Monthly Archives: December 2011

Living Up to Your Seeding

Listen to the commentary during tennis tournaments and you’ll hear a lot about “living up” or “playing up” to one’s seed.  In other words, a seed implies a certain level of performance. If you’re #10, you should reach the round of 16, but it would take an upset to get to the quarterfinals.

Of course, most players aren’t that consistent.  Sometimes they beat expectations (even Igor Kunitsyn won a tournament) and sometimes they crash out early (hello, Andy Murray!).  While guys like David Ferrer seem to steer a middle course, each player’s ranking is really just a weighted average of the tournaments where they ruled the world and the events where they shouldn’t have gotten out of bed.

And the more you think about it, the more the notion of “living up to your seeding” falls apart.  In order for the top seed at a tournament to meet expectations, he has to win.  That happens considerably less than half the time.  For the second seed to go home happy, he needs to reach the final.  But with rare exceptions, someone who lost in the final every week would quickly amass enough ranking points to be #1.  So at least at the top, we shouldn’t expect that level of consistency.  Also, the whole idea sets the same expectations for the 9th seed as the 16th, the 17th seed as the 32nd.  We can do better.

I looked at the last 20 years of slam results and figured out the average result for every seed.  In that time span, the top seed has won 5.0 matches per slam–on average, then, he has lost in the semifinals.  That number has increased since the majors started seeding 32 players in 2002: In the last 10 years, the top seed has won 5.3 matches per slam, as he has generally coasted through the first two rounds.

Here’s a look at how each seed has done over the last 20 years.  After the top few guys, no one should be expected to reach the quarters–certainly not the #8 seed!

Seed       Wins            
1          5.0   SF        
2          4.2   QF+       
3          3.7   QF-       
4          3.4   R16+      

5          2.7   R16-      
6          2.9   R16-      
7          2.5   R32/R16   
8          2.1   R32+      

9          2.5   R32/R16   
10         2.7   R16-      
11         2.2   R32+      
12         2.6   R16-      

13         2.1   R32+      
14         2.2   R32+      
15         2.1   R32+      
16         1.6   R64/R32   

17-32      1.6   R64/R32   
UNR 92-01  0.7   R64-      
UNR 02-11  0.6   R128/R64

A more sophisticated way of looking at this is with probabilities.  Sure, the smart money is on the top seed winning five matches, but beyond knowing that he wins the tournament between 35 and 40 percent of the time, what are the odds that he reaches the final?  Crashes out early?

Here are those odds for the same sets of players:

Seed         R64    R32    R16     QF     SF      F      W  
1          97.3%  90.5%  83.8%  75.7%  62.2%  48.6%  36.5%  
2          88.5%  78.2%  70.5%  60.3%  51.3%  34.6%  24.4%  
3          93.5%  80.5%  70.1%  57.1%  36.4%  19.5%   5.2%  
4          84.4%  75.3%  64.9%  55.8%  39.0%  14.3%   7.8%  

5          84.2%  71.1%  47.4%  36.8%  15.8%   7.9%   2.6%  
6          84.2%  67.1%  56.6%  38.2%  21.1%  13.2%   7.9%  
7          81.3%  69.3%  52.0%  32.0%  16.0%   4.0%   0.0%  
8          80.3%  61.8%  47.4%  22.4%   2.6%   1.3%   0.0%  

9          86.3%  70.0%  53.8%  28.8%  13.8%   5.0%   0.0%  
10         88.2%  69.7%  52.6%  31.6%  10.5%   5.3%   2.6%  
11         93.2%  63.0%  34.2%  15.1%   4.1%   1.4%   0.0%  
12         84.8%  70.9%  51.9%  34.2%  19.0%   5.1%   2.5%  

13         79.5%  61.5%  48.7%  12.8%   7.7%   3.8%   2.6%  
14         82.7%  60.0%  42.7%  18.7%   9.3%   2.7%   0.0%  
15         81.8%  67.5%  41.6%  15.6%   7.8%   3.9%   0.0%  
16         72.7%  44.2%  28.6%   7.8%   5.2%   2.6%   1.3%  

17-32      72.5%  51.8%  19.7%   8.2%   2.2%   0.9%   0.4%  
UNR 92-01  42.6%  15.8%   5.7%   1.9%   0.6%   0.2%   0.0%  
UNR 02-11  40.1%  12.8%   4.3%   1.2%   0.4%   0.2%   0.0%

The same sample of no more than 80 slams means that these numbers don’t give us a smooth curve, but they still provide a pretty good idea.  In fact, they look awfully similar to my pre-tournament slam predictions, with the exception of the big gap between the top two seeds and the rest of the field.

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What Happens When You Win an Aussie Warmup?

Because of its placement on the calendar, the Australian Open is unique.  It almost immediately follows the offseason (such as it is), so the common perception is that some players show up less ready than for the other three slams.

For this reason, the tournaments in the two weeks before the Australian Open are both important and difficult to predict.  At Chennai next week, who will be in shape? Who is mentally ready for the new season?  And once we get the results from Chennai, Doha, Auckland, Sydney, and Brisbane, what does that tell us about the Aussie Open itself?

It’s this last question that I’ll try to answer today.  If there’s ever a time that rankings don’t seem to count for quite as much, it’s January–after all, that’s when Yevgeny Kafelnikov won his hard-court slam.  It would stand to reason if the warmups were particularly predictive.  Perhaps tourneys like Doha serve as sneak previews of each player’s readiness for the big event in Melbourne.

Alas, it doesn’t look that way.  Winning a tournament in the two weeks before Melbourne doesn’t predict better performance at the Australian Open.  In fact, it more reliably forecasts a disappointing showing at the first grand slam of the year.

Since 1992 (and not counting 2007, when some of the warmups tinkered with a round-robin format), there have been 93 tournaments in the two weeks before Melbourne.  42 of those were the week before the slam, and 51 were two weeks before the slam.  For each one, I noted the winner of the event, their seeding in Melbourne, and their performance in Melbourne.  With the last two data points, we can determine whether each player performed equal to, above, or below expectations.

(Aussie Open seeding isn’t a perfect way to determine expectations, since results from two weeks before are reflected in the rankings.   But it was much easier than any alternative, and since this approach doesn’t recognize a difference between, say, the 5th seed and the 8th seed, I doubt it makes much difference.)

