Physics Proves It: Everyone Should Shoot Granny-Style — or, rather, they should probably shoot free throws underhand:
Using lots of trigonometry, Brancazio calculated the optimal angle of the arc from the free throw line. If tossed at 32 degrees or less, the ball will most likely hit the back of the rim. “That doesn’t mean it won’t go in, but it will certainly bounce off the metal and reduce the chance of success,” Brancazio says. At angles greater than that, the ball has a chance of making a nice swish. The optimum angle for the shot, he finds, is 45 degrees—plus half the angle from the top of the player’s hand to the rim. “The shorter you are, the steeper that angle has to get to give you the best chance of making the shot,” he says. Of course, lobbing a ball very high so that it comes down nearly straight into the basket would be the most efficient technique, but a shot like that “is almost impossible to aim,” Brancazio says. Instead, he says, his formula makes it possible for a player to shoot with the largest possible margin for error.