Band 14, Heft 3

We present a one parameter family of ratings and rankings that includes the Markov method, as well as the methods of Colley and Massey as particular cases. The rankings are based on a natural network diffusion process that unites the methodologies above in a common framework and brings strong intuition to how and why they differ. We also explore the behavior of the ranking family using both real and simulated data.

A Bayesian model is used to evaluate the probability that a given skill performed in a specified area of the field will lead to a predetermined outcome by using discrete absorbing Markov chains. The transient states of the Markov process are defined by unique skill-area combinations. The absorbing states of the Markov process are defined by a shot, turnover, or bad turnover. Defining the states in this manner allows the probability of a transient state leading to an absorbing state to be derived. A non-informative prior specification of transition counts is used to permit the data to define the posterior distribution. A web application was created to collect play-by-play data from 34 Division 1 NCAA Women’s soccer matches for the 2013–2014 seasons. A prudent construction of updated transition probabilities facilitates a transformation through Monte Carlo simulation to obtain marginal probability estimates of each unique skill-area combination leading to an absorbing state. For each season, marginal probability estimates for given skills are compared both across and within areas to determine which skills and areas of the field are most advantageous.

Because of the advent of GPS techniques, a wide range of scientific literature on Sport Science is nowadays devoted to the analysis of players’ movement in relation to team performance in the context of big data analytics. A specific research question regards whether certain patterns of space among players affect team performance, from both an offensive and a defensive perspective. Using a time series of basketball players’ coordinates, we focus on the dynamics of the surface area of the five players on the court with a two-fold purpose: (i) to give tools allowing a detailed description and analysis of a game with respect to surface areas dynamics and (ii) to investigate its influence on the points made by both the team and the opponent. We propose a three-step procedure integrating different statistical modelling approaches. Specifically, we first employ a Markov Switching Model (MSM) to detect structural changes in the surface area. Then, we perform descriptive analyses in order to highlight associations between regimes and relevant game variables. Finally, we assess the relation between the regime probabilities and the scored points by means of Vector Auto Regressive (VAR) models. We carry out the proposed procedure using real data and, in the analyzed case studies, we find that structural changes are strongly associated to offensive and defensive game phases and that there is some association between the surface area dynamics and the points scored by the team and the opponent.

This paper builds on a recently developed Markov Decision Process-based (MDP) handicap system for tennis, which aims to make amateur matches more competitive. The system gives points to the weaker player based on skill difference, which is measured by the point-win probability. However, estimating point-win probabilities at the amateur level is challenging since point-level data is generally only available at the professional level. On the other hand, tennis rating systems are widely used and provide an estimate of the difference in ability between players, but a rigorous determination of handicap using rating systems is lacking. Therefore, our goal is to develop a mapping between the Universal Tennis Rating (UTR) system and the MDP-based handicaps, so that two amateur players can determine an appropriate handicap for their match based only on their UTRs. We first develop and validate an approach to extract server-independent point-win probabilities from match scores. Then, we show how to map server-independent point-win probabilities to server-specific point-win probabilities. Finally, we use the estimated probabilities to produce handicaps via the MDP model, which are regressed against UTR differences between pairs of players. We conclude with thoughts on how a handicap system could be implemented in practice.

Although there is no consensus on how to measure and quantify individual performance in any sport, there has been less development in this area for soccer than for other major sports. And only once this measurement is defined, does modeling for predictive purposes make sense. We use the player ratings provided by a popular Italian fantasy soccer game as proxies for the players’ performance; we discuss the merits and flaws of a variety of hierarchical Bayesian models for predicting these ratings, comparing the models on their predictive accuracy on hold-out data. Our central goals are to explore what can be accomplished with a simple freely available dataset comprising only a few variables from the 2015–2016 season in the top Italian league, Serie A, and to focus on a small number of interesting modeling and prediction questions that arise. Among these, we highlight the importance of modeling the missing observations and we propose two models designed for this task. We validate our models through graphical posterior predictive checks and we provide out-of-sample predictions for the second half of the season, using the first half as a training set. We use Stan to sample from the posterior distributions via Markov chain Monte Carlo.