Let’s start with winners the week before Melbourne.  I didn’t expect much here, since the best players tend to take a week off before slams.  It seems, though, that a win the week before at least helps you through the first round or two.

Of the 42 champions of week-before tourneys, 12 met expectations (that is, played as their Aussie Open seeding would have predicted), 17 exceeded expectations, and 13 didn’t meet expectations (including one who withdrew from the slam).  Of the last group, only four players lost their opening round in Melbourne, and none of those players were seeded.  Several week-before winners lost in the second round; the most painful of those was 6th-seed Michael Chang’s exit in 1993.

On the flip side, Pete Sampras played Sydney and won in 1994, then went straight to Melbourne, where he made it two trophies in a row.  He is the only player in the last 20 years to have won the Australian in addition to an event the previous week.

For champions two weeks before Melbourne, the results aren’t as pleasant.  Of those 51 tournament winners, 15 met expectations at the slam, 12 exceeded them, and 24 failed to play up to their seed (again, including one who withdrew from the Open).

A whopping 14 of those 51 champions didn’t win a single match in Melbourne, including 4-seed Boris Becker in 1993, 5-seed Carlos Moya in 2005, and 9-seed Andy Murray in 2008.  Only two of the 51 players won the tournament: Petr Korda in 1998 and Roger Federer in 2006, both of whom won Doha in their respective years.

In other words, winning a warmup doesn’t say much about your form for the Open itself–in fact, next week’s winners won’t deserve much additional hype, no matter how good they look in their season debuts.

The question I haven’t answered is: What if you skip warmups altogether?  With the exception of exhibitions, that’s what Novak Djokovic is doing this year, along with several others.  Most notable from the list: Marin Cilic, who won in Chennai two years ago.  After that performance, he failed to get past the round of 16 in Melbourne.  Maybe this year, fresher legs will translate into a deeper run.

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Grand Slam Forecasting for Dummies

It’s one thing to predict a winner–it’s another thing to quantify how likely a player is to become that winner.

In most tennis tournaments, it’s not hard to pick a favorite.  For most of the last year, it was Novak Djokovic, no matter the surface or who he might face.  Before that, it was Federer on hard courts, Nadal on clay courts.  While every one likes to identify a dark horse, there’s rarely much debate at the top.

Given that agreement, though, what odds would you have placed on Novak Djokovic winning Wimbledon?  Or the French?  Or an in-form Federer winning the tour finals over an injured Djokovic and a tired Nadal?  Usually, my numbers spit out something between 20 and 30 percent–in theory, even the best player in the tournament has a better than two-thirds chance of going home a loser.

Intuitively, this is difficult to believe.  Djokovic seemed so dominant for much of the year that his slam victories felt like foregone conclusions.  Anyone who watched Novak on a good day found it impossible to imagine anyone outplaying him.  When Carl Bialik wrote a column asking whether Djokovic could keep up his dominance for the entire season, most responses were some variation of “What are you, stupid? Numbers are irrelevant when someone is so good.”

But, all good things must come to end, and a combination of injuries and good opponents proved that even Djokovic is human.

That said, Djokovic’s dominance–and Nadal’s before him, and Federer’s before him–raises questions about forecasting tennis matches.   The questions are complicated, but rest easy: today’s attempt at an answer will be simple.

Do the rules apply to the very best?

My ranking and forecasting system starts by assigning a number to every player, not unlike ATP ranking points.  To keep things simple, let’s use ranking points.  If we want to predict the outcome of, say, Mardy Fish against Feliciano Lopez, we take their point totals (2965 and 1755) and divide one by the sum of the others: 2965/(2965+1755) = 62.8%.  (It’s a little more complicated than that, but not much.)  Setting aside concerns like home court advantage and surface, that sounds about right to me.

Do the same with Djokovic and Lopez, and you get 88.6%.  Work the numbers with Djokovic and world #100 Michael Berrer, and you get 96.0%.  That’s pretty dominant, suggesting that Berrer would win only 1 in 25 matchups, but wait a minute–we’re saying Berrer’s going to beat Djokovic, ever?

And therein lies the problem.  The formulas I use to generate points and generate predictions are reasonably accurate, tested against years of ATP results.  And in the aggregate, individual match percentages pass the smell test.  But at the extremes, the numbers seem questionable.

And it is at the extremes where the exact percentages matter the most.  Consider my pre-tournament predictions for Wimbledon this year.  While Nadal was the top seed, I picked Djokovic as the favorite, giving him a 21.6% chance of winning.  But look at those first few rounds: I gave him only an 87% chance of getting past Jeremy Chardy (Jeremy Chardy!) in the first round, then only an 88% chance of beating Kevin Anderson or Ilya Marchenko, then only an 85% chance of winning against (probably) Marcos Baghdatis.

Only the last of those three numbers is plausible.  And when combined, they meant that I gave Djokovic less than a 65% chance of reaching the round of 16.  With all due respect to myself, that was almost as ridiculous then as it it sounds now.

It’s those early-round numbers that result in such minute chances that the favorite will win the tournament.  Even if we give a player a 90% chance of winning all his matches, he’ll still only win the seven consecutive matches required for a grand slam 48% of the time.  Lower it to 80%, and we’re down to 21% for the tournament.  Since the odds of winning a semifinal match against the likes of Murray, Federer, or Nadal is probably much lower, it seems that early round odds should be much more favorable.

To summarize, one of two things is going on here.  Either (1) my numbers underestimate the likelihood that the pre-tournament favorite wins a grand slam; or (2) our intuition overestimates the likelihood that the favorite takes home the trophy.

Forecasting for dummies

One way to pick between the two is to look at the recent past.  Are pre-tournament favorites winning more or less than expected?

For now, let’s set aside the question of the likelihood that Djokovic beats Chardy or Marchenko, and look only at winning the tournament.  We’re going to make two major assumptions here: (1) it’s possible to identify the pre-tournament favorite years later, and (2) favorites are generally created equal–Djokovic towers over his competitors to the same degree that Courier, or Lendl, or Sampras, or Federer towered over his.  As usual, both of these assumptions probably aren’t true, but they aren’t so hideously wrong that they’ll stop us from reaching some worthwhile conclusions.

