Author: jsackmann

What Matters in Tiebreaks?

Italian translation at settesei.it

Players and fans tend to look at tiebreaks as a unique part of the sport of tennis, perhaps one susceptible to special skills.  The ATP website last week devoted an article to what those skills might be.  Players generally seemed to agree that it was nice to have a good serve, and a good return would also be handy.  Clearly, more analysis is needed.

Let me give you my hypothesis.  Tiebreaks are pressure packed, and pressure can affect any part of a player’s game.  But in general, they should impact some parts more than others.  You could make the case for either side of the ball–on the one hand, serving is a more “automatic” activity; on the other, there’s more time to think before each serve, and thinking can be dangerous when the pressure is on.  This is where it’s nice to have some data.

I found 388 tiebreaks from the last eight ATP slams.  For each one, I compared each player’s winning percentage on serve during the first 12 games of the set to his winning percentage on serve during the tiebreak.  If players were robots, there might be a difference between the set and the tiebreak for any given match, but in general, the numbers should be the same.

But players aren’t robots.  As it turns out, players win more return points than expected during tiebreaks.  The difference is noticeable if not enormous: about one more return point than expected every three matches.

Thus, tiebreaks are different from the sets that precede them in one of two ways.  Either some players are unable to serve up to their usual standard during tiebreaks, or some players manage to raise their return game in tiebreaks.

A breakdown by tournament suggests the answer.  The difference between server winning percentage in sets and tiebreaks is about the same for the Australian Open, the US Open, and Wimbledon, but is less than half as much at the French.  It seems, then, that faster courts give returners a bigger boost in the breaker.  A more likely interpretation is that servers are unable to hold on to their advantage on faster courts.  There’s less of an advantage to lose on clay.

My hypothesis at the outset focused on pressure, and combined with the numbers, it suggests that players are more affected by pressure when serving than when returning.  It’s also possible that players find it more difficult to get into a serving rhythm with only two serve points at a time.  It’s also possible that returners are less likely to concede aces during tiebreaks, meaning that the same serve quality and return potential results in more return points won.

Whether it is a matter of server timidity or returner aggression, there are certainly fewer aces in tiebreaks.  In these 388 tiebreaks, there were 83 fewer aces than would be expected if players kept acing at the rate of their first twelve games.  Given the relative infrequency of aces, that’s a more striking decrease than that of service winning percentage in general.

This analysis is hardly the final word.  But for aspiring tiebreak masters, it does offer a slightly more specific prescription than “get better at tennis.”  Rather than assuming that the tiebreak is all about the serve, recognize that returners have a slight advantage.  On serve, players can improve simply by ignoring the pressure (easy, right?) and serving as well as they did during the set.  When returning, players can be more aggressive in the knowledge that in general, servers will not be.

After all, a good serve may be the key to tiebreak success, but only if the serve is as good as usual in the breaker.

The Case for the Race

Last week, Peter Bodo argued in favor of giving the ATP year-to-date “Race to London” more weight over the traditional rolling 52-week ranking.  It’s a relevant point right now, when Roger Federer leads in the 52-week tally, but Novak Djokovic dominates in the year-to-date numbers.

In other words, Fed is racking up more records at #1 while Djokovic will almost certainly go in the books as the top player of 2012.  Bodo doesn’t go far enough: The old-fashioned rankings are weird, confusing, and–why stop there?–bad for tennis.

In most of the world’s most popular sports, everybody starts the year with a clean slate.  Imagine if a baseball team opened their schedule having to “defend” their previous year’s April winning streak.  Or if your favorite football team started the season seventh in their division.  This is essentially what happens when the ATP heads to Australia in January, altering rankings only when players do something different than what they accomplished last year.

Not only does this make it hard too root for underdogs in tennis, it makes it hard for the underdogs themselves.  You may not pity Bernard Tomic, but he surely spoke for many mid-pack players when he spoke about the mental challenge of defending points, not just beating world-class tennis players.  In other sports, hope springs eternal.  In tennis, it’s an immense struggle to crack the top 20 for a single week.

The greatest advantage of the Race is that it is so easy to understand.  Tomas Berdych reached the semifinals last week, so he gets 360 points.  Simple as that.  No comparison to last year’s totals, no concern about whether points are going on or coming off at a stagger from last year because of the Olympics, and–blessedly–nary a mention of zero-pointers.  Tennis rankings will always be more than simply incrementing the win column, but this is pretty close.

Bodo cites the unpredictability of the turn-of-the-century Australian Open as a reason why the Race didn’t catch on.  It doesn’t make sense to have Petr Korda atop much of anything, right?  In fact, that’s the beauty of it.  The 52-week rankings simply entrench the Big Four in our minds, while an emphasis on the race would make us think twice the next time a Korda, or a Marcos Baghdatis, or a Marin Cilic, makes a January splash.  Fans are smart enough to realize that leading the rankings early in the season isn’t the same as finishing at the top.

Some version of the 52-week ranking system will never go away, and that’s how it should be.  It’s purpose is to rate players–for seeding, and even more importantly, for tournament entry.  As I’ve written at length, it’s not a very good system for that purpose.  If we focused on the Race instead, the tournament entry methodology could become much more sophisticated and do a better job of putting the best players on court every week.

