Plus-Minus Player Ratings for Soccer

The paper presents plus–minus ratings for use in association football (soccer). We first describe the general plus–minus methodology as used in basketball and ice-hockey and then adapt it for use in soccer. The usual goal-differential plus–minus is considered before two new variations are proposed. For the first variation, we present a methodology to calculate an expected goals plus–minus rating. The second variation makes use of in-play probabilities of match outcome to evaluate an expected points plus–minus rating. We use the ratings to examine who are the best players in European football, and demonstrate how the players’ ratings evolve over time. Finally, we shed light on the debate regarding which is the strongest league. The model suggests the English Premier League is the strongest, with the German Bundesliga a close runner-up

Flexible Regression Models for Count Data Based on Renewal Processes: The Countr Package

A new alternative to the standard Poisson regression model for count data is suggested. This new family of models is based on discrete distributions derived from renewal processes, i.e., distributions of the number of events by some time t. Unlike the Poisson model, these models have, in general, time-dependent hazard functions. Any survival distribution can be used to describe the inter-arrival times between events, which gives a rich class of count processes with great flexibility for modelling both underdispersed and overdispersed data. The R package Countr provides a function, renewalCount(), for fitting renewal count regression models and methods for working with the fitted models. The interface is designed to mimic the glm() interface and standard methods for model exploration, diagnosis and prediction are implemented. Package Countr implements stateof-the-art recently developed methods for fast computation of the count probabilities. The package functionalities are illustrated using several datasets