There are three easy ways of picking the pre-tournament favorite for a grand slam: using (a) the winner of the last slam; (b) the defending champion, and (c) the top seed–almost always the world #1.  The top seed is probably best, while the defending champion might identify a player who is particularly good on the surface, and the winner of the last slam might pick out someone who is riding a hot streak.

The last 21 years (back to 1991, inclusive), give us 84 slams to work with.  Our sample is a bit smaller than that, because occasionally the winner of the last slam or the defending champion did not play, and on three occasions, the top seed pulled out before the tournament began.  Here is how the favorites did:

  • Of the 75 players who had won the previous slam, 18 (24%) won the tournament.
  • Of the 76 defending champions, 26 (34%) won the tournament.
  • Of the 81 top seeds, 29 (36%) won the tournament.  If we exclude the French (where the top seed is often #1 on the basis of hard court performance), we get a more dramatic result here–26 of 60 (43.3%) won the tournament.

All of these measures are much higher than the 21.6% shot I gave Djokovic at Wimbledon.  And most are higher than the 27-28% chances I gave him at the French and US Open.  The 43.3% likelihood that the top seed wins a hard-court slam (thank you, Pete and Roger!) suggests that a more sophisticated measure of identifying the favorite might allow us to predict slam champions with, say, 40% accuracy.

40% is considerably higher than my models are spitting out right now, but I suspect it is much lower than many fans imagine for their favorite.  It suggests that, at the extremes, my predictions aren’t quite one-sided enough.  It might take Michael Berrer more than 25 chances before he finally catches Djokovic on a bad day.

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Bernoulli and Court Tennis

As if you needed more proof that there’s nothing new under the sun.

Most of us are fairly new to the mathematical study of tennis.  It turns out that probabilistic analysis of tennis goes back almost as far as probability theory itself, to Jacob Bernoulli, a Swiss mathematician best known for the Law of Large Numbers.

In the late 17th century, Bernoulli wrote a Letter to a Friend on Sets in Court Tennis.  I haven’t given it a thorough reading yet, but for now, I have to share a line that ought to be the epigram to just about every work of statistical analysis in sport:

You cannot conceive, as you say, that one could measure the strengths of players with numbers, much less that one could draw from these numbers all the conclusions I have drawn.

Bernoulli was born, taught, and died in Basel, which must be why tennis is still so popular there today.

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Point-by-Point Profile: Jo-Wilfried Tsonga

Continuing with our point-by-point player profiles, let’s look at Jo-Wilfried Tsonga. If anyone from outside can break into the big four, he’s got to be on the short list after his big finish to the season.

Using all of his grand slam matches from 2011, we can begin to analyzes his tendencies on serve and return.

The first table shows the frequency of different outcomes in the deuce court, in the ad court, and on break point, relative to Tsonga’s average. For instance, the 0.974 in the upper left corner means that Tsonga wins 2.6% fewer points than average in the deuce court.

OUTCOME       Deuce     Ad  Break  
Point%        0.974  1.028  0.931  
                                   
Aces          1.005  0.994  0.718  
Svc Wnr       1.013  0.985  0.826  
Dbl Faults    1.082  0.909  0.758  
1st Sv In     1.017  0.981  0.955  
                                   
Server Wnr    0.884  1.127  0.986  
Server UE     1.030  0.967  1.140  
                                   
Return Wnr    1.054  0.941  1.567  
Returner Wnr  1.073  0.920  1.136  
Returner UE   0.887  1.124  1.026  
                                   
Rally Len     0.992  1.009  1.036  

Unlike all of the right-handers we’ve looked at so far, Tsonga wins more points in the ad court. He doesn’t win quite as many cheap points, as he hits a few more aces and service winners in the deuce court. But the end result is what matters, and it seems that he sets up the point better in the ad court, as shown by his high rate of winners in the rally, and his avoidance of return winners at any stage of the point.

Unfortunately for Jo-Willy, his success in the ad court doesn’t always transfer to break points. Winning 7% fewer service points than average on break points isn’t bad, but given the inherent advantage of his ad-court tendencies, it seems within reach for him to fight off a few more break points.

Next, this is how he performs on a point-by-point basis. Win% shows what percentage of points he wins at that score; Exp is how many he would be expected to win (given how he performs in each match), and Rate is the difference between the two. A rate above 1 means he plays better on those points; below 1 is worse.

SCORE   Pts   Win%    Exp  Rate  
g0-0    302  63.6%  66.6%  0.95  
g0-15   108  64.8%  65.3%  0.99  
g0-30    38  68.4%  62.9%  1.09  
g0-40    12  75.0%  58.8%  1.27  
                                 
g15-0   188  66.5%  67.4%  0.99  
g15-15  133  60.9%  66.2%  0.92  
g15-30   78  71.8%  65.7%  1.09  
g15-40   31  54.8%  63.2%  0.87  
                                 
g30-0   125  63.2%  68.2%  0.93  
g30-15  127  66.9%  66.5%  1.01  
g30-30   98  73.5%  65.5%  1.12  
g30-40   43  58.1%  62.9%  0.92  
                                 
g40-0    79  74.7%  68.8%  1.08  
g40-15  105  66.7%  67.7%  0.98  
g40-30  107  72.0%  66.8%  1.08  
g40-40  108  65.7%  65.7%  1.00  
                                 
g40-AD   37  75.7%  64.6%  1.17  
gAD-40   71  64.8%  66.3%  0.98  

As with so many other players, there is a gap in performance between logically equivalent points. 30-40 and 40-AD should be about the same; the only difference is that returners might be a little better at 30-40, having won 60% of points instead of 57% to get to the first 40-AD point. But while Tsonga dominated at 40-AD (admittedly with only 37 such points to draw on), one of his weakest points was 30-40. There’s a similar gap between 30-30 (another of his best) and 40-40 (precisely average).

Serving Against Tsonga

We can go through the same exercises for Tsonga’s return points. The next two tables are trickier to read. Look at them as Serving against Tsonga. Thus, the number in the upper-left corner means that when serving against him, players win 3.3% more points than average in the deuce court; he is a better returner in the ad court. That’s partly attributable to the fact that righties serve better in the deuce court, but while JW’s tendencies aren’t quite as extreme as David Ferrer’s, they are more than we would expect.

