This is a review of the sports research conducted by Stephen Devlin and Thomas Treloar applying network diffusion methods (Massey, Colley’s and Markov chain methods).
Ranking is a natural phenomenon within the world of sports. Teams are ranked and so are individual players. In leagues consisting of a small number of teams and playing a large number of games, the ranking process is quite straight forward. However, when a league consists of many teams playing relatively few games a unique problem arises when ranking teams who have not faced each other during the season nor played any common opponents. The Massey method, Colley method, and Markov method are three methods used for ranking in sports situations. A framework is created to understand the three methods and their similarities and differences.
The Massey method is based on the idea that the difference in two teams’ ranks should predict the point differential in a game featuring the two teams. It employs a least squares ranking approach.
Colley’s method uses a modified winning percentage. The percentage is found in the form of one plus the number of wins divided by two plus the number of games played.
The Markov chain method represents each team as a node in a network with edges between teams that play one another. The Markov rating is normalized by the number of games played by the team in order to remove any bias related to teams having played different numbers of games.
A one parameter family of rankings interpolates between the Markov method with p equal to zero and the Colley and Massey methods with p equal to one. The distribution process is determined by specifying the flow of rank from one team to another in terms of face-to-face wins, weighted by face-to-face losses, and a rank-infusion vector, which is determined by the team’s overall record. This allows similarities and differences between the three methods to be analyzed especially in regards to the parameters chosen and the normalizations made by each method.
Analysis shows that there appears to be no single optimal value for p. To make face-to-face results relevant to a team’s ranking, beyond their winning average, the value of p needs to be less than one. If an emphasis is to be placed on a team’s record and strength of schedule, then p should equal one. It is also likely that an optimal value for p will vary depending on the sport or even the league.
The Massey and Colley methods produce ratings in a perfect season that are equally spaced and highly stable while the Markov rating is non-uniform in its distribution of values and therefore less stable.
Analytics Used: Massey’s Method, Colley’s Method, Markov Method, Least Squares Ranking
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