Five

How to Outguess Tennis Serves

Tennis pro and coach Daryl Fisher of Ann Arbor, Michigan, came up with a secret weapon to give almost any tennis player an advantage. It’s one of the few sweat-free ways to improve your game.

“There was one opponent who would serve to my backhand,” Fisher explained. “When he succeeded, I would position myself for the same serve the next time.” The guy always repeated a successful serve. When Fisher deftly returned the serve, the too-predictable player would switch to something else on his next serve. Fisher predicted that, too.

This player had a “rhythm” that Fisher could recognize and anticipate. He discovered a parallel when he happened to read about the outguessing machine in Robert Lucky’s 1989 history of Bell Labs, Silicon Dreams. Tennis players are as predictable as the outguessing machine’s players, Fisher realized. They are smart people with short strategic memories. They base decisions mainly on what worked or didn’t work the last time.

To oversimplify things a bit, the server has three main options: to hit the ball to the left of the receiver, to the right, or directly at him. Because the receiver does not know where the ball is going, he must be prepared to move quickly in order to return the serve.

A player aware of his and his opponent’s strengths knows that some serves are more likely to succeed. But a player who always uses his “best” serve is predictable. “It’s very easy to become one-dimensional,” Venus Williams once said, “and just serve to your favorite space and the person is just waiting there.” To avoid this, the strategic server will randomly pick a disfavored option some of the time.

One hurdle is getting the probabilities right. A rock, paper, scissors player knows to pick each throw with a probability of 1/3. In physical sports, it is hard to know the “correct” probabilities with any precision. A distinct challenge is generating random choices in the heat of a game. This is where Fisher’s opponent failed. He fell back on a simple, easily outguessed pattern.

In recent years psychologists, economists, and game theorists have asked, how well do athletes randomize? Much of this research has made the point that athletes do not follow game theory exactly. Okay, but that’s like saying their tweets aren’t always grammatical and politically correct. You wouldn’t expect an athlete’s instinctive strategy to match the mathematical ideal. A more provocative finding is that athletes, like everyone else, are unable to generate credible random sequences. Tennis has been studied extensively because it offers so much data. A match may have hundreds of serves between the same two players.

In a 2001 article, Mark Walker and John Wooders examined videos of ten matches at Wimbledon and other pro tournaments, involving such stars as Andre Agassi, Petr Korda, John McEnroe, and Pete Sampras. Some players served to the left and right almost equally, while others strongly favored one direction. The opponent, and whether the server had the ad or deuce side, mattered. But overall, Walker and Wooders found that the pros alternated serves too much. A sequence of tennis serves will be too close to right-left-right-left (like the heads of spectators watching tennis). However, the players were not as predictable as typical subjects in nonathletic randomness experiments. Apparently tennis pros had learned to simulate randomness better than those who didn’t have a career riding on it.

These findings offer several guidelines that ought to apply (perhaps especially) to amateur tennis. When you’re receiving, expect the serve to alternate. A serve to the right this time means: be prepared for left next time. A different serve is especially likely when the last serve failed, or after two or more consecutive serves in the same direction.

When you’re the one serving, you need to remember that making your own random choices is like cutting your own hair. You need help. That brings us to Fisher’s secret weapon: a heart-rate monitor.

Many players wear wristband monitors, and some are obsessive about checking their cardio rate midmatch—so there’s nothing too suspicious about glancing at them. Because a player’s heart rate is always changing in an intense match, the rightmost digit is unpredictable. Whether the last digit is odd or even is, for practical purposes, random.

Fisher advises servers to first decide their percentage strategy against a given opponent. Maybe you want to serve to the right 40 percent of the time, to the left 40 percent, and to the body 20 percent. In that case you might decide that even numbers 2, 4, 6, and 8 mean “serve right”; odd numbers 3, 5, 7, and 9 mean “serve left”; and low numbers 0 and 1 mean “serve to the body.” Should the monitor read 167 when you glance at it, you’d serve to the left.

Most heart-rate monitors double as digital watches. Fisher notes that the time readout’s last digit can be used to randomize spin or whether you follow a serve by remaining at the baseline or going to the net. A further advantage of the heart-rate monitor scheme is that there’s no great harm, should your opponent suspect what you’re doing. She can’t see your heart monitor.

Those not wanting to use a heart-rate monitor can use a watch, a digital clock, or a scoreboard. The even- or oddness of the seconds figure is good for deciding two-way, equal-probability choices. When choices aren’t equally favored or are more than two, you can invent a rule like Fisher’s. Of course, the problem with a clock or scoreboard is that it’s not private.

In my own experience, an analog watch with a second hand is easy for weekend players to use. Many choices in sports are left or right. Glance at the watch and note the second hand’s position at that exact (“random”) instant. If the second hand is on the right half of the dial, choose right; if it’s on the left side, choose left. I find this natural because I can quickly relate the second hand’s direction to a direction in space. There’s no need to bring numbers into it.

Typically, you want to favor one direction but still be random. Instead of dividing the watch dial straight down the middle, do a pie slice. The sizes of the slices are in proportion to the intended probabilities. When you want to favor left, the rightward zone shrinks, and you go right only if the second hand falls in that zone. When necessary, you can add a third zone for “body” or “center.”

The zones are imaginary and inexact. That’s okay; the mental pie slices probably capture your intuition as well as guesstimated numbers could. They also save time. You don’t have to invent a percentage number and then convert that to a percentage of a clock dial. You just go with what looks right.

Recap: How to Outguess Tennis Serves

• Expect the direction of serve to alternate, especially with novice players.

• When playing a good opponent, use a watch or heart-rate monitor to randomize your own serves.