The Perron–Frobenius Theorem and the Ranking of Football Teams

James P. Keener

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Sports Analytics and Performance Matrix Theory and Algorithms Game Theory and Voting Systems

Abstract

The author describes four different methods to rank teams in uneven paired competition and shows how each of these methods depends in some fundamental way on the Perron–Frobenius theorem.

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1951Remarks on the Method of Paired Comparisons: I. The Least Squares Solution Assuming Equal Standard Deviations and Equal Correlations 1955Further Contributions to the Theory of Paired Comparisons

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