Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In such settings, the standard derivations of the methods can produce nonsensical rankings. This paper introduces the idea of including a super-user into the rankings and considers the effect of this fictitious player on the ratings. We apply such techniques to rank batters and pitchers in Major League baseball, professional tennis players, and participants in a free online social game. The ideas introduced in this paper can further the scope that such methods are applied and the depth of insight they offer.
This is the publisher's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.
Chartier, T.P., et al. "Reducing the Effects of Unequal Number of Games on Rankings." IMAGE - The Bulletin of the International Linear Algebra Society 52 (Spring 2014), 15-23.
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