A New Way of Looking at Lottery Matches

When Rafael Nadal was eliminated from the US Open last week, a bit of bad luck was involved. He won only two fewer points than his opponent, Fabio Fognini, claiming 49.7% of the total points played. In his career up to that point, Rafa had won 8 of 18 matches in which he won between 49% and 50% of total points. It doesn’t take much to flip the result of such a match.

Matches in which neither player wins more than 51% of points represent nearly one in ten contests on the ATP tour. As Michael Beuoy demonstrated last year, those matches are very much up for grabs: the player with the most points wins less than 65% of the time.

In writing about the small subset of matches in which the loser wins a higher percentage of return points than the winner, Carl Bialik has coined the useful term “lottery matches.” However, Bialik has limited the term to those matches that have an unexpected result. I’d like to expand the definition a bit to all those tight matches that could go either way, even if the player who wins the most points ends up winning as expected.

(A quick side note: Bialik prefers comparing return points, the building blocks of his Dominance Ratio metric. Matches are won a bit more frequently when the winner’s DR is below 1.0 than when he wins fewer than 50% of total points played. These metrics often overlap, of course. To make this arcane subject a bit more accessible, I’m going to stick with the traditional total-points-won stat.)

As Beuoy showed, matches aren’t guaranteed to go to the player who wins the most points unless that guy wins at least 53% of points. (Even then, there’s a slight possibility of an upset, but it’s sufficiently rare that, for today’s purposes, I’m going to ignore it.) 52.5% is much better than 50.5%, but at 52.5%, you’re still going to lose about one of every 25 matches.

By extending the “lottery match” umbrella to all those matches in which neither player wins 51%, 52%, or even 53% of total points, we acknowledge that none of these matches are sure things, and we can look at a broader range of matches to determine whether players are winning as many tight matches as they should. Further, by considering such a category of tight matches, we’ll be able to identify those men who play a lot of them–and by doing so, leave themselves vulnerable to lucky upsets.

Winning the lottery (matches)

Let’s start with the broadest category: all matches in which neither player won more than 53% of total points. These represent everything from true toss-ups at 50% to near-guarantees at 52.9%. Using Beuoy’s model, we can take the total points won from each of these matches and calculate the likelihood that the player with the greater number of points won the match.

Nadal, for instance, is one of the more effective players in these tight matches. Going into the US Open, he had played 168 of them, winning 115. By taking the total points won from each of these matches, we find that he “should have” won only 102.5 of them, meaning that by some combination of clutch play and luck, he’s outperformed expectations by 12%.

Among active players with at least 100 of these matches, Nadal ranks an impressive fourth overall, behind John Isner, Fognini, and Jurgen Melzer. Novak Djokovic and Andy Murray are just inside the top 20, exceeding expectations by 6% and 5%, respectively, while Roger Federer is much further down the list, winning 7% fewer of these tight matches than he should.

Finding Fed on the negative end of this list is a surprise, since Federer, Nadal, and Isner are among the very, very few players who consistently beat expectations in tiebreaks. Tiebreak skill should be closely related to outperforming expectations in tight matches. In any event, my collaborator on a related project, Ryan Rodenberg, has written at length about Federer’s lack of success in some lottery matches.

When we narrow the focus to matches in which neither player won more than 51% of points–true toss-up matches–Nadal is still among the best. In fact, the top four of Rafa, Fognini, Melzer, and Isner remains the same, as each of those players has won between 36% and 38% more often than they should in contests with these extremely slim margins.  Once again, Djokovic and Murray are positive, at +16% and +6%, respectively, while Federer trails far behind, at -9%.

Careening downward

A big advantage of using the broader, 53-percent-of-points definition of lottery matches is that it gives us a larger sample to work with. Nadal has only played 27 matches in his career when the loser won more points than the winner did, and only 40 when neither player topped 51% of total points won.

In the 53% category, though, Nadal has amassed several matches each year of his career, allowing us to look at more meaningful trends. Each season from 2005-11, he averaged about 15 tight matches per year, and won at least one more than we would’ve expected of him, often two or three. Since the beginning of last year, though, he’s played 25, winning only 13 when he should have won 16.

