In his senior colloquium last fall advised by Frank Morgan, Davide Carozza ’09 investigated the fastest path around the bases in baseball, assuming a bound of say 10 ft/sec2 on acceleration/deceleration. Following the baseline, stopping at each base, takes about 22.2 seconds. The standard recommended “banana” path follows the baseline maybe halfway to first base and then veers a bit to the right to come at first base from a better angle to continue towards second. That cannot be ideal. It would have been better to start at an angle to the right to head directly to an outer point on the banana path. Davide found that a circular path at 17.8 seconds is roughly 20% faster than following the baseline at 22.2 seconds. Stewart Johnson then computed the following optimal path at 16.7 seconds. The record time according to Guiness is 13.3 seconds, set by Evar Swanson in 1932 (with larger acceleration than our assumed 10 ft/sec2).
Is it legal to run so far outside the base path? The relevant official rule of Baseball says:
7.08 Any runner is out when—
(a) (1) He runs more than three feet away from his baseline to avoid being tagged unless his action is to avoid interference with a fielder fielding a batted ball. A runner’ s baseline is established when the tag attempt occurs and is a straight line from the runner to the base he is attempting to reach safely.
The rule just says that after a tag attempt the runner cannot deviate more than three feet from a straight line from that point. The rule doesn’t apply until the slugger is almost home, when our fastest path is nearly straight. So our path is legal.
Our model is, of course, an oversimplified one, since it assumes that maximum deceleration equals maximum acceleration and that maximum acceleration remains possible at high speeds, leading to a final speed coming into home of about 42 ft/sec, faster than the highest recorded human speed of 40 ft/sec by Usain Bolt.
For more, see the web version of our “Baserunner’s Optimal Path,” published online in The Mathematical Intelligencer, November, 2009, Johnson’s interview on NPR, the citation in Rob Neyer’s Monday Mendozas on how to get more triples in baseball, the Berkshire Eagle (front page, see below), the Williams College news release, “World Series Take Notice,” Live Science, Science News, and Math Goes Pop.
Davide Carozza, Stewart Johnson, and Frank Morgan