Heavy Topspin

In professional tennis, it’s a given that the server has an advantage.  The size of that advantage depends on the abilities of the two players and the surface, but especially in men’s tennis, it’s a sizable edge.  On average, a server in an ATP match starts a point with a roughly 65% chance of winning.

But how long does it last?  It seems that, at some stage in the rally, the server’s advantage has disappeared.  Four or five strokes in, the server may still be benefiting from an off-balance return.  But by ten strokes, one would assume that the rally is neutral–that the advantage conferred by serving has evaporated.

As usual with tennis analysis, one question begets several more.  Does the server’s advantage last longer on faster surfaces?  Do women settle into “neutral” rallies sooner than men do?  Do dominating players, like this year’s edition of Novak Djokovic, take away the server’s advantage faster than the average player?

Using the rally counts provided by Pointstream at the last three majors, we can start to answer these questions.

Neutralizing the serve

The first step is to take all the matches we have rally-count data for, and average them out.  Then, for each point length, we calculate the odds that the server wins a point of at least that length.  So, for instance, we look at all points of five shots or more, and figure out how many of those the server wins.

Each one of these numbers is biased, because a rally of exactly five-strokes is, by definition, won by the server.  The server either hits a winner on his third shot (the fifth overall), or the returner makes an error attempting to hit his own third shot (the sixth overall).  Thus, if we look at all points of at least five strokes, the exactly five-stroke rallies virtually guarantee that the server will have the advantage.

However, the same reasoning shows us that a six-stroke rally will be biased in favor of the returner.  When we do the math for at-least-five, at-least-six, at-least-seven, and so on, we’ll see a yo-yo effect.  When the biases have equal effect, that means the serve is neutralized.

Here are the results for the approximately 150 grand slam matches with Pointstream data so far this year:

At least…  Win%  Notes                          
0          63%   before point begins            
1          66%   if serve goes in               
2          50%   if serve is returned           
3          60%   if server makes second shot    
4          46%   if returner makes second shot  
5          58%                                  
6          45%                                  
7          57%                                  
8          44%                                  
9          56%                                  
10         44%                                  
11         56%                                  
12         43%                                  
13         56%                                  
14         43%                                  
15         56%

In the table, “Win%” refers to the server’s chance of winning the point.  The biases even out somewhere between the 4th and 8th shot, meaning that in that zone, the server’s advantage is neutralized.

While the server retains the advantage at least until the fourth shot, it is interesting to see how quickly it decays.  Dropping from 66% upon making a serve to 56% once the advantage is neutralized, it loses more than half the difference between the first and third shots.  Thus, the returner doesn’t negate the server’s advantage simply by getting the ball back in play, but he does take a large step toward doing so.

Does surface matter?

As usual, it sure does.  The numbers for the Australian and French Opens are similar, and since they make up 2/3 of the data set, they are close to the aggregate numbers shown above.  But Wimbledon, as is so often the case, seems to play by a different set of rules:

At least…    Wimby    Austr    French  
0            66%        62%       62%  
1            68%        64%       67%  
2            52%        50%       48%  
3            62%        59%       58%  
4            48%        46%       45%  
5            61%        57%       57%  
6            47%        44%       44%  
7            61%        55%       56%  
8            47%        44%       44%  
9            59%        55%       54%  
10           47%        43%       43%  
11           60%        54%       55%  
12           46%        43%       43%  
13           59%        55%       55%  
14           43%        45%       42%  
15           56%        54%       56%

The biases don’t balance out until the very bottom–at 14 or more shots!  That’s only about 3% of points.  I’m not sure how to explain this, except perhaps psychologically, that on grass (considered the best surface for servers), players are less successful in return games simply because that’s what they expect to happen.  Regardless of surface, I can’t understand why else the server’s advantage would persist into double-digit shot counts.

What about the ladies?

WTA players (on average) start each service point with a smaller advantage than their male counterparts, and as it turns out, that advantage evaporates more quickly.

We saw a moment ago that, by putting the return in play, an ATP returner gives himself a 50% chance of winning the point–at least until his opponent hits another shot.  Women, however, knock the server’s winning percentage down to 47% by making the return.