Even with the bigger sample, these are small margins. If Nadal comes roaring back next year and beyond, again winning more close matches than expected, we’ll ultimately see these two seasons as outliers. Yet most of Nadal’s peers post surprisingly consistent records in tight matches. In the last decade, Djokovic and Murray have each had only one season each below -10%, and Federer has reliably underperformed, never reaching +7% for a full season. Not every player is as good in these matches as Nadal, but the ones who do excel post roughly similar numbers from one year to the next.

The bigger picture

Winning tight matches is useful, but as Federer’s experience demonstrates, it’s hardly necessary. And in the case of Fognini, exceeding expectations in lottery matches is hardly sufficient for more general success.

Even better than winning tight matches is winning easy matches, and a useful side effect of studying lottery matches is generating measurements of who plays them the most–and, of course, the least.

Lottery matches–again, those in which neither player wins more than 53% of points–represent fewer than 20% of Rafa’s career matches. His 19.7% rate of close contests is lower than any other player since 2000 (minimum 100 matches). In this category, the big four are bunched together as expected. Among active players, Federer is second lowest, Djokovic is third, and Murray is eighth. Kei Nishikori and David Ferrer are also among the top ten.

At the other end of the spectrum, we find the usual big-serving suspects. Vasek Pospisil tops the list at 49.5%, with Ivo Karlovic (44.5%), Isner (41.9%), and Jerzy Janowicz (40.5%) filling out the top four.

Analyzing the results of very close matches–whichever definition you prefer–is a useful way of identifying players on lucky or unlucky streaks, or even those who appear to play particularly well on big points. However, the more meaningful metric–certainly the one that more closely correlates with elite-level success–is the one that tells us who is avoiding tight matches. The only thing better than luck is not needing it.

Statistical Quirks in Munich and Oeiras

From Monday to Sunday last week, the ATP 250s in Munich and Oeiras were filled with statistical quirks.  Here’s a rundown of some of the oddities you might have missed:

  • In both events, the top four seeds in qualifying advanced to the main draw. Since the beginning of the decade, there have been 173 ATP 250s, and these two events were only the 7th and 8th of those in which the four qualifiers were the top four seeds.
  • Not only that, but the four players those qualifiers defeated were the 5th through 8th seeds. Put another way, the eight players in the qualifying round were the top eight seeds.  That hadn’t happened in the 2010s–and it happened in two different tournaments last week.   Of the previous 171 events, seven seeds reached the qualifying round on four occasions, but never eight.
  • In Munich, Tommy Haas won his first two matches as a 36 year old. He wasn’t the first man that old to win a match this year–Marc Gicquel beat him to it in Montpelier–but he’s only the 12th player to do so since 2000.  Still, he has a long way to go to catch Ken Rosewall, who won over 350 tour-level matches after his 36th birthday.
  • In four matches, Fabio Fognini reached the Munich final, but he didn’t play a single direct entrant. After a first round bye, he faced Dustin Brown, a wild card, followed by three qualifiers, Thomaz Bellucci, Jan Lennard Struff, and Martin Klizan. In ATP history, no one has ever played every round of an event without facing another direct entrant.  There have been a few instances when a player faces four non-direct entrants (notably Richard Gasquet‘s 2007 Wimbledon run).  I also found a couple of WTA $10Ks in which a player faced five non-direct entrants, but there are eight qualifying and four wild card spots at that level.
  • Fognini lost to Klizan in the final, a repeat of the final result in 2012 in St. Petersburg. Klizan’s two titles both came against Fognini, making him only the fifth player in ATP history to win his only two finals against the same player.  The Slovak is in good company: The most recent guy on the list is David Ferrer, and before that was Carlos Moya.
  • Back in Portugal, the heavy favorite Tomas Berdych won the first set over Carlos Berlocq by the score of 6-0. That’s rare enough in a tour-level final. Berlocq made it much more unusual, though, when he came back to win.  It was only the 10th time in ATP history that a player won a final after dropping the first set 0-6. The last occurrence was quite recent, when Marcel Granollers came back to win in the Kitzbuhel final last year.
  • Berlocq is known as a fighter, but he had never come back from a 0-6 hole in a tour-level match before. He had done so only once as a pro, in a Challenger match against Marcos Daniel in 2004.
  • Berdych’s record was even more pure, having never lost a professional match after winning the first set 6-0.

