Baseball Science

Mathematicians investigate baseball! One way for a major league hitter to win a baseball game is to veer toward the dugout on the way to first base. While at first glance this route might not seem the best way to start a sprint toward home plate, it’s the actually fastest way around the diamond.

Although the quickest path to first base is (of course) a straight line, for baseball players who hit a long ball, the best way around the bases takes a more circular shape. By cutting off the corners, an average runner can round the bases 20% percent faster, saving approximately four seconds.

Mathematician Davide Carozza says, “I’m a huge baseball fan. I picked it up and ran with it,” and he literally did just that: He began his research by racing around a baseball field to get a feel for what a reasonable baseline acceleration speed might be, and to see which simple paths and shapes might work the best.

Fellow mathematician Frank Morgan tested it as well, and joined with Carozza to refine the optimal path. He says, “If you hit that ball and you know you’re going to go farther than first base, you shouldn’t run straight for first base. Right from the beginning, you should head to the right, 25 degrees off to toward the dugout, right from the base path to the outside. Don’t wait. Do it right away.” He says that as the runner rounds first, he should continue the curve as he heads to second base, and then bulge out even further between second and third so that he is lined up to make the straight sprint home.

In contrast, a base runner following the recommended “banana path” stays on the baseline halfway to first base before veering to the right to set up a better angle as he continues to second base. According to math professor Stewart Johnson, it should be obvious that this is not the optimal path. He says, “By the time you’re done curving to the right and then curving back to the left with the banana path, you’ve wasted a lot of energy and time and distance. It’s much better to start out running angled off to the right and run around first base in one smooth arching curve.”

Morgan explains their obsession by saying, “That’s what mathematicians do all the time: We’re always thinking about things. After a while, you just see relationships everywhere. That’s sort of our job. You’re always thinking about things and saying, ‘Maybe that’s like something else. Maybe this concept of curvature that I’m teaching in my senior seminar, maybe this would be useful to baseball runners, because they have to decide how much to curve when they’re running around the field.’ It’s not that math is life. It’s that life is math. There’s math in everything. It’s a way of looking at the universe and seeing so much more of it. When you like math, you like everything.

“We haven’t heard from the major leagues yet, but I don’t see why they shouldn’t give this more attention. We’ll see what happens. By the next World Series, maybe they

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