University of Twente Student Theses


A rating model for individual player qualities based on team results, applied in football

Babič, Anatolij I. (2017) A rating model for individual player qualities based on team results, applied in football.

Abstract:There are abundant situations where teams of players compete. The competing players have qualities that in uence the outcome of a match, but in some cases, individual contributions are not recorded and only team results can be observed. Examples can be found in sports (football, basketball, volleyball, etc.), e-sports (Dota, StarCraft, League of Legends, etc.), Film-making and company management. In this research, we developed an individual player quality inference algorithm which only requires historical team results. Whenever groups of individuals produce collective results and we do not have the data regarding individual contributions, our model can be applied. Most existing models that are used to estimate individual qualities deal with 1-vs-1 matches, with a single quality per player and a single binary outcome per match. Our model is an extension of existing models; providing a structure to deal with multiple individual qualities, for many-vs-many matches and multiple outcomes per match, each with an ordinal outcome space. The goal was to create a model for any environment where groups of players compete with each other while only the collective results are observed. The research was conducted in partnership with SciSports, a football data analytics company, therefore we chose to apply the model to football. We considered multiple existing models like ELO, Glicko, Bradley-Terry, Thurstone-Mosteller and the Microsoft TrueSkill. We combined ideas from these models with novel insights to define a probability model, defining the relationship between participating player's qualities and the match-outcome distribution. This relationship is essential for the inference of player quality parameters. The unknown parameters that define the player specific qualities are modeled as latent traits within a latent variable model. We started with a general model, developed in the field of psychometrics, and showed that it is equivalent to our desired model under certain assumptions. Furthermore, we discuss how ordinal observations should be interpreted and we find accurate and useful approximations for the ordinal outcome probability distribution given player participation. We list several existing estimation methods that can be used to extract estimators from the data by applying our probability model. The methods were taken from other research and modified such that they can be applied to our specific case. Eventually, we decided to use the Conditional Gaussian Inference method, which has been successfully implemented in Python. We applied the model to a historical football dataset, yielding two qualities per player; attack and defense. The results were tested with a subjective and an objective method, both methods show that our model produces useful results.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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