# Kagan: The physics of going from first to third

From SABR member David Kagan at The Hardball Times on March 4, 2015, with mention of SABR member Michael Clair:

Euclid, the Greek mathematician known as the “Father of Geometry,” was the first to establish the rules for laying out a ball diamond. Yeah, I know baseball wasn’t even invented yet. Nonetheless, he built the mathematics to describe the behavior of lines and points on flat planes.

You see Euclid’s work whenever you marvel at the exact right angle created by the foul lines as they intersect precisely at the back point of home plate. The perfection of the square with bases at each corner is another jewel of his theorems.

While Euclid never got around to proving a straight line is the shortest distance between two points, it certainly seems reasonable enough. When the runners go “station-to-station” a straight line is certainly their best bet. However, when trying to collect two or more bases at a time, straight lines are not the best choice.

Let’s understand this by looking at a runner on first trying to go to third base on a single to right field. The defense usually has its outfielder with the best arm in right, so the key for the runner is to minimize the time needed to touch second and move on to third.