Why Roger Federer (and the entire women's tour) should never hit a second serve

In the 2012 Wimbledon Men's Championship match, Roger Federer beat Andy Murray to win his record tying 7th Wimbledon title and record 17th major overall.  But it was a rough start for Federer, as he lost the first set, which included losing his first 7 second serve points (he won 3/11 overall in the first set).  Federer was having a much easier time with his first serve (as do most players), winning 65% of the points when he made his first serve.  This got me thinking ... does it ever make strategical sense for a player to never hit a slower second serve but always hit a first serve?  The answer may surprise you (although I guess I give it away in the title).

I went through several matches for both men and women at this year's Wimbledon.  Let's use the men's final as an example.  Over the whole match, Federer made his first serve 68.7% of the time, winning 75.6% of those first serve points.  Multiplying these two numbers together, we see that 51.9% of time time Federer made his first serve and won the point (conversely, 48.1% of the time he either made his first serve and lost the point or had to hit a second serve).  Federer won 48.8% of the points when he hit a second serve.  This shows that Federer would have been better off going for his first serve even when hitting a second serve, as he would be expected to win an additional 3.1% (51.9 - 48.8) of second serve points. Federer hit 41 second serves, so he would expect to win an additional (41)*(3.1%) = 1.3 points in the match had he not hit his regular second serve.  This doesn't sound like much, especially since Federer won the match, but it could translate to winning an additional game.

One drawback of only hitting first serves is an increased number of double faults.  Because Federer made 68.7% of his first serves, we would expect him to miss his first serve 31.3% of the time.  If we consider two serves as independent events, the probability that he would miss two in a row and double fault is (31.3%)(31.3%) = 9.8%, resulting in an expected 12.8 double faults (he served 131 points in the match), much higher than the 3 double faults he actually served.  But he would have also been expected to serve an additional 3.75 aces (work not shown, but trust me).  So this turn out to a net decrease of (12.8 expected double faults) - (3 actual df's) - (3.75 additional aces) = 6.05 points.  How can this make sense if I just said that we expect Federer to win a net of 1.3 additional points?  When he does make his first serve, he wins a much higher percentage of those points compared to second serve points (75.6% to 48.8%) that it more than makes up for the double faults.  In other words, the risk of only hitting first serves pays off for Roger Federer.

I decided to look at all men's matches starting with the 4th round of Wimbledon.  Of the 30 matches (or 60 players, some counted more than once), 10 of the players would have expected to benefit by only hitting first serves.  Roger Federer was the only player to show up twice on the list (Finals and QF matches).  Of these 10, 7 lost the match (Federer won both matches and Djokovic won his QF).  In 3 of Andy Murray's 4 matches that I looked at, his opponent would have been better off only hitting first serves (Federer, Tsonga and Cilic), showing how great of a returner Murray is (the other opponent was Ferrer, who doesn't have a big first serve).  The largest expected gain was for Tsonga, who could have expected to win an additional 7.7 points (2 games) against Murray in the semis.

I wanted to look a little more closely at how this strategy may impact the match.  My original thought was that a player probably loses a set when he is serving poorly, so only hitting first serves would result in a lot more double faults and a net loss of points.  I was surprised to see that this was not the case.  Looking at the QF through the Finals, players lost 26 sets.  In 10 of these 26 sets, the player who lost the set would have expected to win more points by serving only first serves.  This definitely supports players only hitting first serves when they lose the set, but I guess this doesn't help much retrospectively.

Looking at sets won, for 19 of 26 sets, the winner would have expected to lose more points by only hitting first serves.  However, only 10 of those 19 would be expected to lose more than 2 points.  Interestingly, Federer could have won more points in 3 of the 9 sets he won by only hitting first serves and never would have expected to lose an additional 2.5 points in the 9 sets that he won.  This shows how great his first serve was working during the Championships.

The players are back at Wimbledon for the next 2 weeks, but this time trying to win an Olympic medal.  My recommendations would be for Federer to only hit first serves, but he is probably the only male player I would recommend this to regardless of opponent.  Plus, this may have the added benefit of screwing up the opponent's game plan.  I would also suggest that all of Andy Murray's opponents to employ this strategy.  But as I said before, no coach will tell their player to use this strategy.  My guess is that this is due to aesthetic reasons - no coach wants to see his player double fault in the double digits even if he would win more points in the long run.

I also performed the same analysis for the women.  To keep things short, every women player should only hit first serves.  Of the final 7 matches (14 players) that I looked at, only 5 players would not have benefited by this strategy.  In fact, 4 of those 5 players who would not have benefited lost the match anyway (the only exception being Serena Williams in the SF).  On average, the women would expect to win an additional 1.1 points per match.  Compare this to the men, who on average would expect to lose an additional 2.5 points.

Will any players employ this strategy at the Olympics?  I'm guessing not.

