The James Function

Like many mathematicians, I’m happy when I can combine my work with my other passions. As a lifelong Red Sox fan, I didn’t realize that all those games I watched when I was young was preparing me for a very productive career in sabermetrics, the science of applying math and stats to analyzing baseball. I’ve written several papers over the years in the subject, most on Bill James’ Pythagorean Won-Loss Formula. Roughly, it says that if a team scores on average RS runs per game and allows RA, its winning percentage is approximately RS^2 / (RS^2 + RA^2). James originally used an exponent of 2, which led to the name; later research now uses a number closer to 1.8. There are analogues of this for other sports; for more details see for example my paper “Pythagoras at the Bat” (with Taylor Corcoran, Jen Gossels, Victor Luo and Jaclyn Porfilio, book chapter in Social Networks and the Economics of Sports).

Recently I had the great fortune to work with Christopher Hammond and Warren Johnson of Connecticut College. We just published a note “The James Function” (the link is to the publicly available arXiv version) in Mathematics Magazine: We investigate the properties of the James function, associated with Bill James’s so-called “log5 method,” which assigns a probability to the result of a game between two teams based on their respective winning percentages. We also introduce and study a class of functions, which we call Jamesian, that satisfy the same a priori conditions that were originally used to describe the James function.

I find these terrific problems to study. They’re fun, they lead to great math, and they’re of interest to many. For students here, there are a lot of great colloquium or thesis topics related to problems along these lines…..

Note: Image of Pythagoras at the Bat created by Theresa McCracken (