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The Formula For The Perfect Free-Throw

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Improving your free-throw percentage is a simple matter of mathematics, according to researchers Drs. Chau Tran and Larry Silverberg of North Carolina State University.

Using three-dimensional computer simulations of hundreds of thousands of basketball trajectories, the two engineers determined the ideal characteristics of a free-throw shot.

They based their data on the assumption of a 6’6” player who would release the ball (assumed to be a men’s basketball) at a height of 7 feet.




The first variable Tran and Silverberg examined was spin. According to them, you should release the ball with about three hertz of backspin – or, so that the ball makes roughly three full backwards rotations before reaching the hoop.

This slows the ball upon contact with the backboard or rim, making it more likely that the shot will go in.

The ball should also be released at 52 degrees to the horizontal, making the peak of its arc only a few inches higher than the top of the backboard.

For aiming, they found the most successful methods put the ball towards the back of the rim, either two inches to the left or two inches to the right of the place where the rim meets the backboard.

How a mathematician sees a free throw.

Their simulation data showed that aiming straight for the center of the backboard decreases the success rate by almost three percent.

Tran and Silverberg also recommend free-throw shooters should release the ball as high above the ground as possible with a smooth, consistent release speed for best results.

Our recommendations might make even the worst free-throw shooters – you know who you are, Shaquille O’Neal and Ben Wallace – break 60 percent from the free-throw line,” Silverberg joked.

Their work is just another example of how mathematical questions can crop up in the most unexpected areas.

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