title: Evaluating Australian football league player contributions using interactive network simulation.
abstract: This paper focuses on the contribution of Australian Football League (AFL) players to their team's on-field network by simulating player interactions within a chosen team list and estimating the net effect on final score margin. A Visual Basic computer program was written, firstly, to isolate the effective interactions between players from a particular team in all 2011 season matches and, secondly, to generate a symmetric interaction matrix for each match. Negative binomial distributions were fitted to each player pairing in the Geelong Football Club for the 2011 season, enabling an interactive match simulation model given the 22 chosen players. Dynamic player ratings were calculated from the simulated network using eigenvector centrality, a method that recognises and rewards interactions with more prominent players in the team network. The centrality ratings were recorded after every network simulation and then applied in final score margin predictions so that each player's match contribution-and, hence, an optimal team-could be estimated. The paper ultimately demonstrates that the presence of highly rated players, such as Geelong's Jimmy Bartel, provides the most utility within a simulated team network. It is anticipated that these findings will facilitate optimal AFL team selection and player substitutions, which are key areas of interest to coaches. Network simulations are also attractive for use within betting markets, specifically to provide information on the likelihood of a chosen AFL team list "covering the line ". Key pointsA simulated interaction matrix for Australian Rules football players is proposedThe simulations were carried out by fitting unique negative binomial distributions to each player pairing in a sideEigenvector centrality was calculated for each player in a simulated matrix, then for the teamThe team centrality measure adequately predicted the team's winning marginA player's net effect on margin could hence be estimated by replacing him in the simulated side with another player.
authors.affiliation: School of Mathematical & Geospatial Sciences, RMIT University , Australia.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Sargent
authors.forename: Anthony
authors.initials: A
authors.lastname: Bedford
keywords: Interaction matrix; eigenvector centrality; negative binomial distribution; player ratings