With its increasing focus on qualification for the Tour Finals, the ATP has taken some big steps toward presenting tennis as a high-stakes, year-long season, not merely a disjointed mishmash of events competing for attention.  Highlighting the Race rankings would make for much more spectator enjoyment.  It might even open the door to more important discussions of the chaotic tour schedule, eventually offering fans a coherent tennis season to follow every week.

Withdrawal Effects

Italian translation at settesei.it

Yesterday, Mardy Fish withdrew from his fourth-round match against Roger Federer.  As we saw earlier today, Federer may gain some benefit from the extra rest, but with the additional rest days built into the grand slam schedule, Roger runs the risk of getting too little time on court.

What’s the true effect, then?  Will the extra rest make Federer an even bigger favorite in his quarterfinal match against Tomas Berdych?  Or will match-court rust hold him back?

As it turns out, there is virtually no effect.  Players handed a walkover win almost exactly half of their next matches, and a closer look at those matches reveals that 50% is about what we would’ve expected from them, walkover or not.

To hunt for a potential relationship, I found 139 ATP main draw walkovers since 2001 where the winner went on to play another match at the same tournament–in other words, excluding finals.  While it may seem that players tend to withdraw when they’re least likely to win a match (as with Fish this week, or like the other two players to withdraw before facing Federer this year), there’s nothing to that theory, either. The average pre-match odds of the withdrawing player are about 51%.

Thus, we can work on the assumption that there’s little bias in the pool of 139 men who received a free pass to the next round.  For every Federer, there’s a Donald Young advancing uncontested over Richard Gasquet.  Balancing the withdrawals of players without a chance may be higher-ranked players who are quicker to withdraw because their success allows them to play it safe and make longer-term decisions.

In the 139 follow-up matches, our players went 67-72, winning 48.2% of the time.  Prematch predictions (generated by Jrank) would have projected a winning percentage of 48.9%.

If we narrow the search to slams, we get a nearly-meaningless pool of only 12 matches.  The player coming off the walkover went 6-6; prematch numbers would’ve predicted 7-5.  Perhaps rust does play a small part; considerably more likely is that the walkover simply doesn’t affect the beneficiary.

For Federer fans, though, there’s little reason for concern.  This is the ninth time in his career he’s advanced via walkover, and he’s only lost the next match twice.  One of those was in 2002.  The other was in Indian Wells in 2008.  The man who beat Fed?  Mardy Fish.

At Slams, Do Shorter Matches Lead to Later Success?

Italian translation at settesei.it

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

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

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

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

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

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

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

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

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

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

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

The Five-Set Advantage

Italian translation at settesei.it

Last night, the heavily-favored Janko Tipsarevic won his first round match against Guillaume Rufin despite dropping the first two sets.  Had Rufin taken the first two sets against Janko in Cincinnati, Monte Carlo, or just about anywhere else on the ATP tour, he would’ve scored his first top-ten scalp.

Other seeds have similar stories.  Milos Raonic, Marin Cilic, Gilles Simon, and Alexandr Dolgopolov all would be headed home had their matches been judged on the first three sets.  Only two seeds had the opposite experience: Juan Monaco and Tommy Haas were each up two sets to love before losing their next three.

Simply (if tongue-twistingly) put, the five-set format favors favorites.

In all grand slam first rounds since 1991, seeds have come back from 0-2 or 1-2 down against unseeded players 125 times, while seeds have squandered 2-0 or 2-1 advantages only 71 times.  Just looking at those 32 matches per slam, that’s almost one upset averted per tournament.  The US Open draw would look awfully different right now if Tipsarevic, Raonic, Cilic, Simon, and Dolgopolov were among the first-round losers, even if Haas and Monaco replaced them in the second round.

Set theory

These numbers shouldn’t surprise us, since longer formats should do a better job of revealing the better player.  There are reasons why the baseball World Series is best-of-7 instead of a single game and the final sets of singles matches aren’t super-tiebreaks.  The difference between best-of-3 and best-of-5 isn’t quite so simple–fitness and mental strength play a part–but from a purely mathematical perspective, there should be fewer upsets in best-of-5s than best-of-3s.

Take Raonic for example.  My numbers (which don’t differentiate between 3-set and 5-set matches–shame on me) gave him approximately a 70% chance of beating Santiago Giraldo.  If 70% is his probability of winning a three-set match and sets are independent (more on that in a minute), that number implies a 63.7% chance of winning any given set.  A 63.7% chance of winning a set translates into a 74.4% shot at winning a best-of-five.

A four- or five-point increase doesn’t radically change the complexion of the tournament, but it does make a different.  My original numbers suggested that we could expect 20 or 21 first-round upsets.  If we adjust my odds in the manner I described for Raonic, the likely number of upsets falls to 18.

The most important implication here is the effect it has on the chances that top players reach the final rounds.  Earlier this week a commenter took me to task for my unintuively low probabilities that Federer and Djokovic would reach the semifinals.  Obviously, if you give an overwhelming favorite a boost in every round, as the five-set format does, the cumulative effect is substantial.  For the top seeds, it can halve their probability of losing against a much lower-ranked opponent.

