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.
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