The returner clearly neutralizes the point by the fourth stroke overall, and–here’s the good part–takes over a slight advantage herself by her third shot, the sixth stroke overall.  By making that sixth shot, the returner has a 57% chance of winning the point, while the server will never reach 57% again.  The advantage is only a percentage or two, but from the sixth stroke on, the returner has the edge.

Finally, presenting Novak Djokovic

Pointstream has tracked 17 of Djokovic’s slam matches this year, giving us a good set of data to work with.  When a man is having a season like this one–in large part because of his return game–it’s fascinating to see how comprehensively he is outplaying his opponents.

In the same terms as the tables above, here are Djokovic’s serve and return points across those 17 matches.  The return points are shown with the server’s winning percentages:

At least…    ND Sv    ND Ret  
0            70%         57%  
1            72%         60%  
2            59%         42%  
3            68%         50%  
4            56%         39%  
5            68%         49%  
6            57%         38%  
7            68%         47%  
8            58%         38%  
9            68%         45%  
10           55%         34%  
11           65%         44%  
12           55%         33%  
13           66%         38%  
14           52%         29%  
15           65%         40%

After seeing the averages above, you might reasonably conclude that these numbers are out of this world.  Even with the bias of 4-, 6-, and 8-stroke rallies, as discussed above, Djokovic still maintains an edge.  For everyone else, once fifth or sixth shot is struck, the point is a 50/50 proposition.  For Novak, it’s at least 60/40 in his favor.

The amazing stats are on his return.  When he gets his return back in play, he’s more than likely to win the point.  That may not surprise anyone who has watched Djokovic play this year, but consider how remarkable that is in the context of modern men’s tennis.  By the 8th stroke or so, he’s back to the 60/40 odds of the service points that turn into longer rallies.

Thanks to Carl Bialik for suggesting this topic.

“Consistency” is one of the many terms that commentators frequently use but rarely define.  It’s often misused, too: we say we want a player to be more consistent, when we really just want him to stop playing badly.

To me, consistency for a tennis player is similar to the notion of “playing up to his ranking.”  In other words, if a player is consistent, he usually beats players ranked lower, and he usually loses to players ranked higher.  No player is perfect in this regard, but clearly, some are much more reliable than others.

A recent poster boy for inconsistency is Ernests Gulbis.  At Roland Garros, he lost to Blaz Kavcic, ranked 82nd in the world.  That was on clay, a surface on which Gulbis had posted some excellent results the previous year.  Two months later, in Los Angeles, he beat Juan Martin del Potro, someone he shouldn’t have even challenged on a hard court.

Quantifying consistency

With my player rankings and match prediction system, I’m able to assign a win probability to each player for every match.  For instance, when Ivan Dodig beat Nadal last week, I had given him a 14.4% chance of doing so.  As you might imagine, that’s a major upset–as I wrote the next day, it was the 10th-biggest upset of the season.

In these terms, an ideally consistent player will never be on either end of an upset.  If he is the favorite, he wins; if he is the underdog, he loses.  In practice, no tour-level player accomplishes this, though over the last two years, Florent Serra and Eduardo Schwank have come very close.

I’ve come up with a metric to measure consistency.  This is how it works:

• Gather a list of all ATP-level matches for the desired time period.  (Today, I’m using everything from January 2010 through Montreal last week.)
• Eliminate matches that ended in retirement or walkover, as well as those where we don’t have enough information to make an educated prediction.  (e.g. the first few comeback matches of Tommy Haas, or one with a wildcard playing his first professional match.)
• For each player, count how many matches he played.
• For each player, find the matches where he was the favorite and lost, or was the underdog and won.
• For each of those matches, take the probability than the eventual winner would win (e.g. 18% — always under 50%), multiply by 100 (e.g. 18, not 18%),  subtract it from 50 (e.g. 50 – 18 = 32), and square the result (e.g. 32*32 = 1024).
• Sum all of the squares, then divide by the number of total matches–not just the ones where the favorite lost.

Whew!  In something more like layman’s terms, we’re taking all the upsets a player was involved in, coming up with a number to represent how big (or surprising) the upset was, then averaging the results.