For Federer, adjusting the odds to reflect the theoretical advantage of the best-of-five format raises his chances of reaching the semis from 52.5% to over 65%.  Djokovic’s numbers are almost identical.

Dependent outcomes

Everything I’ve said so far seems intuitively sound, with one caveat.  Earlier I mentioned the assumptions that sets are independent.  That is, a player has the same chance of winning a particular set no matter what the outcome of the previous sets–there is no “hangover effect” based on what has come before.

Tennis players, even professionals, aren’t robots, so the assumption probably isn’t completely valid.  Sometimes frustration with one’s own performance, the environment, or line calls can carry over into the next set and give one’s opponent an advantage.  Perhaps more importantly, the result of one set sometimes reveal that pre-match expectations were wrong in the first place.  Had David Nalbandian played this week instead of withdrawn, no number of sets would reveal that he was a better player–his health would prevent him from playing at his usual level.

Another related caveat is that beyond a certain match length, the outcome is no longer dependent on the same skills.  When Michael Russell played Yuichi Sugita in the Wimbledon qualifying round, the two men looked equal for four sets.  In the fifth, Russell’s fitness gave him an advantage that didn’t exist in the first couple of hours.  In this case, an estimate of Russell’s probability of winning a set against Sugita may be independent of previous outcomes, but it is not the same for every set.

These allowances aside, there is little doubt that favorites are more likely to win best-of-five matches than best-of-threes.  Whether you want to watch the entire thing … that’s another story.

2012 US Open Men’s Projections

Here are my pre-tournament odds for the 2012 US Open.  For some background reading, follow the links for more on my player rating system, current rankings, and more on how I simulate tournaments.

I’ve made one tweak to the algorithm (for men only) since last posting odds.  As many of you have noticed, I seem to underestimate the chances that the very best players will progress through the draw.  Some analysis of past results showed that this is correct, so for now, there’s a bit of a band-aid in the system, boosting the odds of the current top ten in a way that reflects how they’ve outperformed my projections in the past.

Still, Federer and Djokovic both have well under 30% chances of winning the Open, and fall just short of 50% between them.  My rankings give Djokovic a very slight edge despite Federer’s big season, and the tournament draw, which places Murray in Federer’s half, firmly tilts the scales in the Serb’s favor.

    Player                    R64    R32    R16        W  
1   Roger Federer           90.6%  84.0%  74.0%    23.2%  
    Donald Young             9.4%   5.4%   2.5%     0.0%  
    Maxime Authom           32.9%   2.3%   0.7%     0.0%  
    Bjorn Phau              67.1%   8.3%   3.7%     0.0%  
    Albert Ramos            50.1%  15.1%   1.7%     0.0%  
    Robby Ginepri           49.9%  14.8%   1.7%     0.0%  
    Rui Machado             15.1%   5.5%   0.4%     0.0%  
25  Fernando Verdasco       84.9%  64.6%  15.4%     0.3%  

    Player                    R64    R32    R16        W  
23  Mardy Fish              77.1%  50.6%  33.9%     1.3%  
    Go Soeda                22.9%   8.8%   3.3%     0.0%  
    Nikolay Davydenko       88.6%  39.4%  21.4%     0.2%  
    Guido Pella             11.4%   1.2%   0.1%     0.0%  
    Ivo Karlovic            67.5%  34.2%  14.7%     0.1%  
    Jimmy Wang              32.5%  10.9%   3.0%     0.0%  
    Michael Russell         35.7%  16.2%   5.4%     0.0%  
16  Gilles Simon            64.3%  38.6%  18.1%     0.3%  

    Player                    R64    R32    R16        W  
11  Nicolas Almagro         52.9%  33.6%  20.2%     0.3%  
    Radek Stepanek          47.1%  28.5%  16.5%     0.2%  
    Nicolas Mahut           48.7%  18.2%   8.6%     0.0%  
    Philipp Petzschner      51.3%  19.6%   9.5%     0.0%  
    Blaz Kavcic             45.9%  15.3%   4.8%     0.0%  
    Flavio Cipolla          54.1%  19.8%   6.9%     0.0%  
    Jack Sock               19.8%   7.7%   1.9%     0.0%  
22  Florian Mayer           80.2%  57.2%  31.6%     0.5%  

    Player                    R64    R32    R16        W  
27  Sam Querrey             64.9%  51.7%  27.6%     0.7%  
    Yen-Hsun Lu             35.1%  23.9%   9.3%     0.1%  
    Ruben Ramirez Hidalgo   31.4%   4.8%   0.8%     0.0%  
    Somdev Devvarman        68.6%  19.6%   5.5%     0.0%  
    Denis Istomin           62.4%  23.8%  11.8%     0.1%  
    Jurgen Zopp             37.6%  10.2%   3.8%     0.0%  
    David Goffin            28.7%  14.8%   6.9%     0.0%  
6   Tomas Berdych           71.3%  51.3%  34.3%     1.7%  

    Player                    R64    R32    R16        W  
3   Andy Murray             87.6%  76.3%  63.9%    13.7%  
    Alex Bogomolov Jr.      12.4%   6.3%   2.7%     0.0%  
    Hiroki Moriya           22.9%   1.8%   0.4%     0.0%  
    Ivan Dodig              77.1%  15.7%   7.8%     0.1%  
    Thomaz Bellucci         65.9%  29.0%   6.6%     0.1%  
    Pablo Andujar           34.1%   9.9%   1.4%     0.0%  
    Robin Haase             31.9%  15.6%   3.0%     0.0%  
30  Feliciano Lopez         68.1%  45.5%  14.1%     0.3%  