(I’ve excluded return points against lefty servers. Since lefties and righties have such different serving tendencies, limiting the sample to righty servers gives us clearer results, even as the sample shrinks a bit.)

OUTCOME       Deuce     Ad  Break  
Point%        1.033  0.963  0.896  
                                   
Aces          1.215  0.756  0.918  
Svc Wnr       1.079  0.911  0.809  
Dbl Faults    0.918  1.093  0.547  
1st Sv In     1.014  0.985  0.997  
                                   
Server Wnr    0.968  1.036  0.930  
Server UE     0.916  1.094  0.948  
                                   
Return Wnr    0.740  1.294  0.381  
Returner Wnr  0.892  1.123  1.466  
Returner UE   0.979  1.023  0.370  
                                   
Rally Len     0.971  1.033  1.136  

By just about every measure, Tsonga is a better returner in the ad court. He prevents aces and service winners at a high rate, hits plenty of winners at every stage of the point, and forces his opponent to try for more, leading to more double faults. That success follows him onto break points, where he is more conservative (very few return winners or unforced errors) but wins 10% more points than average.

Here’s more on Tsonga’s return game, again with numbers from the perspective of players serving against him.

SCORE   Pts   Win%    Exp  Rate  
g0-0    297  67.0%  65.1%  1.03  
g0-15    97  58.8%  64.6%  0.91  
g0-30    40  62.5%  64.4%  0.97  
g0-40    15  60.0%  64.1%  0.94  
                                 
g15-0   194  66.0%  65.4%  1.01  
g15-15  123  70.7%  64.4%  1.10  
g15-30   61  42.6%  63.6%  0.67  
g15-40   44  45.5%  63.5%  0.72  
                                 
g30-0   128  68.8%  66.0%  1.04  
g30-15  127  65.4%  65.0%  1.01  
g30-30   70  64.3%  64.2%  1.00  
g30-40   45  55.6%  63.8%  0.87  
                                 
g40-0    88  69.3%  66.6%  1.04  
g40-15  110  73.6%  65.4%  1.13  
g40-30   74  66.2%  64.5%  1.03  
g40-40   82  65.9%  63.8%  1.03  
                                 
g40-AD   28  53.6%  65.0%  0.82  
gAD-40   54  68.5%  63.2%  1.08  

Unfortunately, the sample sizes are getting a little small–Tsonga didn’t play as many grand slam matches as the big four, so it’s tough to do much analysis here. There is some evidence that he dominates more than expected once he gets ahead of the server, as seen in the rates at 15-30, 15-40, 30-40, and 40-AD. Tsonga seems to be a streaky player–anyone capable of reeling off several consecutive games against Federer on a hard court would need to be–and these numbers support that, at least in his return game.

Tsonga wraps up our point-by-point profiles. Because we only have point-by-point data for the grand slams, there just isn’t enough information to work with for players outside of the top six.

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Point-by-Point Profile: David Ferrer

Continuing with our point-by-point player profiles, let’s look at David Ferrer. He is firmly on the outside of the big four, but remains a threat, especially on clay.

Using all of his grand slam matches from 2011, we can begin to analyzes his tendencies on serve and return.

The first table shows the frequency of different outcomes in the deuce court, in the ad court, and on break point, relative to Ferrer’s average. For instance, the 1.014 in the upper left corner means that Ferrer wins 1.2% more points than average in the deuce court.

OUTCOME       Deuce     Ad  Break  
Point%        1.012  0.986  0.914  
                                   
Aces          1.018  0.980  0.940  
Svc Wnr       1.082  0.909  0.899  
Dbl Faults    0.993  1.008  0.256  
1st Sv In     0.991  1.010  0.983  
                                   
Server Wnr    0.945  1.061  0.855  
Server UE     0.988  1.013  1.012  
                                   
Return Wnr    0.909  1.102  0.490  
Returner Wnr  0.956  1.048  1.458  
Returner UE   0.938  1.069  0.898  
                                   
Rally Len     0.960  1.044  1.031  

Of all the players we’ve looked at so far, Ferrer has the smallest differences between serving in the deuce and ad courts. Double faults and first serve rate are almost exactly even. He also seems to have figured out how to guarantee a rally at break point, with virtually no double faults and almost as few return winners. It doesn’t translate into an impressive number of break points won, though.

Next, this is how he performs on a point-by-point basis. Win% shows what percentage of points he wins at that score; Exp is how many he would be expected to win (given how he performs in each match), and Rate is the difference between the two. A rate above 1 means he plays better on those points; below 1 is worse.

SCORE   Pts   Win%    Exp  Rate  
g0-0    279  72.0%  68.6%  1.05  
g0-15    76  57.9%  67.7%  0.86  
g0-30    32  50.0%  66.1%  0.76  
g0-40    16  50.0%  64.0%  0.78  
                                 
g15-0   200  77.0%  69.0%  1.12  
g15-15   90  68.9%  68.6%  1.00  
g15-30   44  65.9%  66.6%  0.99  
g15-40   23  65.2%  65.9%  0.99  
                                 
g30-0   154  66.9%  69.2%  0.97  
g30-15  113  68.1%  69.2%  0.98  
g30-30   65  67.7%  67.0%  1.01  
g30-40   36  66.7%  66.3%  1.01  
                                 
g40-0   103  67.0%  69.7%  0.96  
g40-15  111  69.4%  69.3%  1.00  
g40-30   78  61.5%  67.8%  0.91  
g40-40   98  69.4%  65.2%  1.06  
                                 
g40-AD   30  60.0%  64.0%  0.94  
gAD-40   68  61.8%  65.7%  0.94  

The sample sizes are small, but it’s still distressing to see Ferrer’s performance at 0-15, 0-30, and 0-40. Anecdotally, it seems that when shorter players don’t have their serve working for them, they can get broken in a hurry. Beyond that, there aren’t a lot of strong tendencies here; I’m sure Ferrer would like to win a few more points at AD-40, but that’s about all.