Wimbledon 2012 wrap-up

Sorry for the long delay in posting - I'm still alive, but have been extremely busy with the new job.  I have also decided to spend more time on "novel" posts where I analyze the data myself to answer new questions, as these seem to get a much better response from readers.  But these posts take more time to write, so I will not be posting as often.  I am finishing up a new analysis with some data from Wimbledon, and I hope to blog about this soon.  For now, I want to give a quick update on my Wimbledon picks (you can read about my picks here).

First the good news: I correctly picked Serena Williams.  The bad news: I picked Novak Djokovic, but he lost to eventual champion Roger Federer.  So I went 1/2, or 3/4 when combining my 2 correct French Open Picks.  When looking at the ESPN expert picks over these past 2 grand slams, only Chris Evert has correctly picked all 4 champions.

Let's hope I can keep up the steam going into the US Open in August/September.

Wimbledon Picks 2012 (Explanation)

With the first week of Wimbledon now a thing of the past, I figured I should actually give my reasoning for my Wimbledon picks.

First, I went with my gut (over data because I didn't have the time) when picking the men's and women's sleepers - players outside the top 10 to go the furthest.  I picked John Isner and Venus Williams who both lost first round.  Guess I shouldn't listen to my gut feeling when making picks anymore.

So let's get to the picks that I actually put some thought into.  I only looked at one stat when choosing my women's champion.  Here are the results of the Williams sisters (both singles and doubles) at Wimbledon since 2000.

Williams Sisters Wimbledon Results 

Year	Doubles Result	Venus Singles	Serena Singles
2000	WON	WON	SF
2001	3RD	WON	QF
2002	WON	RUP	WON
2003	3RD	RUP	WON
2004	-	2RD	RUP
2005	-	WON	3RD
2006	-	3RD	-
2007	2RD	WON	QF
2008	WON	WON	RUP
2009	WON	RUP	WON
2010	QF	QF	WON
2011	-	4RD	4RD

Since 2000, every year that the Williams sisters have played doubles at Wimbledon (highlighted), one of them also wins the singles title (8/8, with both Williams reaching the Final 4 times).  Notice that it doesn't matter how they perform in the doubles, as long as they are playing.  The 4 years that the Williams did not play doubles, often due to one sister being injured, only once did one of them win the singles title (Venus in 2005).  

Serena and Venus entered to play doubles this year (they are currently in the 2nd round).  Looking at past results, the probability that a Williams wins the single title given they play doubles is 1.  So all I had to do was choose between Serena or Venus winning.  I went with Serena because she is the higher ranked and Venus is coming back from injuries.  As of this post, Serena has won her first 3 singles matches and is still alive.

For the men's, I looked at the winner's seed and previous year's performance since 2003 (Federer's first Wimbledon win).

Men's Wimbledon Champions 

Year	Winner	Seed	Previous Result
2003	Roger Federer	4	1st
2004	Roger Federer	1	WON
2005	Roger Federer	1	WON
2006	Roger Federer	1	WON
2007	Roger Federer	1	WON
2008	Rafael Nadal	2	RUP
2009	Roger Federer	2*	RUP
2010	Rafael Nadal	2	-
2011	Novak Djokovic	2	SF

* Federer was the 2 seed, but he was technically the top seed after Nadal withdrew as the number 1 seed with injury before the 2009 tournament began.

Because Federer, Nadal and Djokovic have won 28 of the last 29 major titles, I have eliminated the rest of the field.  I eliminated Federer because it has been one of the top 2 seeds to win every year since 2004.  I went with Djokovic over Nadal because the defending champion has won 6 of the last 9 years (if I consider Federer the defending champ in 2009 since Nadal withdrew and Nadal the defending champ in 2010 since he had not defended his title.**)  Also, Federer and Nadal each defended their first Wimbledon title by winning the following year that they played.  This gives me belief that Djokovic will continue this trend and win his second straight Wimbledon title.  

My men's pick is looking even better after Nadal lost in the second round.  (Still, I'll be cheering for Roger Federer to win the title as he is my favorite player.)

** Under this argument, both Federer and Nadal would have been considered defending champions in 2010, so you could change the fraction to 6/10 defending champs winning. 

Wimbledon 2012 predictions

Wimbledon starts on Monday and I wanted to announce my picks (I was 2/2 for the French Open).  

I am going to follow ESPN's format for their picks (which you can see here):

Men's winner: Novak Djokovic

Men's sleeper (someone outside of the top 10 to go the furthest): John Isner

Men's toughest road (top 10 player to lose earliest): Janko Tipsarevic

Women's winner: Serena Williams

Women's sleeper: Venus Williams

Women's toughest road: Samantha Stosur

Things are very busy for me, so I do not have the time to justify my picks right now - but I hope to later in the week.