One more quirk from the week: By winning the Tallahassee Challenger, Robby Ginepri ended an 11-year-long title drought at that level.  (Though he did win several ATP titles in that time.)  Amazingly, that isn’t a record.  Thomas Johansson went 12 years and two months between Challenger titles, and Tommy Robredo, who ended his own nearly 12-year drought when he won Caltanissetta in 2012.

The Madrid Masters has star power, but this year it’s unlikely to produce as many historical oddities as the week it follows.

The Misleading Stat Sheet

A glance at the stat sheet from Serena Williams’s third-round match against Jie Zheng suggests that Serena dominated.  23 aces to 1, 3 break point conversions to none, 54 winners to 21, 84% 2nd-serve points won to 50%, and 55% of the total points played.

Of course, according to the more important stats–games and sets–Serena didn’t dominate.  She barely snuck through, losing a first-set tiebreak and going to 9-7 in the third.

Rick Devereaux, who brought this contrast to my attention, suggests that grass-court tennis–with more clean winners and fewer unforced errors than slower-paced styles–may be responsible.  That’s certainly part of the equation.

In fact, the Serena/Zheng match highlights the limits of the traditional stat sheet, especially on a surface that particularly favors the server.  Except for winners and unforced errors, nearly every stat directly captures some aspect of serving prowess–either yours or your opponent’s.  And in an era where nearly everyone is an excellent server, it doesn’t matter much whether you’ve set down a great serving performance or merely a good one.

To get to tiebreaks (or 9-7, or 70-68), you don’t have to be as good as your opponent, you just need to be good enough to hold.  Even the “winners” stat has to do with serving dominance, since so many are third shots behind a serve.  The vast majority of the stats from Serena’s match tell us that the American was more dominant on her serve than Zheng was.  And, of course, while Zheng was good enough to hold to 6-6 and 7-7, she lost the second set fairly badly, so the stats are a weighted average of two almost-even sets and one lopsided one.

When we find a mismatch between stat sheet and scoreline, we’re usually seeing one of two things:

  1. One player was much more dominant on serve (think 4 or 5-point games instead of 6+)
  2. One player won a lot of clutch points (like deuce, on serve) — losing unimportant ones (like 40-0 on serve), thus padding her opponent’s stat sheet.

Oddly, in the men’s game, the players who we think of as most dominant on serve rarely give us mismatched score sheets like this–quite the opposite.  Note the wording: “one player was much more dominant.”  There’s no doubt John Isner can dominate on serve, but since almost all his opponents are also good servers, Isner’s weak return game means that he is often the less dominant server, winning service games at 40-30 and losing return games at 0-40 or 15-40.  In fact, Isner has won more than 20 career matches despite losing more than half of the points played!

The same reasoning doesn’t apply to Serena.  She may be as big a server (relative to her opponents) as Isner, but her return game is also world-class.  And in the WTA, there are far more weak-to-middling servers.  On grass, as Rick points out, those weak-to-middling servers are (usually) still able to hold, making it more likely that a dominant performance on paper ends at 9-7 in a deciding set.

The Simon/Monfils 61-Shot Rally: In Perspective

A couple of weeks ago, Gael Monfils and Gilles Simon made the unorthodox decision of extending their warm-up into the first game of the match.  Or somthing.  At 40-40 in the opening game, they counterpunched each other into oblivion, needing sixty-one shots before Monfils finally sent a slice long to end the point.

If you haven’t seen it, or you suffer from insomnia, click the link here.

What might be most remarkable about the rally is that, when Monfils made his error, there was no sign of the point drawing to a close — it isn’t hard to imagine those two hitting another 61 shots like that.  But even at 61, it’s an awfully long point.

