Statistical Properties of Massey’s Rating and Their Application to Network Analysis

Abstract

Massey's method is a rating system that provides individual teams or players ranking. It is known that Massey's rating is related to the Katz centrality measure of the networks. Analyzing the node centrality of networks provides useful information on how important a node is. This study investigates a sampling distribution of Massey's rating and provides the test statistics of the null hypothesis of equal rating against the alternatives. Monte Carlo simulations are performed to compare the power of the proposed test and show that the asymptotic distribution of the ratings is well approximated by the normal distributions. Real dataset applications using men's tennis ATP ratings are illustrated.