    Player                    R64    R32    R16        W  
24  Marcel Granollers       63.8%  37.7%  19.2%     0.2%  
    Denis Kudla             36.2%  16.4%   6.3%     0.0%  
    Lukas Lacko             46.7%  20.6%   8.4%     0.0%  
    James Blake             53.3%  25.2%  10.8%     0.1%  
    Paul-Henri Mathieu      45.6%  14.3%   5.9%     0.0%  
    Igor Andreev            54.4%  19.2%   8.7%     0.0%  
    Santiago Giraldo        30.9%  16.5%   7.7%     0.0%  
15  Milos Raonic            69.1%  50.0%  33.0%     1.0%  

    Player                    R64    R32    R16        W  
12  Marin Cilic             70.6%  56.4%  31.1%     0.9%  
    Marinko Matosevic       29.4%  18.6%   6.5%     0.0%  
    Daniel Brands           70.6%  20.5%   6.0%     0.0%  
    Adrian Ungur            29.4%   4.5%   0.7%     0.0%  
    Tim Smyczek             53.1%  15.1%   5.8%     0.0%  
    Bobby Reynolds          46.9%  12.1%   4.3%     0.0%  
    Guido Andreozzi          5.7%   0.9%   0.1%     0.0%  
17  Kei Nishikori           94.3%  71.9%  45.6%     1.7%  

    Player                    R64    R32    R16        W  
32  Jeremy Chardy           84.1%  55.5%  23.6%     0.3%  
    Filippo Volandri        15.9%   4.3%   0.7%     0.0%  
    Tatsuma Ito             44.6%  16.6%   4.5%     0.0%  
    Matthew Ebden           55.4%  23.6%   7.3%     0.0%  
    Martin Klizan           42.3%   8.7%   3.2%     0.0%  
    Alejandro Falla         57.7%  14.7%   6.4%     0.0%  
    Karol Beck              16.7%   8.2%   3.2%     0.0%  
5   Jo-Wilfried Tsonga      83.3%  68.5%  51.2%     3.9%  

    Player                    R64    R32    R16        W  
8   Janko Tipsarevic        81.6%  69.4%  49.7%     1.9%  
    Guillaume Rufin         18.4%  10.4%   3.8%     0.0%  
    Brian Baker             40.9%   7.1%   1.8%     0.0%  
    Jan Hajek               59.1%  13.1%   4.5%     0.0%  
    Grega Zemlja            55.9%  22.5%   8.1%     0.0%  
    Ricardo Mello           44.1%  15.5%   4.7%     0.0%  
    Cedrik-Marcel Stebe     39.2%  21.6%   8.2%     0.0%  
29  Viktor Troicki          60.8%  40.4%  19.2%     0.2%  

    Player                    R64    R32    R16        W  
19  Philipp Kohlschreiber   54.1%  32.9%  16.2%     0.3%  
    Michael Llodra          45.9%  26.1%  11.9%     0.2%  
    Grigor Dimitrov         54.9%  23.7%   9.8%     0.1%  
    Benoit Paire            45.1%  17.4%   6.4%     0.0%  
    Mikhail Kukushkin       46.2%  14.5%   6.0%     0.0%  
    Jarkko Nieminen         53.8%  18.3%   8.2%     0.1%  
    Xavier Malisse          33.7%  19.2%   9.6%     0.1%  
9   John Isner              66.3%  48.0%  31.9%     1.6%  

    Player                    R64    R32    R16        W  
13  Richard Gasquet         82.1%  51.9%  27.6%     0.9%  
    Albert Montanes         17.9%   5.3%   1.3%     0.0%  
    Jurgen Melzer           82.7%  39.6%  18.1%     0.3%  
    Bradley Klahn           17.3%   3.1%   0.5%     0.0%  
    Steve Johnson           35.5%   5.3%   1.1%     0.0%  
    Rajeev Ram              64.5%  15.4%   4.7%     0.0%  
    Ernests Gulbis          27.6%  18.4%   7.6%     0.0%  
21  Tommy Haas              72.4%  60.9%  39.1%     2.5%  

    Player                    R64    R32    R16        W  
28  Mikhail Youzhny         68.2%  49.4%  22.9%     0.6%  
    Gilles Muller           31.8%  17.4%   5.2%     0.0%  
    Tobias Kamke            48.9%  15.9%   4.2%     0.0%  
    Lleyton Hewitt          51.1%  17.2%   4.6%     0.0%  
    Igor Sijsling           69.4%  17.1%   7.3%     0.0%  
    Daniel Gimeno-Traver    30.6%   4.0%   1.0%     0.0%  
    Kevin Anderson          27.6%  18.3%   9.8%     0.1%  
4   David Ferrer            72.4%  60.6%  44.9%     3.9%  

