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Players risk defeat by going for safe second serves

You're tied at one set apiece, five games all, at deuce. You're a right-handed player serving to your righty opponent. You've missed your first serve. Do you hit your second serve down the T, at your opponent's weaker backhand, or do you risk serving out wide to the forehand?

Tennis players are athletes and shot-makers -- but also decision-makers. Hundreds of times during each match, they decide where, when and how to hit the ball. Whether they win a match is determined in large part by how good those decisions are.

At least a dozen times in a typical match, each player must decide where to hit second serves. When facing right-handers, a serve down the T goes to the opponent's backhand, usually the less dangerous wing; a serve out wide goes to the more lethal forehand. Common sense suggests hitting more often down the T. But the stats show players are hitting down the T too often. That can make the tactic predictable, which can render it less effective than the less-frequent serve out wide.

The effect is small but persistent. At recent Grand Slam tournaments -- going back to Wimbledon 2014 -- men typically win 57 percent of the time when serving down the T and 60 percent out wide. (Sticking, as I will throughout this article, to righties serving to righties, second serve, deuce court.) Women typically win 51 percent of the time when they serve down the T and 56 percent out wide. Second serves are just one of many types of shots in a match, and where players hit them is just one variable. Where opponents return them, for instance, also matters, as Roger Federer has shown lately. If players adjusted their mix of serve locations, it could win them a point or two more each match. That's not much, but that point could be a break point -- or a match point.

I first noticed this effect when working with David Flatow, a data-science graduate student at Stanford University, to seek patterns in a remarkable tennis data-collection effort called the Match Charting Project. More than 50 people collectively have charted more than 1,100 matches, marking the location of every shot from the serve to the point-ending stroke. Flatow and I went looking for tendencies and patterns: Where do players hit the ball, and what happens next?

The second-serve disparity was striking. Players went down the T more but won more when they went out wide. That effect held no matter the surface, no matter whether it was a men's match or a women's. And it accounted for all second-serve attempts, whether they went in or not. Including the misses, going out wide works more often.

To double-check, we looked at an independent data source: the official stats from Grand Slams, kept by scorers trained to track every shot. Flatow helped pull the data for some recent events, and I copied some manually myself. The results were largely consistent: more serves down the T but better results when serving out wide. For men and women in each of the past six Slams, serving out wide was the better strategy in every case but one: for men at the 2014 US Open.

The science of sports strategy suggests players aren't choosing where to serve optimally. The answer isn't to always hit the serve that wins points more often. That would become entirely predictable, and that serve would no longer win you the point as often. In other words, the proportion of the time you hit a serve affects how likely it is to be successful. So the answer is more complicated. It lies in a branch of economics called game theory, which can tell us how competitors should choose among alternative strategies -- tennis serves, say, or penalty kicks in soccer.

If your T serve is better than your wide serve, hit the T serve more. But don't hit it 100 percent of the time because if you do, your opponent knows you'll hit it and can stand in the middle of the court waiting for it instead of guarding against the wide serve. So how often should you hit it? Exactly as often as it takes to make it just as successful, but no more, than when you hit a wide serve. If your success rates on different choices are different, you're not serving optimally.

In any given match, you might not get this mix right. Perhaps your wide serve is off today, or your returner's backhand is better than you expected, or random chance and luck -- such as a few bad bounces off the net cord -- skew the results. But over a large set of matches, you'd expect these effects would even out -- that half the time the T serve was more successful and half the time the wide serve was. Instead, when we looked at more than 600 men's and women's singles matches from recent Grand Slams -- more than 1,200 servers in all -- we found that 55 percent of the time, the server won a higher percentage of points out wide than down the T. If servers really were choosing between their options optimally, you'd expect a percentage at least that high less than one in 10,000 times.

We don't yet have enough data on individual players to be sure how smart they are about choosing serve spots. But we have some hints. Take, for instance, the matchup between No. 1 Novak Djokovic and No. 2 Roger Federer, both right-handers. Our amateur match charters have analyzed 11 of their 42 career matches, as well as dozens of matches each man played against opponents other than each other. Djokovic is unusually successful serving down the T in the deuce court to Federer's backhand, and he uses that serve far more often against Federer than he does against other opponents.

Federer is much more successful serving out wide to Djokovic's forehand than he is when serving to Djokovic's backhand -- but he uses that serve no more often against his archrival than he does against other opponents. Whomever he's playing, Federer serves down the T far more often than out wide -- but he is more successful when going out wide.

So why do players insist on serving down the T so much? Perhaps because even though they lose more often, they lose less painfully. When returners get a look at a forehand, they swing away. And they hit more return winners -- at least twice as many -- but also more errors, forced and unforced. Points are over faster, and the returner often gets to decide how the point ends.

That's consistent with a 2010 study of pro tennis, which found "that at crucial junctures of the match, both men and women adopt a more conservative and less-aggressive playing strategy."

I asked the author, economist M. Daniele Paserman of Boston University, what he made of the serve finding. He said it was consistent with what he found and with the concept of omission bias in psychology: "Errors of omission are considered to be less severe than errors of commission."

In other words, in tennis and in life, you're judged less harshly by others, and by yourself, if you err by not doing something rather than if you err by doing something. Go for a second serve out wide but hit it too softly or too centrally or with too little kick, and your opponent rips a forehand winner. That could feel like your mistake. But hit a second serve down the T that your opponent is expecting so she neutralizes the point quickly, then wins it after a long rally, and your choice of serve seems less tied to the bad outcome. You lost, but it's not your fault.

Players grow comfortable sticking to the familiar tactic. After Gilles Simon upset Tomas Berdych at Wimbledon while hitting almost no deuce-court second serves out wide -- just as he did in his three prior matches -- I asked the Frenchman if the serve down the T is his favorite one to hit.

"I'm just worrying it can become predictable and my opponent will use it, but I hope that they are not," Simon said. "I have no reason to change."

He didn't in his next match, hitting 15 second serves in the deuce court down the T to Roger Federer and none out wide -- and lost in straight sets. (That his opponent was Federer probably hurt Simon more than his mix of second serves did.)

Players such as Simon who hardly use the serve out wide wouldn't know if they have any reason to change because they haven't tried the tactic enough to know if it'd be more successful. But on the same day Simon eschewed the tactic, Andy Murray used it 11 times against 6-foot-10 Ivo Karlovic -- and won eight times. Karlovic's favorite return is his forehand, but sometimes that means he moves toward the T when returning to hit a forehand instead of a backhand -- making him vulnerable to serves out wide. Alexandr Dolgopolov exploited that tendency of Karlovic's in their second-round match at Wimbledon, and Murray did the same.

"He likes to take chances on the second-serve return," Murray said. "I just tried to use some variety there throughout the match to not allow him to be too comfortable. It worked at a few important moments."

A few important moments can swing the match. And match winners generally mix their serves better than their opponents did. The winners won a higher percentage of the time they went out wide than down the T just 53 percent of the time, which could have arisen by random chance. But the losers did 58 percent of the time, which we'd see just one in about 34,000 times if they were optimal strategists.

Maybe those few important moments when the winner chose the better serve made the difference. Or maybe this one type of decision among the hundreds a player makes -- one that is particularly easy to study because of the fixed position of servers and returners -- can tell us who was the better decision-maker in all aspects of the game. More often than not, the player who is brave enough to make the decision that could backfire spectacularly but will pay off in the long run is the player who wins.

Carl Bialik is the lead writer for news at FiveThirtyEight.com.