Testing and ranking on round

By modelling results of sport matches as a set of paired fixed effect linear models, the goal of the present article is showing that traditional scoring outputs can be used to do inference on parameters related to the net relative strength or weakness of teams within a league. As hypothesis testing method, we propose either a normal-based and a non-parametric permutation-based approach. As an extension to round-robin of the ranking methodology recently proposed by Arboretti Giancristofaro et al. (2014) and Corain et al. (2016), results of pairwise testing are then exploited to provide a ranking of teams within a league. Through an extensive Monte Carlo simulation study, we investigated the properties of the proposed testing and ranking methodology where we proved its validity under different random distributions. In its simplest univariate version, the proposed methodology allows us to infer on the teams average net scoring within a league, while in its more intriguing multivariate layout it is suitable for looking for any team-related global dominance using a wide set of performance indicators. Finally, by using traditional basketball box scores, we present an application to the Italian Basket League