    Player                    R64    R32    R16        W  
7   Juan Martin Del Potro   70.1%  55.3%  45.2%     4.6%  
    David Nalbandian        29.9%  18.4%  12.2%     0.3%  
    Benjamin Becker         48.9%  12.7%   7.0%     0.0%  
    Ryan Harrison           51.1%  13.6%   7.7%     0.1%  
    Lukasz Kubot            71.1%  38.8%  11.8%     0.1%  
    Leonardo Mayer          28.9%  10.0%   1.5%     0.0%  
    Tommy Robredo           31.0%  11.8%   2.1%     0.0%  
26  Andreas Seppi           69.0%  39.5%  12.5%     0.1%  

    Player                    R64    R32    R16        W  
20  Andy Roddick            89.4%  57.3%  36.9%     1.1%  
    Rhyne Williams          10.6%   2.0%   0.4%     0.0%  
    Carlos Berlocq          23.0%   5.2%   1.5%     0.0%  
    Bernard Tomic           77.0%  35.5%  19.7%     0.3%  
    Edouard Roger-Vasselin  44.4%  14.4%   4.3%     0.0%  
    Fabio Fognini           55.6%  21.1%   7.3%     0.0%  
    Guillermo Garcia-Lopez  38.8%  22.5%   8.9%     0.0%  
10  Juan Monaco             61.2%  41.9%  21.0%     0.4%  

    Player                    R64    R32    R16        W  
14  Alexandr Dolgopolov     61.8%  36.8%  19.6%     0.3%  
    Jesse Levine            38.2%  18.1%   7.7%     0.0%  
    Marcos Baghdatis        67.8%  34.5%  17.2%     0.2%  
    Matthias Bachinger      32.2%  10.6%   3.5%     0.0%  
    Steve Darcis            59.5%  23.6%  10.8%     0.1%  
    Malek Jaziri            40.5%  12.6%   4.6%     0.0%  
    Sergiy Stakhovsky       28.8%  14.1%   5.8%     0.0%  
18  Stanislas Wawrinka      71.2%  49.8%  30.9%     0.8%  

    Player                    R64    R32    R16        W  
31  Julien Benneteau        64.7%  43.7%   9.6%     0.3%  
    Olivier Rochus          35.3%  18.7%   2.8%     0.0%  
    Dennis Novikov          34.1%   9.6%   1.0%     0.0%  
    Jerzy Janowicz          65.9%  28.1%   4.4%     0.0%  
    Rogerio Dutra Silva     39.5%   2.5%   0.6%     0.0%  
    Teymuraz Gabashvili     60.5%   5.4%   1.9%     0.0%  
    Paolo Lorenzi            6.4%   3.6%   1.2%     0.0%  
2   Novak Djokovic          93.6%  88.6%  78.5%    26.5%

2012 US Open Women’s Projections

Here are my pre-tournament odds for the 2012 US Open.  For some background reading, follow the links for more on my player rating system, current rankings, and more on how I simulate tournaments.

    Player                         R64    R32    R16        W  
1   Victoria Azarenka            92.6%  83.5%  70.0%    12.5%  
    Alexandra Panova              7.4%   3.2%   1.0%     0.0%  
    Barbora Zahlavova Strycova   46.8%   6.0%   2.1%     0.0%  
    Kirsten Flipkens             53.2%   7.3%   2.7%     0.0%  
    Su-Wei Hsieh                 56.4%  24.1%   5.4%     0.0%  
    Magdalena Rybarikova         43.6%  16.0%   2.9%     0.0%  
    Virginie Razzano             41.4%  22.8%   5.2%     0.0%  
28  Jie Zheng                    58.6%  37.1%  10.6%     0.2%  

    Player                         R64    R32    R16        W  
18  Julia Goerges                80.7%  66.0%  37.5%     0.8%  
    Kristyna Pliskova            19.3%  10.1%   2.6%     0.0%  
    Mandy Minella                50.2%  12.0%   3.0%     0.0%  
    Olivia Rogowska              49.8%  11.9%   2.9%     0.0%  
    Stephanie Foretz Gacon       43.0%   7.4%   2.0%     0.0%  
    Anna Tatishvili              57.0%  12.4%   4.0%     0.0%  
    Sorana Cirstea               40.3%  30.8%  16.9%     0.2%  
16  Sabine Lisicki               59.7%  49.4%  31.2%     0.8%  

    Player                         R64    R32    R16        W  
9   Na Li                        85.7%  75.7%  41.9%     4.6%  
    Heather Watson               14.3%   8.0%   1.6%     0.0%  
    Lesia Tsurenko               45.0%   6.6%   1.0%     0.0%  
    Casey Dellacqua              55.0%   9.7%   1.8%     0.0%  
    Samantha Crawford            14.0%   0.5%   0.0%     0.0%  
    Laura Robson                 86.0%  14.2%   3.6%     0.0%  
    Victoria Duval                0.9%   0.1%   0.0%     0.0%  
23  Kim Clijsters                99.1%  85.3%  50.1%     5.5%  

    Player                         R64    R32    R16        W  
31  Varvara Lepchenko            66.9%  44.1%  15.7%     0.0%  
    Mathilde Johansson           33.1%  16.1%   3.7%     0.0%  
    Anastasia Rodionova          55.9%  23.4%   5.9%     0.0%  
    Julia Cohen                  44.1%  16.4%   3.5%     0.0%  
    Edina Gallovits-Hall         44.2%   7.1%   2.7%     0.0%  
    Stefanie Voegele             55.8%  10.8%   4.7%     0.0%  
    Petra Martic                 25.5%  17.6%  10.7%     0.0%  
7   Samantha Stosur              74.5%  64.5%  53.0%     2.1%  