Using this method, we give big upsets considerably more weight than mini-upsets.  If a player had a 45% chance of winning a match and ends up winning, it barely counts as an upset–and this system treats it accordingly.  By dividing by the total number of matches, we give consistency credit to players who win the matches they’re “supposed to” win, and lose those they are supposed to lose.

Most importantly, the numbers this algorithm spits out are completely believable, matching up well with the conventional wisdom of which players are consistent and inconsistent.

The consistency of the top ten

The most consistent player on the tour, since the beginning of 2010, has been … Florent Serra.  Amazingly, Igor Kunitsyn comes in second.  But I doubt many of you care much about the consistency of guys like that.

Let’s start with the current top 10, ranked from most to least consistent:

Player              Upsets  Matches    Up%  UpsetScore  
David Ferrer            25      119  21.0%          55  
Rafael Nadal            16      131  12.2%          68  
Novak Djokovic          18      119  15.1%          69  
Roger Federer           21      123  17.1%          69  
Jo-Wilfried Tsonga      20       80  25.0%          75  
Mardy Fish              19       77  24.7%          82  
Tomas Berdych           32      113  28.3%         106  
Gael Monfils            24       89  27.0%         107  
Robin Soderling         23      115  20.0%         130  
Andy Murray             24       97  24.7%         151

The relevant column is the rightmost, “UpsetScore,” which is the result of the algorithm described above.  Ferrer has been part of more upsets than any of the top three (“Up%”), but his upsets are more minor.  Except for losses to Ivo Karlovic and Jarkko Nieminen early in the year on hard courts, Ferrer has not lost a match he had a 60% or better chance of winning.

The two ends of this list certainly line up with what I would have expected: Ferrer and Nadal are rock-solid (last week’s loss to Dodig notwithstanding), while Soderling and Murray both can be picked off by anybody, and frequently threaten higher-ranked players.

Right now, you may be tempted to put Djokovic higher on the list–after all, he’s ranked #1 and he’s beating everybody.  However, in the slightly longer term of 20 months, his movement around the top three has included some unexpected results, like losing to Ljubicic at Indian Wells last year, and victories over Federer and Nadal before his ranking suggested he would do so.

Tour wild cards

Outside of the top 10, there are a handful of players who are almost impossible to predict.  Some names that come to mind are Marcos Baghdatis, Ernests Gulbis, and Nikolay Davydenko, men who can take out one of the top three on a good day (well, maybe not Gulbis), but can lose to a qualifier on the next.

Player                 Upsets  Matches  Up%  UpsetScore  
Nikolay Davydenko          32       73  44%         273  
Marin Cilic                27       91  30%         180  
Marcos Baghdatis           38       89  43%         177  
Olivier Rochus             20       52  38%         164  
Milos Raonic               16       41  39%         164  
Juan Martin del Potro      11       48  23%         154  
Andy Murray                24       97  25%         151  
Jurgen Melzer              28       96  29%         150  
Fernando Verdasco          40      104  38%         150  
Ivan Ljubicic              27       69  39%         149  
Florian Mayer              30       72  42%         147  
Samuel Querrey             26       66  39%         146  
Andrei Goloubev            24       55  44%         143  
Ernests Gulbis             22       69  32%         140  
Jeremy Chardy              31       65  48%         133  
Juan Monaco                26       73  36%         131  
Robin Soderling            23      115  20%         130  
Michael Llodra             26       67  39%         130  
Rainer Schuettler          15       42  36%         119  
Mikhail Youzhny            25       78  32%         116

The “upset score” number tells the story for Davydenko.  The man who beat Nadal at the beginning of the year and threatened Djokovic last week recently suffered defeat at the hands of Cedrik-Marcel Stebe (twice!) and Antonio Veic.

While no one is in Davydenko’s league, names like Cilic, Baghdatis, Murray, and Verdasco seem appropriate.  Verdasco, along with Melzer and Milos Raonic suggest a flaw in this approach: the algorithm reads very fast improvement or decline as inconsistency, which isn’t quite right.  Yes, Raonic has shocked the tennis world repeatedly this season, but he hasn’t mixed in too many disastrous losses alongside the surprise upsets.  I tinkered with ways to include that in the model, but nothing worked very well.

