, Part Two

Italian translation at settesei.it

Earlier this week, I published a deep dive into the possible outcomes of four-player round robin groups and offered an ideal schedule that would minimize the likelihood of dead rubbers on the final day. I’ve since heard from a few readers who pointed out two things:

  1. You might do better if you determined the schedule for day two after getting the results of the first two matches.
  2. Major tournaments such as the ATP and WTA Tour Finals already do this, pairing the winners of the first two matches and the losers of the first two matches on day two.

This is an appealing idea. You’re guaranteed to end the second day with one undefeated (2-0) player, two competitors at 1-1, and the last at 0-2. The two participants at 1-1 have everything to play for, and depending on day three’s schedule and tiebreak factors, the 0-2 player could still be in the running as well.

Best of all, you avoid the nightmare scenario of two undefeated players and two eliminated players, in which the final two matches are nearly meaningless.

However, this “contingent schedule” approach isn’t perfect.

Surprise, surprise

We learned in my last post that, if we set the entire schedule before play begins, the likelihood of a dead rubber on the final day is 17%, and if we choose the optimal schedule, leaving #4 vs #1 and #3 vs #2 for the final day, we can drop those chances as low as 10.7%.

(These were based on a range of player skill levels equivalent to 200 points on the Elo scale. The bigger the range of player skills–for instance, the ATP finals is likely to have a group with a range well over 300–the more dramatic the differences in these numbers.)

In addition, we discovered that “dead/seed” matches–those in which one player is already eliminated and the other can only affect their semifinal seeding–are even more common. When the schedule is chosen in advance, the probability of a dead rubber or a “dead/seed” match is always near 40%.

If the day two schedule is determined by day one outcomes, the overall likelihood of these “mostly meaningless” (dead or “dead/seed”) matches drops to about 30%. That’s a major step in the right direction.

Yet there is a drawback: The chances of a dead rubber increase! With the contingent day two schedule, there is a roughly 20% chance of a completely meaningless match on day three.

Our intuition should bear this out. After day two, we are guaranteed one 2-0 player and one 0-2 player. It is somewhat likely that these two have faced each other already, but there still remains a reasonable chance they will play on day three. If they do, the 0-2 player is already eliminated–there will be two 2-1 players at the end of day three. The 2-0 player has clinched a place in the semifinals, so the most that could be at stake is a semifinal seeding.

In other words, if the “winner versus winner” schedule results in a 2-0 vs 0-2 matchup on day three, the odds are that it’s meaningless. And this schedule often does just that.

The ideal contingent schedule

If the goal is to avoid dead rubbers at all costs, the contingent schedule is not for you. You can do a better job by properly arranging the schedule in advance. However, a reasonable person might prefer the contingent schedule because it completely avoids the risk of the low-probability “nightmare scenario” that I described above, of two mostly meaningless day three matches.

Within the contingent schedule, there’s still room for optimization. If the day one slate consists of matches setting #1 against #3 and #2 against #4 (sorted by ranking), the probability of a meaningless match on day three is about average. If day one features #1 vs #2 and #3 vs #4, the odds are even higher: about a 21% chance of a dead rubber and another 11% chance of a “dead/seed” match.

That leaves us with the optimal day one schedule of #1 vs #4 and #2 vs #3. It lowers the probability of a dead rubber to 19% and the chances of a “dead/seed” match to 9.7%. Neither number represents a big difference, but given all the eyes on every match at major year-end events, it seems foolish not to make a small change in order to maximize the probability that both day three matches will matter.

How To Keep Round Robin Matches Interesting

Italian translation at settesei.it

Round robins–such as the formats used by the ATP and WTA Tour Finals–have a lot going for them. Fans are guaranteed at least three matches for every player, and competitors can recover from one (or even two) bad outings. Best of all, when compared to a knockout-style draw, it’s twice as much tennis.

On the other hand, round robins have one major drawback: They can result in meaningless matches. It’s fairly common that, after two matches, a player is guaranteed a spot in the semifinals (sometimes even a specific seed) or eliminated from contention altogether. At a high-profile event such as the Tour Finals, with sky-high ticket prices, do we really want to run the risk of dead rubbers?

I don’t claim to have the answer to that question. However, we can take a closer look at the round robin format to answer several relevant questions. What is the probability that the final day of a four-player group will include at least one dead rubber? What about the final match? And most importantly, before the event begins, can we set the schedule in such a way to minimize the likelihood of dead rubbers?

The range of possibilities

As a first step, let’s determine all of the possible outcomes of the first four matches in a four-player round robin group. For convenience, I’ll refer to the players as A, B, C, and D. The first day features two matches, A vs B and C vs D. The second day is A vs C and B vs D, leaving us with a final day of A vs D and B vs C.

Each match has four possible outcomes: the first player wins in two sets, the first player wins in three, the second wins in two, or the second wins in three. (Sets won are important because they are used as a tiebreaker when, for instance, three players win two matches apiece.) Thus, there are 4 x 4 x 4 x 4 = 256 possible arrangements of the group standings entering the final day of round robin play.

