Sports ranking methods, 2

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

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

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