The geometry of tennis
To learn all about it, I consulted Gene Mayer, whom Tennis magazine once called “the smartest man in tennis.”
“I began to study tennis from the standpoint of geometry and physics, began to work out carefully a strategic and psychological approach to the game. Thus my first real pupil, and my most successful, was myself.” — Bill Tilden, the first tennis superstar and its most profound seminal thinker.
“Mighty is geometry; joined with art, resistless.” — Euripides.
“Geometry is a skill of the eyes and the SPORTSTAR NOVEMBER 2, 2019 hands as well as of the mind.” — Jean J.
Pedersen, in “Why We Still Need to Teach Geometry.”
Former NBA star Steve Nash once said playing soccer as a kid helped him enormously when he later switched to basketball. Transferring his soccer knowledge of how to “find creative ways to get the ball to the right spot... made ball-handling a lot easier... It was almost like cheating,” he told Playboy magazine.
Nash cleverly used all the angles to become one of the greatest playmaking guards in NBA history.
Much like Nash in basketball, you can play all the angles in tennis. But first, you have to understand the geometry of tennis. It’s a complicated but fascinating subject.
To learn all about it, I consulted Gene Mayer, whom Tennis magazine once called “the smartest man in tennis.” Mayer ranked No. 4 in the world in singles in 1980 and twice captured the French Open doubles title, in 1978 with Hank Pfister and in 1979 with his brother Sandy. He also helped the US win the Davis Cup in 1982, taking four of six singles matches.
After retiring from the pro tour, Mayer coached former doubles No. 1 Leander Paes and singles No. 17 Fabrice Santoro, both renowned for their ingenious tactics and diverse skills. Recently, Mayer guided American teenager Cannon Kingsley to the US Open junior singles semifinals.
In this interview, Mayer explains the geometry of tennis from every conceivable angle. His insights and advice will make you a better player and a more educated tennis watcher.
Your father Alex, the European doubles champion in 1938 and a distinguished coach in Hungary before emigrating to the US, taught you and your brother Sandy at a very young age to play European billiards in order to learn angles. Specifically, how did you apply
what you learned about billiards angles to your tennis game in the 1970s and 1980s?
Basically everything I did was related to angles and geometry. I didn’t hit the ball terribly hard. My opponents usually hit the ball bigger than I did. But my biggest strength was that I used (every part of) the court well. I had the ability to move people left and right and up and down the court and in every possible direction. I was so young when my father started teaching me so that my whole perception of tennis then was that it was a chess match of progressive moves to get a particular (advantageous) position, as opposed to a warrior style of just grinding and hitting lots of balls in the style of Bjorn Borg.
You hit both your forehand and backhand with two hands. Specifically, how did you apply that chess-like approach to those shots?
My backhand was crossed over, so my forehand was more natural and better. I would roll (topspin) balls to my opponent’s backhand to get an opportunity to attack, and then I would “spread the court” by moving him from left to right. I would also force opponents with the weight of my shot to retreat and then try to defend. That also created opportunities for me to hit a lot of drop shots.
The amateur and pro games have changed greatly in the past 40 years.
What principles of geometry should players today incorporate into their games, both offensively and defensively?
One of the major ways the pro game has changed is that with players generally hitting the ball harder than we did in generations past, the ball moves through the court faster, but it often doesn’t move off the court as much, as players like me used to do. So the harder you hit, the more difficult it is to hit very sharp angles. Now there is less use of geometry and more reliance on shot power. That’s a large transformation.
Today the ability to open up the court is not treasured as much as it was 40 years ago because we didn’t have the opportunity to force opponents purely with the weight of the shot. This transformation has made it less enjoyable for me, as a fan, to watch.
Please elaborate about this transformation.
If I hit the ball a certain way and my opponent is standing in a certain spot on the court with certain opportunities, then, to use one of my father’s favourite expressions, “How do I bisect the angle now of the opportunities that they can hit (target)?” If it’s a ground stroke I have to cover, particularly if I’ve moved my opponent out wide but not extremely wide, what are the viable balls (my shot options)? And how do I cover the greatest amount of the court? For example, how do I cover the wide serve — which is so dangerous and opens up the court so much
— against a great server like (Roger) Federer?
So, even with today’s power game, the “read” of how I use the court offensively and create opportunities using angles and geometry as well as how I now respond to my opponent’s shots defensively are enormously important as far as positioning and shot selection.
What about the women’s game?
On the female side, this transformation is true even more because the ball is hit flatter and harder than ever. There are now some emerging players who are starting to show more of that versatility and variety. So tennis is still a geometric game.
How do Ashleigh Barty, the French Open champion, and Bianca Andreescu, the US Open champion, use geometry effectively?
Barty and Andreescu brought tactical elements that (most) other ladies are not using. They both are great at lifting the ball up when needed and adding topspin and not just hitting harder and straighter (flatter). They both use the width of the court and open up the court. They also both use slices to bring opponents into the court and force them to hit lower(-bouncing) balls. So, by varying speeds and spins, they really bring enormous changes to the game. They also use, when needed, drop shots effectively. They use sharp angles to open up the court. They use every inch of the court.
Are there any important connections between the physics of tennis and the geometry of tennis?
If you think of the physics of tennis and the geometry of tennis, then you have tennis in a nutshell. You’re talking about the speed of the ball coming at you, the direction of the ball coming at you, the type of spin on the ball, and the (amount of) rotations on the ball. All of those (variables) have a dramatic impact on your ability to handle various shots. For example, if you’re playing Rafa (Rafael Nadal) on clay, particularly if it’s a warm, sunny day, his ball is going to bound high off the court to your backhand. That wicked topspin forehand has basically made his career. Almost no one has been able to return that shot well. (Novak) Djokovic, who is tall and handles balls well that bounce high and out of his strike zone, is probably better than anyone I can think of on the backhand. Djokovic has learned to stay near the baseline and not give up much position against Rafa, who generally pushes opponents around with his forehand. Once Rafa gains the offensive with his forehand, it’s the beginning of the end for his opponents. Djokovic has been able to turn that around, even on clay, when he’s playing well. (Djokovic has seven career wins over Nadal on clay.)
