Yet Another Mathblog

This is the second of a series of expository posts on matrix-theoretic sports ranking methods. This post discusses Keener’s method (see J.P. Keener, The Perron-Frobenius theorem and the ranking of football, SIAM Review 35 (1993)80-93 for details).

See the first post in the series for a discussion of the data we’re using to explain this method. We recall the table of results:

XY Army Bucknell Holy Cross Lafayette Lehigh Navy
Army x 14-16 14-13 14-24 10-12 8-19
Bucknell 16-14 x 27-30 18-16 23-20 10-22
Holy Cross 13-14 30-27 x 19-15 17-13 9-16
Lafayette 24-14 16-18 15-19 x 12-23 17-39
Lehigh 12-10 20-23 13-17 23-12 x 12-18
Navy 19-8 22-10 16-9 39-17 18-12 x

sm261_baseball-ranking-application_teams-digraph Win-loss digraph of the Patriot league mens baseball from 2015

Suppose T teams play each other. Let $latex A=(a_{ij})_{1leq i,jleq T}$ be a non-negative square matrix determined by the results of their games, called the preference matrix

View original post 326 more words

Advertisements