How the new substitution rule affected Bundesliga results

This study empirically analyzes the influence of the so-called five-substitution rule on the results of the German Bundesliga. The rule, which was first introduced for the 2019/20 season as a temporary solution to the strains of the Covid-19 pandemic, was permanently incorporated into the regulations starting from the season 2022/23. While the primary goal of the rule change was to relieve the burden on players, it may also have an impact on match outcomes and dynamics. We show that while the total number of goals has increased, the probability of match outcomes remained constant. One could therefore conclude that the rule change has at least increased the entertainment value of the matches.