Are Nadal and Federer the two best exponents of using the geometry of tennis to their best advantage?
Rafa is superb. Roger, with his forehand particularly, has relied a little more on power and is, maybe, not quite as good as Rafa. (Andy) Murray, because he hits with a little less pace, was excellent. I would put Novak on a par with Roger. But Rafa, because of the extremely high topspin revolutions (per second) on the ball, is the pre-eminent practitioner today of highly geometric and court-opening tactics.
Which other players this century excelled in this area?
Fabrice Santoro was very clever. I coached Fabrice for several years. He came to me when he was a very solid, grinding player, a very different player from the Fabrice you saw at the end of his (22-year) career. As a junior, he was very one-dimensional and played pretty straight-ahead tennis. I knew Fabrice was never going to play mega-power tennis. But I could see that he had a knack for this (tactical style) because of the way his mind worked, his body type (his 5’9½” stature), and his (racquet) talents. At the time, though, he was not really comfortable playing this more creative style because he hadn’t done it a lot. But he learned it pretty quickly. He developed the magic with his racquet becoming a wand, and earned the nickname “The Magician.” Fabrice was extraordinary. He was one of the most engaging players to watch, I can remember.
What exactly did Santoro do to bedevil and befuddle opponents, using the geometrical advice you gave him?
Fabrice used off-speeds (for his shots) better than any player I’ve ever seen. Even though he could hit the ball with pace, he almost never did off his forehand and only a little bit with his backhand. Unlike the women I
mentioned, he seldom used power. Fabrice sliced and diced and used the short parts of the court with low-bouncing slices to throw his opponents off, particularly against Andre Agassi and the 1990s power-hitters like (Pete) Sampras. Against Sampras, Fabrice was able to transform the whole look of the points so that they didn’t look like standard points where the other player was better. He subtly got other players to play his game.
Is there a connection between spin — topspin and underspin — and the geometry of tennis?
Yes, absolutely. Placing the ball low and forcing opponents to contend with the net makes it much more difficult for players to do certain things. For example, when Roger is on the defensive, he “knifes” short backhands that bounce very low. That reduces the amount of court he has to cover by dramatically limiting his opponent’s options. Opponents can’t hit Federer’s slice backhands with a lot of pace. It’s very hard for opponents to get their racquet under the ball and angle it the way they’d like if they have a little more time and a higher bounce.
Similarly, once the ball bounces high and out of your strike zone, your ability to pinpoint (place) your shots goes down dramatically for most players. So when Rafa gets the ball up very high to someone’s backhand, players are just happy to return the ball solidly, as opposed to hitting a strong shot to a target.
Are left-handed players often better at understanding and using geometry than right-handed players? And, if so, why?
Strangely, I think so. Lefties seem to learn very quickly the great value of spreading the court when they serve. They have a huge advantage when they serve in the ad court with their natural slice to the righty’s backhand. That right away creates an understanding of geometry. Whereas, if you take a righty in the same situation, he now can slice his serve in the opposite direction, but it goes to a righty’s forehand. So it’s harder to win points for righties that way, and they don’t use this tactic as much, whereas lefties use it as a go-to shot. Most of the lefties I’ve known have learned through serving to spread the court also with their ground strokes and volleys because they were already programmed by the serving mode.
There are four choices for hitting volleys: down-the-line, deep crosscourt, short crosscourt and drop volleys. What are the geometric plus and minuses of each volley for the first volley and the second volley?
In general, unless you have an extraordinarily weak forehand or backhand volley, it’s best to hit first volleys deep and down the line. For “approach” first volleys of moderate height from around the service line, unless you’re attacking a weak short or your opponent is on the run, you’re hitting more of an approach shot and establishing position (at the net). When you move forward and are about halfway between the service line and the net, now the world opens up in terms of geometric opportunities. For low volleys, I tend to prefer drop volleys and angle volleys, finesse shots that land short. On volleys net high or higher, now depth and power factor into your choice of crosscourt versus down the line.
You won two Grand Slam doubles titles with different partners. Which geometrical principle did you adopt most in doubles?
In doubles, power can often be less effective because it’s harder to hit through two opponents who are covering space that is not twice the size of a singles court.
I usually played the deuce court because my partners liked the ad court. So the ability to hit my forehand short, low, and angled into the alley created lots of opportunity on the next shot to either drive the ball down the line or up the middle or to hit a lob. If I didn’t have that forehand angle, my partner and I would not have had the opportunity to hit those other (offensive) shots. These acute angles created more openings because if our opponents reached the ball, they were usually stretching and lunging.
Opponents usually served up the T to my backhand, and the “off return” is the hardest. So I would return the ball low at their feet, and then if my partner (at the net) didn’t pick off their return, I had a forehand, my favourite shot, and I had a lot of good options: a lob down the line or crosscourt, a drive down the line or up the middle, or a short angle. So I very often neutralised their serve with my return and then hit a shot that was very hard for even two guys to cover. I stopped playing doubles because it was too tiring and risked injury when I went deep in singles. But I missed playing doubles because it was more enjoyable than singles.
❝If you think of the physics of tennis and the geometry of tennis, then you have tennis in a nutshell. You’re talking about the speed of the ball coming at you, the direction of the ball coming at you, the type of spin on the ball, and the (amount of) rotations on the ball. All of those (variables) have a dramatic impact on your ability to handle various shots.