Serving Against Ferrer

We can go through the same exercises for Ferrer’s return points. The next two tables are trickier to read. Look at them as Serving against Ferrer. Thus, the number in the upper-left corner means that when serving against him, players win 4.7% more points than average in the deuce court; he is a better returner in the ad court. That’s partly attributable to the fact that righties serve better in the deuce court, but Ferrer’s tendencies are considerably more pronounced.

(I’ve excluded return points against lefty servers. Since lefties and righties have such different serving tendencies, limiting the sample to righty servers gives us clearer results, even as the sample shrinks a bit.)

OUTCOME       Deuce     Ad  Break  
Point%        1.047  0.948  0.910  
                                   
Aces          0.964  1.039  0.244  
Svc Wnr       1.102  0.888  0.762  
Dbl Faults    0.799  1.221  1.172  
1st Sv In     1.040  0.956  1.004  
                                   
Server Wnr    1.017  0.982  0.802  
Server UE     0.877  1.135  1.260  
                                   
Return Wnr    1.328  0.639  0.701  
Returner Wnr  1.084  0.908  1.029  
Returner UE   1.074  0.918  0.945  
                                   
Rally Len     0.959  1.046  1.168 

These are some confusing numbers. Ferrer wins more points in the ad court, more than would be expected against right-handed servers. It appears that his opponents know he is more dangerous returning in the ad court; they go for more on the first serve, double-faulting more oftne and landing fewer first serves. But Ferrer hits far more winners, both on the return and later in the point, in the deuce court. It may be that Ferrer’s ad-court return is good enough to set up the point in his favor, but rarely good enough to push the point to a quick conclusion.

Also of note is Ferrer’s returning on break point. Maybe it’s just a fluke; reducing aces to one-quarter of their usual rate is remarkable.

Here’s more on Ferrer’s return game, again with numbers from the perspective of players serving against him.

SCORE   Pts   Win%    Exp  Rate  
g0-0    273  58.6%  58.3%  1.01  
g0-15   113  59.3%  57.5%  1.03  
g0-30    46  56.5%  55.5%  1.02  
g0-40    20  65.0%  56.0%  1.16  
                                 
g15-0   158  53.8%  58.7%  0.92  
g15-15  140  63.6%  57.7%  1.10  
g15-30   77  50.6%  56.4%  0.90  
g15-40   51  54.9%  55.0%  1.00  
                                 
g30-0    85  63.5%  60.5%  1.05  
g30-15  120  61.7%  58.0%  1.06  
g30-30   85  52.9%  57.3%  0.92  
g30-40   68  51.5%  56.8%  0.91  
                                 
g40-0    54  59.3%  62.0%  0.96  
g40-15   96  64.6%  59.2%  1.09  
g40-30   79  57.0%  57.8%  0.99  
g40-40  143  58.0%  55.7%  1.04  
                                 
g40-AD   60  53.3%  54.9%  0.97  
gAD-40   83  49.4%  56.3%  0.88  

Unlike in his service game, Ferrer is more successful than expected at 40-AD and AD-40, winning more than half of return points at AD-40. He also excels at 15-30, 30-30, and 30-40, suggesting that he may be a bit streaky, returning well when he works himself into a hard-fought game.

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Point-by-Point Profile: Andy Murray

Continuing with our point-by-point player profiles, let’s look at Andy Murray. The Scot finished strong and performed up to expectations at the grand slams despite a dreadful stretch following the Australian Open.

Using all of his grand slam matches from 2011, we can begin to analyze his tendencies on serve and return.

The first table shows the frequency of different outcomes in the deuce court, in the ad court, and on break point, relative to Murray’s average. For instance, the 1.014 in the upper left corner means that Murray wins 1.7% more points than average in the deuce court.

OUTCOME       Deuce     Ad  Break  
Point%        1.017  0.981  1.020  
                                   
Aces          1.034  0.963  1.048  
Svc Wnr       1.036  0.960  1.043  
Dbl Faults    1.104  0.886  0.872  
1st Sv In     1.007  0.993  0.957  
                                   
Server Wnr    1.009  0.990  0.860  
Server UE     0.968  1.035  1.013  
                                   
Return Wnr    0.775  1.246  0.558  
Returner Wnr  1.019  0.979  1.012  
Returner UE   0.988  1.013  1.003  
                                   
Rally Len     1.015  0.984  1.037  

Like most righties, Murray is a little better in the deuce court. The substantial difference in return winners hints at a larger issue: When he serves cautiously, he serves very cautiously, leading to horrible second-serve results. That’s a topic for another day.

What’s remarkable about the above table, though, is Andy’s results serving against break point. Sure, 2% better than average doesn’t sound like much, but keep in mind that when fighting off breakers, he’s generally playing his best opponents. As we’ve seen, both Nadal and Federer perform serve more than 10% worse than average on break point for this reason; Murray bucks that trend, all the more remarkable because most break points are in the ad court.

Next, this is how he performs on a point-by-point basis. Win% shows what percentage of points he wins at that score; Exp is how many he would be expected to win (given how he performs in each match), and Rate is the difference between the two. A rate above 1 means he plays better on those points; below 1 is worse.

SCORE   Pts   Win%    Exp  Rate  
g0-0    398  66.6%  65.5%  1.02  
g0-15   131  58.8%  64.5%  0.91  
g0-30    54  61.1%  63.3%  0.97  
g0-40    21  66.7%  61.0%  1.09  
                                 
g15-0   262  62.2%  66.0%  0.94  
g15-15  176  68.2%  65.1%  1.05  
g15-30   89  65.2%  63.5%  1.03  
g15-40   45  66.7%  61.5%  1.08  
                                 
g30-0   163  69.9%  66.7%  1.05  
g30-15  169  60.4%  65.5%  0.92  
g30-30  125  64.0%  64.7%  0.99  
g30-40   75  65.3%  63.0%  1.04  
                                 
g40-0   114  64.9%  68.0%  0.96  
g40-15  142  66.2%  66.5%  1.00  
g40-30  128  72.7%  65.0%  1.12  
g40-40  148  60.8%  62.0%  0.98  
                                 
g40-AD   58  58.6%  59.6%  0.98  
gAD-40   90  66.7%  63.5%  1.05  

None of the numbers in this table are that extreme, but the overall picture they paint is of a player with better clutch serving abilities than Murray gets credit for. He serves better than expected at both 15-40 and 30-40, and he is barely below average at 30-30, 40-40, or 40-AD. According to these numbers, his game doesn’t change much according to the score–at least at the slams this year.