So (asks the statistician) … how long was it?  Rally length is not widely available for ATP matches.  But thanks to IBM Pointstream, I do have rally length for each point on a Hawkeye court from the French Open.  (I’ve played around a bit with those numbers.)

From the French Open, we have roughly 20,000 men’s points to look at, which doesn’t count double faults.  About 35% of those points lasted only one stroke: an ace, a service winner, or an error of some sort on the return.  Only 15% of the points went 8 strokes or longer, and fewer than 10% reached 10 strokes.

In the entire tournament, only 12 rallies hit the 30-shot mark–only halfway to the Simon/Monfils level.  You won’t be surprised at most of the names involved in those dozen extreme points:

Mardy Fish    Gilles Simon       38  
Andy Murray   Viktor Troicki     37  
Gilles Simon  Robin Soderling    36  
David Ferrer  Sergiy Stakhovsky  33  
Andy Murray   Viktor Troicki     33  
David Ferrer  Gael Monfils       33  
Rafael Nadal  Pablo Andujar      32  
Tobias Kamke  Viktor Troicki     31  
David Ferrer  Sergiy Stakhovsky  31  
Rafael Nadal  Andy Murray        31  
Rafael Nadal  Pablo Andujar      30  
Andy Murray   Viktor Troicki     30

Both Simon and Monfils make an appearance, with Ferrer, Murray, and Nadal showing up multiple times.  What surprises me a bit are some of the guys who hung in there with the counterpunchers, especially Fish and Troicki.

In any event, 61 shots still stands out as a once-in-a-blue-moon accomplishment.

WTA rally length

Incidentally, you might suspect (as I did) that some WTA players would slug it out even longer.  Again using Pointstream data from the Hawkeye courts at the French, it turns out that ladies only reached the 30-shot threshold twice.  First, Marion Bartoli went to 33 against Olga Govortsova, and Na Li got to 32 shots against Silvia Soler-Espinosa.  The tongue-tying Wozniacki-Wozniak matchup comes in third, with a 28-stroke rally.

Wimbledon rallies

While we’re at it, let’s check the Wimbledon data.  Surprise, surprise–tied for the longest rally of the tournament is a 31-stroke exchange between Juan Martin del Potro and … Gilles Simon.  In fact, that match featured four of the 20 longest rallies of the tournament.

Also notable is Novak Djokovic, who reached 31, 30, and 29 against Bernard Tomic, and 25 (twice) and 24 against Marcos Baghdatis.

The true oddity in the top ten is John Isner and Nicolas Mahut, who somehow took a break from aces and errant groundstrokes to go 25-deep.  It was the  only point of the match that went longer than 12 shots.


Stuttgart, De-Seeded

At the Mercedes Cup in Stuttgart this week, only two rounds have been completed, and all eight seeds are gone.  It isn’t even a particularly weak top of the field–five of the eight seeds are ranked in the top 20, and all eight are 37th or better.

Six of the eight lost their first-rounders, including #1 Gael Monfils (to Hanescu) and #2 Jurgen Melzer (to Giraldo).  The remaining two seeds–#3 Mikhail Youzhny and #8 Guillermo Garcia-Lopez–lost today.  Youzhny may be the only man in the draw without something to be ashamed of–he won a match, then lost to Juan Carlos Ferrero on clay.

The remaining draw almost makes Newport look good.  Of the eight unseeded players, we have two wild cards (Cedrik-Marcel Stebe and Lukasz Kubot) and two qualifiers (Pavol Cervenak and Federico Del Bonis).  The two qualifiers will play each other tomorrow, so at least one man from the qualifying draw will reach the final four.

It’s a project for another day, but it would be interesting to see which tournaments are most upset-prone.  The post-Wimbledon clay circuit seems like a prime contender, if only because of its awkwardness on the schedule.  And as friend-of-HT Tom Welsh pointed out, there seems to be a post-Davis Cup swoon, evident at Stuttgart with the losses to Mayer and Monfils.