A couple more interesting notes from the “most inconsistent” players are found in the upset percentage column.  Guys like Davydenko, Baghdatis, Mayer, Goloubev, and Chardy are involved in upsets nearly half the time.  Chardy is highest in that category.  In fact, if I expanded the study to challenger events, he might rocket to the top of this list, as he plays quite a few, and often manages to lose against players outside the top 100.

The consistent ones

The flip side is considerably less star-studded.  In the 20 most-consistent players of the last 19-20 months, Ferrer is the only top-10 guy present, though #11 Nicolas Almagro is there as well.

Here’s my seat-of-the-pants theory.  In this sense, “consistent” isn’t good.  Yes, “consistent” sounds good, especially when “inconsistent” means Davydenko losing to Antonio Veic or Mayer falling to Federico del Bonis.  But inconsistent means Davy beating Federer and Mayer beating Soderling.  So, the players who show up on as “most consistent” are in fact consistent, but they are also mediocre.  Their consistency (perhaps a mental advantage) has helped them move up from the top 200 to the top 50 or 100, but that’s all they can do.

Ferrer and Almagro are good examples of this, actually.  Neither has the weaponry that makes commentators say, “This guy could be number one!”  But they’ve earned their rankings by regularly reaching the quarters and semis of tournaments, not suffering the boneheaded losses that afflict the likes of Cilic and Baghdatis.

All that said, here’s the list:

Player            Upsets  Matches  Up%  UpsetScore  
Florent Serra         11       56  20%          23  
Igor Kunitsyn         14       40  35%          33  
Ilia Marchenko        14       46  30%          40  
Potito Starace        28       81  35%          46  
Victor Hanescu        26       77  34%          50  
Tobias Kamke          12       41  29%          52  
Andreas Seppi         24       81  30%          53  
Julien Benneteau      23       59  39%          53  
Viktor Troicki        25      101  25%          54  
David Ferrer          25      119  21%          55  
Fabio Fognini         18       71  25%          55  
Pere Riba             13       41  32%          56  
Lukas Lacko           14       44  32%          57  
Igor Andreev          17       62  27%          58  
Lukasz Kubot          26       63  41%          59  
Nicolas Almagro       22      112  20%          59  
Frederico Gil         15       40  38%          60  
Denis Istomin         25       76  33%          65  
Jarkko Nieminen       25       74  34%          66  
John Isner            21       82  26%          67

These lists hardly represent the final word on who is or is not consistent–for one thing, I haven’t said anything about consistency within matches, which may be a completely separate issue.  But this approach does, I think, provide some insight into who is more likely to be part of an upset, and suggests that consistency might not be such a good thing after all.

On Friday, some interesting ideas were batted around in the comments to my post on the 61-shot rally.  One of the simpler ones boils down to the question that titles today’s post: Do points get shorter as the match progresses?

Two forces seem to work in opposite directions:

• As players get used to each other’s games (and specifically their serves), more balls get returned.  Before looking at the numbers, I would’ve bet that this was the case, meaning that aces and service winners decline as you go deeper into a match.
• The longer the match, the more tired the players.  Tired (or even slightly injured) players take more risks and probably have shorter rallies.

To answer the question, I looked at rally lengths shown in Pointstream at the last three grand slams.  That gives us close to 250 men’s matches, all best-of-five sets.

The short, unsatisfying conclusion is: The results are mixed.  At Wimbledon and Roland Garros, rally length increased later in matches–as much as 10% in London and 20% in Paris.  At the Australian Open, the result was the exact opposite, with rally length decreasing substantially.  Perhaps rally length increases in most cases, except when it is extremely hot or the players are not yet in top shape.  The blistering heat in Melbourne is certainly a plausible reason for a decrease in rally length.

As we’ll see when we move into more specific findings, the results get even more jumbled.  It seems that points generally get longer as a match progresses, but not necessarily because players read and return serves better.  While rally lengths increase, the number of one-stroke points (aces, service winners, service return errors) often increases, as well.

Follow the jump for my methodology and full results.

Continue reading Do Points Get Shorter as the Match Progresses?