Winning the World Series with math

To figure out just how critical the turns are, Carozza did a calculation comparing the straight-line path with a circle around the bases. A path that follows a circle turned out to be a whopping 25 percent faster.

When Carozza presented his calculation at a colloquium talk in the math department at Williams College, Stewart Johnson, one of the professors in the audience, got intrigued. The circular path is so long that it can hardly be the fastest, he figured. So what path

isthe fastest?Johnson ran a simulation on his computer, tweaking the circular path in tiny ways to make it shorter and faster, until no more tweaks could improve it. The result was surprisingly close to a circle, both in its shape and its speed: It swung nearly as wide and was only 6 percent faster than Carozza’s circle.

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“This cries out for an empirical test,” Winston says. “It would be easy to do. If it holds up, God, that goes in the New York Times sports section.”

Assuming that the maximum acceleration magnitude of a runner is constant regardless of speed or direction is a horrible simplification. Simply giving the runners a top speed would do a lot to ‘square off’ the optimal trajectory.