    Player                         R64    R32    R16        W  
3   Maria Sharapova              86.5%  77.7%  67.0%     9.3%  
    Melinda Czink                13.5%   7.9%   4.1%     0.0%  
    Lourdes Dominguez Lino       48.9%   6.9%   3.0%     0.0%  
    Sesil Karatantcheva          51.1%   7.4%   3.3%     0.0%  
    Timea Bacsinszky             70.8%  19.4%   2.5%     0.0%  
    Mallory Burdette             29.2%   3.9%   0.3%     0.0%  
    Lucie Hradecka               38.0%  27.1%   5.7%     0.0%  
27  Anabel Medina Garrigues      62.0%  49.6%  14.1%     0.1%  

    Player                         R64    R32    R16        W  
19  Nadia Petrova                67.0%  36.1%  19.5%     0.2%  
    Jarmila Gajdosova            33.0%  12.0%   4.4%     0.0%  
    Simona Halep                 49.9%  25.8%  12.8%     0.1%  
    Iveta Benesova               50.1%  26.1%  13.0%     0.1%  
    Alexandra Cadantu            21.3%   4.5%   1.0%     0.0%  
    Aleksandra Wozniak           78.7%  37.7%  18.7%     0.2%  
    Melanie Oudin                30.9%  13.9%   5.3%     0.0%  
15  Lucie Safarova               69.1%  43.9%  25.4%     0.4%  

    Player                         R64    R32    R16        W  
11  Marion Bartoli               78.4%  46.4%  28.9%     1.2%  
    Jamie Hampton                21.6%   6.4%   2.1%     0.0%  
    Romina Oprandi               24.5%   7.1%   2.3%     0.0%  
    Andrea Petkovic              75.5%  40.2%  23.9%     0.7%  
    Kristina Mladenovic          37.5%   7.2%   1.4%     0.0%  
    Marina Erakovic              62.5%  17.6%   4.9%     0.0%  
    Daniela Hantuchova           48.8%  36.5%  17.6%     0.4%  
17  Anastasia Pavlyuchenkova     51.2%  38.7%  18.9%     0.5%  

    Player                         R64    R32    R16        W  
25  Yanina Wickmayer             82.8%  64.6%  26.3%     0.6%  
    Julia Glushko                17.2%   7.3%   1.2%     0.0%  
    Pauline Parmentier           45.4%  11.9%   2.1%     0.0%  
    Michaella Krajicek           54.6%  16.2%   3.3%     0.0%  
    Nicole Gibbs                 23.5%   1.7%   0.3%     0.0%  
    Alize Cornet                 76.5%  15.0%   5.8%     0.0%  
    Polona Hercog                15.7%   9.2%   3.9%     0.0%  
5   Petra Kvitova                84.3%  74.0%  57.1%     6.9%  

    Player                         R64    R32    R16        W  
8   Caroline Wozniacki           85.1%  72.5%  52.5%     4.1%  
    Irina-Camelia Begu           14.9%   7.6%   2.4%     0.0%  
    Silvia Soler-Espinosa        57.0%  12.3%   4.3%     0.0%  
    Alla Kudryavtseva            43.0%   7.6%   2.2%     0.0%  
    Tsvetana Pironkova           68.7%  48.3%  22.8%     0.5%  
    Camila Giorgi                31.3%  16.4%   5.2%     0.0%  
    Ayumi Morita                 37.6%  10.7%   2.6%     0.0%  
26  Monica Niculescu             62.4%  24.5%   8.0%     0.0%  

    Player                         R64    R32    R16        W  
22  Francesca Schiavone          55.4%  41.9%  18.9%     0.2%  
    Sloane Stephens              44.6%  31.9%  12.9%     0.1%  
    Akgul Amanmuradova           52.9%  14.2%   3.3%     0.0%  
    Tatjana Malek                47.1%  12.0%   2.5%     0.0%  
    Kimiko Date-Krumm            29.2%   5.8%   1.8%     0.0%  
    Sofia Arvidsson              70.8%  25.3%  13.4%     0.1%  
    Elina Svitolina              13.8%   4.5%   1.4%     0.0%  
12  Ana Ivanovic                 86.2%  64.4%  45.8%     1.6%  

    Player                         R64    R32    R16        W  
14  Maria Kirilenko              67.6%  50.9%  31.6%     0.6%  
    Chanelle Scheepers           32.4%  19.5%   8.6%     0.0%  
    Agnes Szavay                 16.2%   1.4%   0.2%     0.0%  
    Greta Arn                    83.8%  28.2%  11.2%     0.0%  
    Galina Voskoboeva            59.1%  30.2%  15.0%     0.1%  
    Arantxa Rus                  40.9%  17.3%   7.1%     0.0%  
    Andrea Hlavackova            30.0%  11.4%   4.0%     0.0%  
24  Klara Zakopalova             70.0%  41.1%  22.3%     0.2%  

