The Value of a Red Card, Part 1

This is part one in a series of posts investigating the value of a red card.

In an article published in the Journal of Quantitative Analysis in Sports entitled Estimating the Effect of the Red Card in Soccer: When to Commit an Offense in Exchange for Preventing a Goal Opportunity authors Jan Vecer, Frantisek Kopriva and Tomoyuki Ichiba analyse red card events from the 2006 World Cup and Euro 2008 and use in-match betting market data to attempt to quantify the value of a red card in terms of the effect it has on a team’s expected goal scoring rate.

Their sample contained 26 matches from the World Cup and 3 matches from Euro 2008, of which 2 were discarded because the red card was awarded at the very end of the match, for a total sample of 27 matches. The complete list of matches along with time and recipient of the red card, as well as before and after goal scoring rates for both teams are given in Table 1.

Table 1: Rates of scoring of the sanctioned and the opposing team immediately before and after the red card.

From this data the authors derive the goal scoring rate for the sanctioned team and goal scoring rate for the opposing team ratios. They found that the goal scoring ratio of the sanctioned team is 0.663 and the goal scoring ratio of the opposing team is 1.237. In other words when a team receives a red card they score roughly two-thirds as many goals as they would have scored had the match continued 11vs11 and the opposing team scores (or equivalently the sanctioned team concedes) roughly five-fourths as many goals as they would have scored (conceded) had the match continued 11vs11.

The method of using in-match betting market data is interesting and a useful alternative to methods used in previous studies (e.g. Ridder et al. (1994) and Bar-Eli et al. (2006)) attempting to quantify the value of a red card. Unfortunately for the authors the tiny sample size of red cards they use for their analysis makes any results they draw largely meaningless. 27 red card events is simply too small a sample size for us to put any weight in their findings. Before the results of this study can be trusted further work and a much larger sample size are needed.

In part two of this series I will present my own work on the value of a red card based on data from past Premier League seasons.