| Popis: |
Professional football is a business worth billions of pounds a year. Player recruitment is a key aspect of the business with expenditures directly related to it (in the form of transfer fees and wages) accounting for the majority of clubs’ budgets. The purpose of this study is to propose methods to assist player evaluation based on statistical modelling that could be used to support recruitment decisions. In this thesis we argue that if such methods are to serve as the basis of player valuation, they need to have predictive utility, since it is players’ future performance that clubs benefit from and thus should be paying for. We present examples of how simplistic approaches to quantifying a footballer’s skill lack such predictive character. The original contribution of this thesis is a framework for evaluating footballers’ worth to a team in terms of their expected contribution to its results. The framework attempts to address one of the key difficulties in modelling the game of football, i.e. its free-flowing nature, by discretising it into a series of events. The evolution of the game from one event to another is described using a Markov chain model in which each game is described by a specific transition matrix with elements depending on the skills of the players involved in this game. Based on this matrix it is possible to calculate game outcome related metrics such as expected goals difference between the two teams at the end of the game. It enables us to establish a link between a specific skill of a given player and the game outcome. The skill estimates come from separate, location specific, models, e.g. the shooting skill for each player is estimated in a model of converting shots to goals given the shot location. We demonstrate how recognising the involvement of random chance in individual performance, together with accounting for the environment in which the evaluated performance occurred, gives our statistical model a predictive advantage when compared to naive methods which simply extrapolate past performance. This predictive advantage is shown to be present when passing and shooting skills are evaluated in isolation, as well as when measures of passing and shooting skills are combined in the proposed comprehensive metric of player’s expected contribution to the success of a team. |
