Compensating tendencies in penalty kick decisions of referees in professional football: Evidence from the German Bundesliga 1963–2006

Abstract

Using a large representative database (12,902 matches from the top professional football league in Germany), I show that the number (441) of two-penalty matches is larger than expected by chance, and that among these 441 matches there are considerably more matches in which each team is awarded one penalty than would be expected on the basis of independent penalty kick decisions (odds ratio = 11.2, relative risk = 6.34). Additional analyses based on the score in the match before a penalty is awarded and on the timing of penalties, suggest that awarding a first penalty to one team raises the referee's penalty evidence criterion for the same team, and lowers the corresponding criterion for the other team.

Keywords:

• Decision-making
• biased decisions
• Bundesliga
• sports statistics

Acknowledgement

I would like to thank Prof. Jeff O. Miller, University of Otago, New Zealand, for his helpful commentaries.