Of those 256 permutations, 32 of them (12.5%) include one dead rubber on the final day. In those cases, the other match is played only to decide semifinal seeding between the players who will advance. Another 32 of the 256 permutations involve one “almost-dead” match, between a player who has been eliminated and a player who is competing only to determine semifinal seeding.

In other words, one out of every four possible outcomes of the first two days results in a day three match that is either entirely or mostly meaningless. Later on, we’ll dig into the probability that these outcomes occur, which depends on the relative skill levels of the four players in the group.

Before we do that, let’s take a little detour to define our terms. Because of the importance of semifinal seeding, some dead rubbers are less dead than others. Further, it is frequently the case that one player in a match still has a shot at the semifinals and the other doesn’t. Altogether, from “live” to “dead,” there are six gradations:

  1. live/live — both players are competing to determine whether they survive
  2. live/seed — one player could advance or not; the other will advance, and is playing to try to earn the #1 group seed
  3. live/dead — one player is trying to survive; the other is eliminated
  4. seed/seed — both players will advance; the winner gets the #1 group seed
  5. seed/dead — one player is in the running for the #1 seed; the other is eliminated
  6. dead/dead — both players are eliminated

All else equal, the higher a match lies on that scale, the more engaging its implications for the tournament. For the remainder of this article, I’ll refer only to the “dead/dead” category as “dead rubbers,” though I will occasionally discuss the likelihood of “dead/seed” matches as well. I’ll assume that the #1 seed is always more desirable than #2 and ignore the fascinating but far-too-complex ramifications of situations in which a player might prefer the #2 spot.

The sixth match

As we’ve seen, there are many sequences of wins and losses that result in a dead rubber on day three. Once the fifth match is played, it is even more likely that the seedings have been determined, making the sixth match meaningless.

After five matches, there are 1,024 possible group standings. (256 permutations after the first four matches, multiplied by the four possible outcomes of the fifth match.) Of those, 145 (14.1%) result in a dead sixth rubber, and another 120 (11.7%) give us a “dead/seed” sixth match.

We haven’t yet determined how likely it is that we’ll arrive at the specific standings that result in dead sixth rubbers. So far, the important point is that dead rubbers on day three aren’t just flukes. In a four-player round robin, they are always a real possibility, and if there is way to minimize their likelihood, we should jump at the chance.

Real scenarios, really dead rubbers

To figure out the likelihood of dead rubbers in practical situations, like the ATP and WTA Tour Finals, I used a hypothetical group of four players with Elo ratings spread over a 200-point range.

Why 200? This year’s Singapore field was very tightly packed, within a little bit more than 100 points, implying that the best player, Angelique Kerber, had about a 65% chance of beating the weakest, Svetlana Kuznetsova. By contrast, the ATP finalists in London are likely to be spread out over a 400-point range, giving the strongest competitor, Novak Djokovic, at least a 90% edge over the weakest.

I’ve given our hypothetical best player a rating of 2200, followed by a field of one player at 2130, one at 2060, and one at 2000. Thus, our favorite has a 60% chance of beating the #2 seed, a 69% chance of defeating the #3 seed, and a 76% chance of besting the #4 seed.

For any random arrangement of the schedule, after the first two days of play, this group has a 17% chance of giving us a dead rubber on day three, plus a 23% chance of a “dead/seed” match on day three.

After the fifth match is contested, there is a 16% chance of that the sixth match is meaningless, with an additional 12% chance that the sixth match falls into the “dead/seed” category.

The wider the range of skill levels, the higher the probability of dead rubbers. This is intuitive: The bigger the range between the top and bottom, the more likely that the best player will win their first two matches–and the more likely they will be straight-setters. Similarly, the chances are higher that the weakest player will lose theirs. The higher the probability that players go into day three with 2-0 or 0-2 records, the less likely that day three matches have an impact on the outcome of the group.

How to schedule a round robin group

A 17% chance of a dead rubber on day three is rather sad. But there is a bright spot in my analysis: By rearranging the schedule, you can raise that probability as high as 24.7% … or drop it as low as 10.7%.

Remember that our schedule looks like this:

Day one: A vs B, C vs D

Day two: A vs C, B vs D

Day three: A vs D, B vs C

We get the lowest possible chance of a day three dead rubber if we put the players on the schedule in order from weakest to strongest: A is #4, B is #3, and so on:

Day one: #4 vs #3, #2 vs #1

Day two: #4 vs #2, #3 vs #1

Day three: #4 vs #1, #3 vs #2

There is a small drawback to our optimal arrangement: It increases the odds of a “dead/seed” match. It turns out that you can only optimize so much: No matter what the arrangement of the competitors, the probability of a “dead/dead” or “dead/seed” match on day three stays about the same, between 39.7% and 41.7%. While neither type of match is desirable, we’re stuck with a certain likelihood of one or the other, and it seems safe to assume that a “dead/seed” rubber is better than a totally meaningless one.

Given how much is at stake, I hope that tournament organizers heed this advice and schedule round robin groups in order to minimize the chances of dead rubbers. The math gets a bit hairy, but the conclusions are straightforward and dramatic enough to make it clear that scheduling can make a difference. Over the course of the season, almost every tennis match matters–it would be nice if every match at the Tour Finals did, too.

(I wrote more about this, which you can read here.)

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.