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.

Are Free Agents Worth the Money? (Plot of the Week 9)

This week I created a few plots to look at the effect of major MLB and NBA free agent players switching teams.

First, I wanted to see if players tended to move to teams with a better chance at winning a championship (think LeBron James), or if they moved to worse teams that would pay them more money (Albert Pujols who left after winning a championship with the Cardinals).  The first plot shows the regular-season team winning percentage for the three years before the player switched teams (old team) and three years after switching to a new team.

Note: Since some players recently switched teams (LeBron, Bosh, Pujols, Fielder), we don't have a full 3 years of data to look at.

1. Teams that win championships are denoted by small squares.  LeBron and Bosh are the only players to win a championship within 3 years of switching teams.  Pujols was the only player to switch teams after winning a championship within the past 3 years.
2. For this small sample size, it looks like basketball players (dashed lines) that switched teams moved to better teams, where baseball players received a lot of money to move to teams that had roughly equivalent records.

Next, let's look at the winning percentage of teams before and after signing a big free agent (i.e, the Heat before and after LeBron).  The thought is that spending all of this money to sign a marquee player will help the team win more.

1. Basketball players have an immediate effect on increasing the win percentage.
2. Baseball teams seem to have a worse record in the year immediately after signing a big free agent.  None of the baseball players brought a championship to their new team within 3 years.
3. This shows that it is worth trying to sign big name basketball free agents.  However, baseball free agents don't seem to be worth the big bucks in terms of immediately winning more games.
4. One could argue that it makes economical sense to sign big name free agents (increased ticket sales, marketing, etc.) even if they don't increase winning percentage.

Finally, I wanted to look at the winning percentage of the teams that lose a free agent (i.e., the Cavaliers before and after LeBron).

1. Again, we see that basketball stars have a huge effect on their team.  Every team had a much lower winning percentage after losing a key free agent.  But the teams seem to recover within a few years, presumably because they are able to rebuild quickly through the draft.
2. Baseball teams do not suffer the same losses after losing a key free agent.  In fact, some teams have a huge increase in win percentage immediately after losing they player.  This includes the 2003 Chicago White Sox who won the World Series the year after Magglio Ordonez left for the Tigers. 
3. The effects of losing a key player may have a longer-lasting impact, with win percentage decreasing 2 and 3 years after losing a free agent.

Overall conclusion: Baseball players don't have as large an impact on win percentage as basketball players.  Thus, they probably don't deserve the huge contracts they are earning.

One caveat about this analysis is that the sample size is very small.  I have limited the analysis to players who sign huge free agent contracts with another team, and exclude players who were traded.  I would love to add more players to this analysis, so leave a comment if you can think of a player who you would like to see included.