Serving Against Murray

We can go through the same exercises for Murray’s return points. The next two tables are trickier to read. Look at them as Serving against Murray. Thus, the number in the upper-left corner means that when serving against him, players win 1.5% more points than average in the deuce court; he is a better returner in the ad court. That’s mostly attributable to the fact that righties serve better in the deuce court, regardless of who is returning.

(I’ve excluded return points against lefty servers. Since lefties and righties have such different serving tendencies, limiting the sample to righty servers gives us clearer results, even as the sample shrinks a bit.)

OUTCOME       Deuce     Ad  Break  
Point%        1.015  0.984  0.977  
                                   
Aces          1.018  0.980  0.741  
Svc Wnr       0.993  1.008  0.979  
Dbl Faults    0.956  1.049  1.811  
1st Sv In     0.998  1.003  0.974  
                                   
Server Wnr    1.066  0.927  0.974  
Server UE     1.016  0.982  1.148  
                                   
Return Wnr    0.704  1.324  1.287  
Returner Wnr  0.885  1.126  0.883  
Returner UE   0.917  1.091  1.170  
                                   
Rally Len     0.999  1.001  0.920  

These numbers continue to challenge the conventional wisdom on Murray. What sticks out is the rally length on break points: 8% shorter than usual. I would have expected that Murray plays extremely cautiously in converting break points, but instead, he hits more return winners, makes more unforced errors, and keeps points shorter.

Here’s more on Murray’s return game, again with numbers from the perspective of players serving against him.

SCORE   Pts   Win%    Exp  Rate  
g0-0    388  59.8%  57.0%  1.05  
g0-15   152  52.0%  55.9%  0.93  
g0-30    73  49.3%  55.6%  0.89  
g0-40    37  51.4%  54.8%  0.94  
                                 
g15-0   231  60.6%  57.7%  1.05  
g15-15  170  53.5%  56.6%  0.95  
g15-30  115  54.8%  55.2%  0.99  
g15-40   71  53.5%  54.5%  0.98  
                                 
g30-0   140  57.9%  58.2%  0.99  
g30-15  150  60.0%  58.0%  1.04  
g30-30  123  56.1%  55.8%  1.01  
g30-40   92  56.5%  54.1%  1.04  
                                 
g40-0    81  56.8%  58.8%  0.97  
g40-15  125  59.2%  58.6%  1.01  
g40-30  120  50.0%  57.3%  0.87  
g40-40  209  56.5%  55.9%  1.01  
                                 
g40-AD   91  53.8%  54.8%  0.98  
gAD-40  118  59.3%  56.8%  1.05  

Murray’s results when returning at 40-30 are the only ones that really stick out. He returns much better than expected, winning exactly half of those points. He also appears to string together more streaks than expected at 0-15 and 0-30. Beyond that, he is fairly steady, much like Djokovic in the return game.

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Point-by-Point Profile: Roger Federer

Continuing with our point-by-point player profiles, let’s look at Roger Federer. Despite a down year, his service game remains one to be envied and emulated. His more conservative return game also provides a contrast to the styles of Djokovic and Nadal.

Using all of his grand slam matches from 2011, we can begin to analyze his tendencies on serve and return.

The first table shows the frequency of different outcomes in the deuce court, in the ad court, and on break point, relative to Federer’s average. For instance, the 1.014 in the upper left corner means that Fed wins 1.4% more points than average in the deuce court.

OUTCOME       Deuce     Ad  Break  
Point%        1.014  0.984  0.875  
                                   
Aces          1.107  0.883  0.738  
Svc Wnr       1.052  0.943  0.861  
Dbl Faults    1.019  0.979  0.453  
1st Sv In     1.030  0.967  0.872  
                                   
Server Wnr    0.989  1.012  0.845  
Server UE     0.941  1.065  1.405  
                                   
Return Wnr    1.109  0.880  0.877  
Returner Wnr  0.955  1.049  1.341  
Returner UE   0.974  1.028  1.020  
                                   
Rally Len     0.957  1.047  1.278  

For a big-serving right-hander, we might expect to see more success in the deuce court. Yet the difference isn’t that large, except in aces and service winners. Federer counterbalances his lack of aces in the ad court by preventing return winners.

Some of his break point tendencies are striking. As with most players, he wins fewer break points than average points (because opponents who push him to break point are better). He serves much more conservatively, particularly the second serve, which he almost never misses when down break point.

Next, this is how he performs on a point-by-point basis. Win% shows what percentage of points he wins at that score; Exp is how many he would be expected to win (given how he performs in each match), and Rate is the difference between the two. A rate above 1 means he plays better on those points; below 1 is worse.

SCORE   Pts   Win%    Exp  Rate  
g0-0    398  74.1%  71.0%  1.04  
g0-15   102  64.7%  68.0%  0.95  
g0-30    36  63.9%  66.9%  0.95  
g0-40    13  61.5%  66.6%  0.92  
                                 
g15-0   291  74.6%  72.1%  1.03  
g15-15  140  69.3%  70.1%  0.99  
g15-30   66  68.2%  68.0%  1.00  
g15-40   29  75.9%  67.3%  1.13  
                                 
g30-0   217  72.8%  72.3%  1.01  
g30-15  156  66.0%  70.9%  0.93  
g30-30   98  70.4%  68.7%  1.02  
g30-40   51  52.9%  68.1%  0.78  
                                 
g40-0   158  73.4%  72.7%  1.01  
g40-15  145  66.2%  71.4%  0.93  
g40-30  118  76.3%  69.7%  1.09  
g40-40   95  72.6%  68.6%  1.06  
                                 
g40-AD   26  53.8%  65.6%  0.82  
gAD-40   69  62.3%  69.8%  0.89  

You don’t have to watch Federer much to realize he likes his service games quick–and often, he has no problem putting another one on the board with only four or five serves. But when he fails to do that, his results aren’t very good.

