The Mathamatics of the Fade

By Richard Millman

Recently I’ve gotten into doing commentary for the streaming of some of the US Squash’s events. One particular criticism about my commentary has resonated with me.

The comment was “Mathematics. What does mathematics got to do with squash?”

First and foremost, the preparation of the racquet solicits the subconscious mind to visualize the future path of the ball based on its direction, trajectory and speed. This process, called hand/eye coordination, is a form of triangulation. Triangulation uses the principles of geometry and trigonometry to take at least two fixed points to calculate the whereabouts of another fixed point.

The best squash players in the world are very good at this form of rapid mathematical calculation. If we were able to use computers to calculate the geometric accuracy of their calculations, we would be stunned at how accurate this math on the fly is. (As points of references, the eye and racquet need to be constant—if the player waves the racquet around or prepares late or slowly, then the fixed points aren’t fixed and the math is off.)

Another use of geometry is when, providing the hand/eye coordination calculation based on the racquet preparation is precise, the player then visualizes the desired path of their own future shot. To do this, they need to calculate the most likely intercept point of the opponent based on the distance and time the opponent will travel and the distance and time the ball will take before intercept occurs. That in itself is some pretty amazing math calculation.

I say calculation not estimation because in my view, the subconscious mind is not in the business of guessing. The subconscious mind is not given to emotion or fear or approximations. It is given to precision and absolutes.

We see this in many top players. They hit a ball six inches from the sidewall and four feet in front of the back wall precisely aimed to fade progressively toward the sidewall as it progresses towards the back wall until it exactly contacts the sidewall at the most difficult point to strike for the retrieving opponent.

This is not a guess. This is a mathematical calculation of a supreme technician who has practiced literally millions of repetitions in seeking the  ultimate mastery of the mathematics of the game. It’s not enough to be able to precisely visualize a fade that is going to exactly bisect a six-inch space over fifty-six feet. You have to be able to make your body approach the ball to create an absolutely clinical point of contact, precisely ninety degrees (perpendicular) to the line you want to travel on. Any impaired movement or thought process in the setting up of this line and the chance of precision is gone—poof.

It means that your subconscious mind has to incorporate multiple variables in the calculation of a) the desired direction of shot, b) the required recovery movement and c) the precise behaviors required to achieve a clinical ninety-degree approach to achieve all this.

Take what I call the Nick Matthew Test. Can you feel the difference between a clinical ninety set up and an eighty-nine or less or ninety-one or more? And does it matter to you like it mattered to Nick Matthew?


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