An Application of Contest Success Functions for Draws on European Soccer

A contest success function (success function) maps the level of efforts into winning and losing probabilities in contest theory. We aim to assess the empirical performance of success functions for draws and analyze the differences between European soccer leagues in terms of home bias, return on talent (ROT), and talent inequality. We use a data set with 10,569 matches acquired manually from transfermarkt.co.uk containing club-based average market values of the lineup of teams for each match played through 12 seasons from 7 major European soccer leagues. The results are obtained estimating the parameters of the success functions with a general maximum-likelihood method, and the hypotheses suggested by success functions are controlled with a probit regression. Two of the success functions outperform one conclusively. The difference in the performance between these two groups results from the contrast in the main determinant of the success function in allocating the probability of a draw. The high-performing success functions take difference in aggregate talent levels as the main determinant in drawing, while the other takes the aggregate talent as the main determinant. The results also show that there are major differences across leagues in terms of ROT, home bias, and talent inequality, despite the similarities in economic environment and the homogeneity in the rules of the game imposed across leagues. Our analysis sheds light on the contributions and implications of microeconomic theory to model sports and presents the differing characteristics of the European soccer leagues that impact match results significantly.