Point Score Systems and Cooperative Incentives: The 3-1-0 Curse

The purpose of this study is to analyze the consequences that point score systems in association football may have on potential collusion between teams. The study applies game theory and empirical analysis to derive and test hypotheses. The main findings of the article include Nash equilibria indicating a higher collusion potential associated with the 3-1-0 point score system than with the 2-1-0 system. Of particular interest is the finding that the competitive balance of the league affects collusion, and that (theoretically) high competitive balance in fact makes collusion more probable. Empirically, we are not able to prove that real-world participants do collude, but we provide circumstantial evidence that is consistent with collusion. The empirical analysis is based on a sample of 25 European top leagues with 823 played matches in the 2017 and 2016/17 seasons. These data are used to estimate uncertainty of outcome and draw ratio. We apply a standard t-test to test our main hypothesis. The main conclusion of the paper may hence be summed up as advice to reinstall the 2-1-0 point score system in association football.