arXiv subjects
Publications and source records attributed to Warren P. Johnson.
We compute the nth derivative of a function given parametrically, and of one given implicitly, and some history for both problems. I am posting this version of the paper at the request of Shaul Zemel, whose forthcoming paper The Combinatorics of Higher Derivatives of Implicit Functions refers to it.
The James function, also known as the "log5 method," assigns a probability to the result of a competition between two teams based on their respective winning percentages. This paper, which builds on earlier work of the authors and Steven J. Miller, explores the analogous situation where a single team or player competes simultaneously against multiple opponents.
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.