In this paper we investigate how the expulsion of a player influences the outcome of a football match. Common sense implies a negative impact for the affected team. However, an old football myth suggests that such an expulsion might also be beneficial since it increases the team spirit as well as the efforts of the affected team. We make use of a unique dataset containing all games played in a World Cup Championship between 1930 and 2002 and follow a twofold econometric strategy: We start with a conditional maximum likelihood estimator which is independent of the relative strength of the teams before we extend this estimator to take the relative strength of the teams and the minute of the expulsion into account. Our results indicate that the scoring intensities of both teams do not differ after the expulsion. Conducting scenario analysis reveals that the impact of a red card depends on the minute of the expulsion and does not have an impact at all if given at the end of the first half or later.
Poisson process (un)conditional likelihood football red card effect