The free throw is basketball's tool of justice. When one player bumps or knocks another, officials reward the victim with what seems like a chance to score easy points. The clock stops, the other players get out of the way, and the shooter stands centered, just 15 feet from the basket, to calmly put the ball through the net.
It should be a cinch, right? But the best players in men's college basketball only hit about 69 percent of free throws. Even NBA players, the best in the world, only make about 75 percent of them. And these averages have not improved in decades.
Leave it to two mechanical and aerospace engineers to find the best technique for the perfect free throw. Chau Tran and Larry Silverberg, professors at North Carolina State University, studied hundreds of thousands of three-dimensional computer simulations of free-throw trajectories to find the best combination of ball aim, rotation and shooting angle. Here's their formula for sailing a shot through the 18-inch rim.
First, aim for back of the rim. Interestingly, choosing what seems like a more logical target -- the center of the basket -- reduces accuracy by almost three percent. Try to leave 2 inches between the back of the rim and the ball.
Next, put about three hertz of backspin on the ball. For those without an engineering degree, this means the ball should spin three full rotations on its way from your hand to the basket. This rate of spin will deaden the ball if it hits the rim, helping it to fall through the hoop.
Finally, release the ball at an angle of 52 degrees to horizontal. The rule of thumb is that, at its highest point, the ball should be less than two inches from the height of the top of the backboard. Coming down at this angle gives the ball the best chance of going through the hoop, even it touches the sides of the rim.
If players get the aim, spin, and angle right, we might finally see the free throw live up to its name.
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