    Player                         R64    R32    R16        W  
32  Shuai Peng                   57.6%  25.3%   5.2%     0.1%  
    Elena Vesnina                42.4%  15.8%   2.6%     0.0%  
    Ekaterina Makarova           80.0%  52.4%  14.9%     0.8%  
    Eleni Daniilidou             20.0%   6.5%   0.8%     0.0%  
    Mirjana Lucic                35.6%   3.0%   0.8%     0.0%  
    Maria Jose Martinez Sanchez  64.4%   8.7%   3.4%     0.0%  
    Coco Vandeweghe               8.2%   4.1%   1.3%     0.0%  
4   Serena Williams              91.8%  84.2%  70.9%    26.1%  

    Player                         R64    R32    R16        W  
6   Angelique Kerber             88.6%  65.7%  48.5%     6.0%  
    Anne Keothavong              11.4%   3.3%   1.0%     0.0%  
    Bethanie Mattek-Sands        30.1%   6.3%   2.4%     0.0%  
    Venus Williams               69.9%  24.7%  13.9%     0.4%  
    Johanna Konta                42.7%  10.2%   1.6%     0.0%  
    Timea Babos                  57.3%  16.6%   3.3%     0.0%  
    Olga Govortsova              18.2%   8.4%   1.4%     0.0%  
29  Tamira Paszek                81.8%  64.8%  27.9%     1.1%  

    Player                         R64    R32    R16        W  
21  Christina McHale             75.7%  61.4%  41.8%     1.0%  
    Kiki Bertens                 24.3%  14.2%   6.0%     0.0%  
    Olga Puchkova                39.7%   7.9%   2.4%     0.0%  
    Irina Falconi                60.3%  16.5%   6.5%     0.0%  
    Vera Dushevina               68.3%  27.2%  10.4%     0.0%  
    Nastassja Burnett            31.7%   7.5%   1.7%     0.0%  
    Garbine Muguruza             36.1%  20.5%   7.9%     0.0%  
10  Sara Errani                  63.9%  44.9%  23.3%     0.2%  

    Player                         R64    R32    R16        W  
13  Dominika Cibulkova           73.9%  54.9%  35.7%     1.3%  
    Johanna Larsson              26.1%  13.2%   5.2%     0.0%  
    Bojana Jovanovski            44.2%  13.1%   4.8%     0.0%  
    Mona Barthel                 55.8%  18.8%   8.0%     0.0%  
    Vania King                   54.1%  25.1%  11.3%     0.1%  
    Yaroslava Shvedova           45.9%  19.7%   8.2%     0.0%  
    Urszula Radwanska            45.1%  23.7%  10.9%     0.1%  
20  Roberta Vinci                54.9%  31.5%  15.9%     0.2%  

    Player                         R64    R32    R16        W  
30  Jelena Jankovic              60.9%  40.0%  14.4%     0.2%  
    Kateryna Bondarenko          39.1%  21.7%   6.0%     0.0%  
    Lara Arruabarrena-Vecino     25.7%   5.6%   0.7%     0.0%  
    Shahar Peer                  74.3%  32.6%   9.1%     0.0%  
    Ksenia Pervak                47.1%  10.4%   4.7%     0.0%  
    Carla Suarez Navarro         52.9%  12.6%   6.1%     0.0%  
    Nina Bratchikova             11.3%   4.2%   1.4%     0.0%  
2   Agnieszka Radwanska          88.7%  72.7%  57.6%     6.7%

The Slam No One Misses

Italian translation at settesei.it

By now you’ve heard: Rafael Nadal will miss the US Open.  It’s hardly a surprise, as Rafa hasn’t played a match since Wimbledon, and his knee has kept him off the tour for long periods in the past.

What is remarkable is the rarity of a top player missing the Open.  Despite its position near the end of the ATP schedule, after eight months of grueling tennis in which every player picks up his share of nagging injuries, New York gets a better turnout from top-10 players than any of the other three slams.

In fact, Nadal is only the third top-three player since 1991 to skip Flushing.  In 1999, #1-ranked Pete Sampras couldn’t play, and in 2004, it was #3-ranked Guillermo Coria who stayed home.  In the tournament’s last 21 editions, a top-ten player has missed the event only ten times.

It’s interesting to speculate as to why top players manage to show up in Flushing at a rate unmatched elsewhere.  Surely the event doesn’t have more cachet than Wimbledon.  Certainly the multiple shifts of surface throughout the spring and summer test every player’s mental and physical stamina.  Perhaps the longish break between Wimbledon and the Open allows players to take time off if they need it.  Most men play Canada and Cincinnati, but as we’ve seen this year, plenty of guys are willing to miss either one, meaning that only a serious injury keeps one out of the New York draw.

Defying conventional wisdom even further, the slam with the second-best turnout among top players is the French, not Wimbledon.  Since 1991, only 13 top-tenners have missed Roland Garros, and three of those were Boris Becker.

Wimbledon may be synonymous with the sport of tennis, but it is a distant third, with 25 top-tenners missing from the last 22 draws.  Here the no-shows are more logical: Alex Corretja three times, Marcelo Rios twice, Sergi Bruguera four times.  In the late 1990s, some guys simply didn’t consider the All-England Club a must.

