In every tennis match, the strategizing begins before a single tennis ball is hit. A coin toss is held before the match, and the winner is given the choice between serving first or returning first.* There are more options, but most people choose to choose between serve and return. See http://www.usta.com/Improve-Your-Game/Rules/Serving-and-Receiving/Winning_the_toss/ for more detail.
Most players choose to serve first because it gives them control of the first game of the match. There is, however, one major exception - Rafael Nadal, one of the most superstitious players in the ATP World Tour, always chooses to return first, regardless of whether he is playing a qualifier or a top 10 player.
In the 2009 Madrid Masters final, Federer took advantage of Nadal’s habit of returning serve by choosing to return first after winning the coin toss, forcing Nadal to serve first. Federer went on to win the match 6-4, 6-4.
Superstition aside, does serving first in a match really affect the chances of winning the match? It also begs the question, does serving first in a set substantially affect the chances of winning the set? Using point-by-point statistics of every match in Grand Slam tournaments from 2011 to the present, we compare the probability of player winning when they serve first versus when they return first. We also conduct hypothesis tests to determine whether serving or returning first significantly affects the chances of winning the set or the match.
Data Analysis Process
Our point-by-point statistics included over 500 players who had played in any of the four Grand Slam tournaments from 2011 to the present. For the top 20-ranked ATP tour players, we plotted their probability of winning a match when returning first versus their probability of winning a match when serving first.
We see a couple interesting observations:
- As expected, most players have a higher probability of winning the match if they serve first. As players win around 70% of their service points, serving first tends to give them a slight lead throughout the set and the psychological upper hand.
- Heavy-servers such as Kevin Anderson, Feliciano Lopez, and Milos Raonic have a higher probability of winning a match if they serve first. Gael Monfils and Gilles Simon, who are known to be good returners, have a higher probability of winning given that they return first. These players tend to put pressure on the person who serves first by initiating long rallies from the outset.
- Rafael Nadal, who prefers to return first, actually has a higher match-win probability if he serves first. Perhaps he should change his coin-toss strategy and take the first serve more often. Similarly surprising is John Isner, who wins more often when returning first even though he has one of the best serves on tour. Andy Murray, known to be a strong returner, actually wins more often when he serves first.
We also plotted, for the top 20 ATP players, the probability of winning a set given that they serve first and given that they return first.
We notice that:
- The majority of players actually have a better probability of winning a set given that they return first. This is because winning one set usually means returning first the next set, since most sets are won by holding serve, not by a service break in the last game. Consequently, in each match, the person returning first in a set more often is likely to be the stronger player, and is more likely to win the set. Thus, the results we see above are mostly circumstantial. Looking at probability of winning given that a player serves first is more useful for matches than for sets, because players do not have a lot of control over who serves first in a set, causing the result that we see in this graph.
- Notable exceptions: Kei Nishikori does better in a set when serving first than when returning first, even though he is known to be a good returner. Rafael Nadal, again, does better when serving first than when returning first. This may be because regardless of the effect discussed above, Nadal and Nishikori still do just as well when serving first in a set against top players as they do when returning against weaker players.
We then analyzed the difference between win probability given serving first versus returning first using hypothesis tests. We found that the difference was not as extreme in both the match and the set case for all players as for the top 20 players, but for all scenarios, the results were statistically significant.