His performance at both 40-AD and AD-40 might be a clue as to why he didn’t win a grand slam this year; in both cases, he should be winning between 65 and 70% of points, but he failed to do so by a large margin. (Though at 40-AD, the sample size is small enough to be discarded altogether.) The success rate at 30-40 is even worse. At least when he reached deuce, he performed better than average.

Serving Against Federer

We can go through the same exercises for Fed’s return points. The next two tables are trickier to read. Look at them as Serving against Federer. Thus, the number in the upper-left corner means that when serving against Roger, players win 1.9% more points than average in the deuce court; he is a better returner in the ad court.

(I’ve excluded return points against lefty servers. Since lefties and righties have such different serving tendencies, limiting the sample to righty servers gives us clearer results, even as the sample shrinks a bit.)

OUTCOME       Deuce     Ad  Break  
Point%        1.019  0.979  0.961  
                                   
Aces          1.073  0.920  0.772  
Svc Wnr       1.027  0.971  1.019  
Dbl Faults    0.912  1.097  0.525  
1st Sv In     1.030  0.967  1.006  
                                   
Server Wnr    1.079  0.914  0.630  
Server UE     0.945  1.060  1.046  
                                   
Return Wnr    1.003  0.997  0.393  
Returner Wnr  1.022  0.976  0.988  
Returner UE   0.954  1.050  1.085  
                                   
Rally Len     0.969  1.034  1.095  

What sticks out here is Roger’s dearth of return winners on break point. He often seems to be an aggressive player–sometimes even too aggressive, but apparently he doesn’t do a lot with his first shot. Considered in light of “The Shot” that Djokovic scored against him, it provides another window into the small differences that kept Federer from winning the biggest matches this year.

Here’s more on Federer’s return game, again with numbers from the perspective of players serving against him.

SCORE   Pts   Win%    Exp  Rate  
g0-0    387  57.9%  58.8%  0.98  
g0-15   161  57.8%  56.9%  1.02  
g0-30    68  51.5%  56.4%  0.91  
g0-40    33  66.7%  55.3%  1.20  
                                 
g15-0   221  57.9%  60.1%  0.96  
g15-15  186  62.9%  57.8%  1.09  
g15-30  104  55.8%  56.4%  0.99  
g15-40   68  61.8%  55.1%  1.12  
                                 
g30-0   128  58.6%  61.4%  0.96  
g30-15  170  59.4%  59.6%  1.00  
g30-30  127  66.9%  57.5%  1.16  
g30-40   84  54.8%  55.5%  0.99  
                                 
g40-0    75  61.3%  61.7%  0.99  
g40-15  130  60.0%  60.9%  0.99  
g40-30  137  59.1%  58.7%  1.01  
g40-40  201  53.2%  56.4%  0.94  
                                 
g40-AD   94  52.1%  55.4%  0.94  
gAD-40  107  53.3%  57.3%  0.93  

Apparently Fed returns under pressure better than he serves under pressure. He wins more points than expected when returning at both 40-AD and AD-40. Oddly, he had a tough time when returning at 30-30 but considerably more success at deuce.

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Point-by-Point Profile: Rafael Nadal

Moving on with our point-by-point player profiles, let’s look at Rafael Nadal. Perhaps more than anyone else on tour, he is one of a kind, exhibiting many tendencies that reflect his left-handedness, but not consistently so.

Using all of his grand slam matches from 2011, we can begin to quantify those tendencies.

The first table shows the frequency of different outcomes in the deuce court, in the ad court, and on break point, relative to Nadal’s average. For instance, the 0.990 in the upper left corner means that Djokovic wins 1.0% fewer points than average in the deuce court.

OUTCOME       Deuce     Ad  Break  
Point%        0.990  1.011  0.849  
                                   
Aces          0.875  1.139  0.884  
Svc Wnr       0.998  1.002  0.792  
Dbl Faults    1.076  0.916  1.421  
1st Sv In     0.980  1.022  1.011  
                                   
Server Wnr    0.942  1.064  1.057  
Server UE     1.028  0.969  1.119  
                                   
Return Wnr    0.771  1.254  1.038  
Returner Wnr  0.986  1.015  1.571  
Returner UE   1.006  0.993  0.950  
                                   
Rally Len     1.017  0.981  1.172  

There are plenty of differences between his deuce and ad-court performance, but they aren’t consistent. He hits far more aces in the ad court, but also allows way more return winners. The safest conclusion seems to be that his ad-court serving generates a different, more explosive kind of tennis. In the deuce court, he hits fewer aces, more second serves, fewer winners..but allows his opponent fewer winners. It’s almost as if he plays clay-court tennis in the deuce court and hard-court tennis in the ad court.

The break point tendencies are even more marked. These points generally go longer (17% longer rallies), which would seem to work in Nadal’s favor, but he doesn’t win points at anywhere near his average rate. To some extent, this is because his break points come against better players, but his break point numbers are generally much worse than Djokovic’s.

Next, this is how he performs on a point-by-point basis. Win% shows what percentage of points he wins at that score; Exp is how many he would be expected to win (given how he performs in each match), and Rate is the difference between the two. A rate above 1 means he plays better on those points; below 1 is worse.

SCORE   Pts   Win%    Exp  Rate  
g0-0    377  67.9%  67.2%  1.01  
g0-15   118  65.3%  64.8%  1.01  
g0-30    41  58.5%  61.8%  0.95  
g0-40    17  70.6%  61.0%  1.16  
                                 
g15-0   252  68.7%  68.3%  1.01  
g15-15  156  63.5%  66.5%  0.95  
g15-30   81  60.5%  64.0%  0.94  
g15-40   44  54.5%  62.0%  0.88  
                                 
g30-0   173  69.4%  69.1%  1.00  
g30-15  152  67.8%  67.5%  1.00  
g30-30   98  66.3%  65.4%  1.01  
g30-40   57  57.9%  63.4%  0.91  
                                 
g40-0   120  71.7%  69.8%  1.03  
g40-15  137  67.2%  68.1%  0.99  
g40-30  110  74.5%  67.0%  1.11  
g40-40  143  59.4%  60.9%  0.98  
                                 
g40-AD   58  72.4%  57.9%  1.25  
gAD-40   85  52.9%  62.9%  0.84  

From the past season, the lingering image I have of Rafa is of him fighting off a slew of break points. That is in evidence at 40-AD, where he wins a staggering 72.4% of points. That’s just remarkable: his 40-AD points come against his best opponents, and he performs considerably better at that score than he does at the logically equivalent 30-40.

