Accessible Unlicensed Requires Authentication Published by De Gruyter May 27, 2013

Ranking rankings: an empirical comparison of the predictive power of sports ranking methods

Daniel Barrow, Ian Drayer, Peter Elliott, Garren Gaut and Braxton Osting

Abstract

In this paper, we empirically evaluate the predictive power of eight sports ranking methods. For each ranking method, we implement two versions, one using only win-loss data and one utilizing score-differential data. The methods are compared on 4 datasets: 32 National Basketball Association (NBA) seasons, 112 Major League Baseball (MLB) seasons, 22 NCAA Division 1-A Basketball (NCAAB) seasons, and 56 NCAA Division 1-A Football (NCAAF) seasons. For each season of each dataset, we apply 20-fold cross validation to determine the predictive accuracy of the ranking methods. The non-parametric Friedman hypothesis test is used to assess whether the predictive errors for the considered rankings over the seasons are statistically dissimilar. The post-hoc Nemenyi test is then employed to determine which ranking methods have significant differences in predictive power. For all datasets, the null hypothesis – that all ranking methods are equivalent – is rejected at the 99% confidence level. For NCAAF and NCAAB datasets, the Nemenyi test concludes that the implementations utilizing score-differential data are usually more predictive than those using only win-loss data. For the NCAAF dataset, the least squares and random walker methods have significantly better predictive accuracy at the 95% confidence level than the other methods considered.


Corresponding author: Braxton Osting, UCLA, Department of Mathematics, 405 Hilgard Avenue, Los Angeles, CA 90095, USA, Tel.: +3108252601

  1. 1
  2. 2

    In equation (2), we take the fraction to be

    if the game results in a 0–0 tie.

  3. 3

    A digraph is weakly connected if replacing its arcs with undirected edges yields a connected graph.

  4. 4

    Recall that for a matrix with non-negative entries, there exists a positive, real eigenvalue (called the Perron-Frobenius eigenvalue) such that any other eigenvalue is smaller in magnitude. The Perron-Frobenius eigenvalue is simple and the corresponding eigenvector (called the Perron-Frobenius eigenvector) has non-negative entries. See, for example, Horn and Johnson (1991).

  5. 5

    The matrices W and S are irreducible if the corresponding directed graph is strongly connected. The matrix W is irreducible if there is no partition of the teams V=V1ߎV2 such that no team in V1 has beat a team in V2.

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Published Online: 2013-05-27
Published in Print: 2013-06-01

©2013 by Walter de Gruyter Berlin Boston