Australia is a bit further back in fourth, with 29 top-tenners who didn’t play.  Melbourne does seem to have the least cachet of the four big events, but the tide may be turning.  Since 2006, only one top-ten player, Nikolay Davydenko in 2009, failed to make an appearance.

It may seem that absences from Grand Slams are random, driven by accidents such as major injuries that can happen at any time.  Any single absence surely does look that way.  There are larger forces at work, however–the value associated with certain tournaments, the demands of the schedule leading to physical breakdowns at some times and not others–that are not random.  In one more way, Rafael Nadal is proving himself a unique player, missing the most unmissable slam on the ATP calendar.

The Unbreakable and Record-Setting Cincinnati Finalists

When Roger Federer and Novak Djokovic met in the Cincinnati final on Sunday, they represented a unique event in tennis history: Neither one had been broken.  Four matches each, no breaks of serve.

That’s not just a Masters-level record, it’s a first for the ATP tour, at least since 1991, the time span for which point-level stats are available.    That’s over 1500 tournaments, including nearly 200 Masters events.

It’s very rare to even come close.  Of the 195 Masters tournaments for which data is available, only four pairs of finalists entered the title match with three or fewer breaks.  Djokovic leads the pack: When he met Rafael Nadal in the 2011 Miami final, Nadal had been broken once, Djokovic not at all.  When Djokovic and Federer met in the 2007 Montreal final, each player had only been broken once.  The Miami achievement is particularly notable because each player had won five pre-final matches, compared to only four each in Cincinnati and Montreal.

Federer set some records on his own, as well.  By holding his serve against Djokovic, he made it through an entire Masters tournament without suffering a break.  That’s the first time it has ever happened at this level.  Eight other times the winner has only been broken once–twice that winner was Federer, including Cincinnati two years ago.  Ten additional times, the winner was only broken twice–and Roger is responsible for three of those.

At lower level tournaments, it’s somewhat more common–the winner of a non-Masters event has made it through without losing serve a total of 17 times.  Surprise, surprise: Two of those are Federer, at Doha in 2005 and Halle in 2008.  Four other men have done it twice: Andy Roddick, Joachim Johanssen, Richard Krajicek, and Ivan Ljubicic.  Milos Raonic did it earlier this year in Chennai.

Federer set at least one more record last week, and it might be the most impressive of all.  He only faced three break points all week–the lowest known total at a Masters tournament.  The previous record was four, set by Andre Agassi at the 2002 Madrid Masters.  Fed’s total in Cinci was only the 10th ever in single digits–and Roger is now responsible for four of those top ten results.

At lower-level events, Fed’s mark has been bettered a couple of times.  At the 2007 Memphis tournament, Tommy Haas claimed the trophy without facing a single break point.   At San Jose this year, Raonic faced only two break points, though Tobias Kamke converted one of them.  Two other players–Andy Murray at 2009 Queen’s Club and Roddick at Lyon in 2005–got through an event facing only three break points.

No breaks, and record-settingly few break points. If hard courts are truly becoming slower, it seems that someone forgot to tell Roger.

The Implications of the 10-Point Tiebreak

Italian translation at settesei.it

I’m not sure how we got here, but we now live in a world where a lot of people consider a 10-point tiebreak equivalent to a set.  Apparently it’s more fan-friendly and better for television.  And of course it’s faster.

Whatever its practical uses, it’s obvious that the first-to-10 breaker isn’t the same as a set.  I’ll leave the moral debate to others; let’s take a statistical approach.

In general, the more points (or games, or sets) required to win a match, the more likely it is that the better player wins.  Some commentators have taken to calling the 10-point breakers “shootouts,” and for good reason.  Reduce the number of points required to win, and you increase the role played by luck.

Of course, sometimes a shootout is the best idea.  You’ve got to end a match somehow, and when players end up equal after two sets, four sets, or four sets and twelve games, it’s all the more likely that luck will have to intervene.  But the structure of the match determines just how much luck is permitted to play a part.

To compare a 10-point tiebreak with the set it replaces, we need to know how much more luck it introduces into the game.  For that, we need an example to work with.

Take two players: Player A wins 70% of points on serve, and Player B wins 67% of points on serve.  Playing best of three tiebreak sets, Player A has a 63.9% chance of winning the match.

If A and B split sets, A’s probability of winning falls to 59.3%.  In other words, the shorter time frame makes it more likely that B gets lucky, or is able to put together an unusually good run of play long enough to win the match.

If the match is decided by a 10-point tiebreak, however, A’s probability of winning falls all the way to 56.0%, erasing more than one-third of the favorite’s edge in the third set.  In fact, the 10-point breaker is barely more favorable to A than a typical 7-pointer, in which A would have a 55.1% chance.

(If you like playing around with this stuff, see my python code to calculate tiebreak odds.)

Somehow I don’t think anyone would advocate replacing the deciding set with a 7-point tiebreak.  Yet a 10-point tiebreak is much closer to its 7-point cousin than it is to a full set.

Adding a few more points doesn’t resolve the discrepancy, either.  To maintain Player A’s 59.3% chance of winning, the third set would have to be replaced by a 26-point tiebreak.  But that, I’m sure, wouldn’t attract many new advertisers.