But 40-AD is the exception. At almost every other crucial score, when Nadal is playing from behind, he plays worse than expected. 15-40 is the most marked, where he wins only 54.5% of points compared to the 62.0% of points he “should” win. Also worrisome is his performance at AD-40; it seems that Nadal is the best in the game when it comes to getting the score back to deuce.

Serving Against Nadal

We can go through the same exercises for Nadal’s return points. The next two tables are trickier to read. Look at them as Serving against Nadal. Thus, the number in the upper-left corner means that when serving against Nadal, players win 1.3% more points than average in the deuce court; Nadal is a better returner in the ad court.

(I’ve excluded return points against lefty servers. Since lefties and righties have such different serving tendencies, limiting the sample to righty servers gives us clearer results, even as the sample shrinks a bit.)

OUTCOME       Deuce     Ad  Break  
Point%        1.013  0.986  1.009  
                                   
Aces          1.150  0.837  0.994  
Svc Wnr       1.098  0.894  0.909  
Dbl Faults    0.860  1.152  0.998  
1st Sv In     1.008  0.991  1.004  
                                   
Server Wnr    1.040  0.956  0.946  
Server UE     0.994  1.006  0.935  
                                   
Return Wnr    0.791  1.227  0.874  
Returner Wnr  0.925  1.082  1.254  
Returner UE   0.918  1.090  1.073  
                                   
Rally Len     1.006  0.993  1.031  

As we might expect, Nadal is a monster returner in the ad court–and servers know it. Righties serve better in the deuce court, but not this much better; Nadal wins 16% more points than average when returning in the deuce court. His opponents help him out, double-faulting at a much higher rate when serving to Rafa’s forehand.

On break point, Nadal isn’t quite so dominant in shutting down the service game, but he does generate a lot more winners later in the point.

Here’s more on Nadal’s return game, again with numbers from the perspective of players serving against him.

SCORE   Pts   Win%    Exp  Rate  
g0-0    380  57.4%  57.2%  1.00  
g0-15   158  50.0%  55.5%  0.90  
g0-30    79  50.6%  54.6%  0.93  
g0-40    39  61.5%  53.6%  1.15  
                                 
g15-0   216  57.9%  58.5%  0.99  
g15-15  170  52.9%  56.6%  0.93  
g15-30  120  54.2%  55.5%  0.98  
g15-40   79  62.0%  52.9%  1.17  
                                 
g30-0   125  61.6%  59.7%  1.03  
g30-15  138  58.0%  57.8%  1.00  
g30-30  123  57.7%  57.5%  1.00  
g30-40  101  50.5%  56.6%  0.89  
                                 
g40-0    77  63.6%  60.7%  1.05  
g40-15  108  60.2%  59.2%  1.02  
g40-30  114  69.3%  57.4%  1.21  
g40-40  160  57.5%  55.9%  1.03  
                                 
g40-AD   68  47.1%  55.7%  0.85  
gAD-40   92  54.3%  56.0%  0.97  

Once again, Nadal loves 40-AD. This time, it’s his chance to convert a break point, and he does so at an alarming rate. And in the return game, he performs nearly as well at 30-40. At 40-AD, he wins more than half of points, a far better performance that we would expect, given the quality of his opponents and his performance on other points against the same players.

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What Does the “Hot Hand” Mean in Tennis?

In sports analytics, the topic of streakiness–the “hot hand“–is a popular one. Nearly everyone believes it exists, that players (or even teams) can go on a hot or cold streak, during which they temporarily play above or below their true level.

To a certain extent, streakiness is inevitable–if you flip a coin 100 times, you’ll see segments of 5 or 10 flips in which most of the flips are heads. That’s not because the coin suddenly got “better,” it’s a natural occurence over a long enough time span. So if you watch an entire tennis match, there are bound to be games where one player seems to be performing better than usual, perhaps stringing together several aces or exceptional winners.

The question, then, is whether a player is more streaky than would occur purely at random. To take just one example, let’s say a player hits aces on 10% of service points. If he did occasionally serve better than usual, we would observe that after he hits one ace, he is more likely (say, 15% or 20%) to hit another ace. A missed first or second serve might make it more likely than he misses his next try.

My last couple of topics–differences in the deuce/ad court, and the “reverse hot hand” at 30-40–have hinted that tennis may be structured in a way that prevents players from getting hot.

One of the most popular subjects for hot hand research is basketball free throw shooting. Researchers like it because it’s as close as basketball players get to a laboratory: every shot is from the same distance, there’s no defensive quality to consider, and even better, players usually get two tries, one right after the other. There’s nothing like it in tennis.

The one thing that seems a bit akin to free throw shooting is serving, especially for more dominant players. John Isner, Roger Federer, and Milos Raonic seem to go on serving streaks; certainly they can play game after game and control play with unreturnable serving. But when we look closer, their experience is much more nuanced. As we’ve seen, players generally are better in the deuce or ad court. It would be as if basketball player shot one free throw, then took two steps to the left and one step forward before attempting his next shot.

And, of course, there’s another player on the court. If Federer uses a relatively slow serve out wide in the deuce court for a service winner at 15-15, he is much less likely to use the same tactic at 30-30 or 40-15. Even if he was capable of hitting 50 perfect serves of that nature, he would never do so in a match. If it has any relevance for professional tennis, the hot hand must refer to something broader than a single skill.

On a more general level, the rules of tennis involve alternation more than more sports. Sure, most sports give the ball to the other team after a goal, but the length of possession–or in baseball, the length of an inning–can vary widely. In tennis, you can only add one game to your tally before handing the ball to your opponent. And even within that game, you are constantly moving from your stronger court to your weaker court; your opponent might be doing the same.

My question to you is this: If there is a hot hand in tennis, where would you expect to find it? Consecutive aces? Aces specifically in the deuce court? Service winners? Short service points? Points won? Return points won? Games won? First serves in? Point-ending winners? Avoidance of unforced errors? It’s possible that any or all of these things could occur in bunches, but which of them would indicate what we think of as a tennis player on a hot streak?

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