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:

XYArmyBucknellHoly CrossLafayetteLehighNavy
Armyx14-1614-1314-2410-128-19
Bucknell16-14x27-3018-1623-2010-22
Holy Cross13-1430-27x19-1517-139-16
Lafayette24-1416-1815-19x12-2317-39
Lehigh12-1020-2313-1723-12x12-18
Navy19-822-1016-939-1718-12x

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

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