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(THE CONVERSATION) Some 20 years ago, my colleague Dr. Chau Tran and I developed a way to simulate the trajectories of millions of basketballs on the computer.

We went to the coaches and assistant coaches at North Carolina State University, where we are based, and told them we had this uncommon ability to study basketball shots very carefully.

Their first question was simple: “What’s the best free throw?” Should the shooter aim towards the front of the hoop or the back? Does it dep...