Power Law and q-Exponential Distribution in Football Goalscoring

In the present study, we investigate the power law distribution as a model for heavytailed statistical distributions. We look at the main parameters of the power law model, as well as statistical methods used to test its applicability. The method is applied to goalscoring data from the top five European leagues from 1977/78 season to 2024/25 season on a season-by-season basis. The p-value is determined, and the results are plotted as a time series. We also consider the Tsallis entropy formalism, and focus on q-exponential distribution, which is a result of maximisation of Tsallis entropy. Particular attention is given to the parameter q. It is fitted to data of top scorers and players with most goalsand- assists (GA) of multiple national leagues across multiple seasons. The obtained values of q are found to be consistent with previously reported results. We also apply both distributions to lists of top scorers from multiple clubs. Finally, we discuss possible connections between the obtained statistical behaviour and tactical or structural aspects of modern football.