Rounding the bases – really

by November 7, 2010

The optimal running path around the bases (Diagram by D. Carozza, S. Johnson, and F. Morgan)

One of the funniest moments in Arthur Hiller’s 1979 comedy, The In-Laws, comes when the fathers of the groom (Peter Falk) and of the bride (Alan Arkin) come under sudden sniper fire at a Central American landing strip. Arkin sensibly darts straight for a car but is held up by Falk’s former CIA agent, who attempts to coach him on his evasive running technique by yelling “Serpentine! Serpentine!” as Arkin frantically dodges bullets. (Yes, it’s on YouTube.)

When sprinting around the bases during a Major League baseball game, “serpentine” is clearly not the way to run. But neither is straight. According to modelling conducted by a Massachusetts undergraduate and his professors, the fastest route around the bases is a near-circle that swings up to 14 feet wide of each of the baselines.

The issue is that turns slow runners down. The tighter the turn, the greater the slowdown, so while the straight-line path between the bases is the shortest, its sharp corners make it one of the slowest. Rounding the corner is faster, making the path a bit longer in favor of an efficient turn. And indeed, baseball players typically do this: They run straight along the baseline at the beginning and then, if they think they’ve hit a double or more, they bow out to make a “banana curve.”

But this can’t possibly be the quickest route, observes Davide Carozza, a math teacher at St. Albans School in Washington, D.C., who studied the problem while was an undergraduate at Williams College in Williamstown, Mass. It’d be faster, he reasons, to veer right from the beginning, running directly from the batter’s box to the widest portion of the curve…

Read the rest of Julie Rehmeyer’s article here.