The trade-off between goals and uncertainty of outcome in professional team sports

Abstract

Based on an assumption of an existing scoring probability difference be- tween two teams engaged in a football match, the conditional probability distri- bution given the number of goals in the match for the low quality team beating the high quality team, is derived. Furthermore, similar distributions for the high quality team beating the low quality team as well as a draw are also derived. Based on a Poisson distribution of goals, we discuss a potential for optimizing expected uncertainty of outcome (UO) by adjusting intra-match rules or league rules for team sports. The main variables in this regard are (i) the typical number of goals scored, and (ii) the evenness of competing teams. We identify a curve defining the optimal expected number of goals as a function of team quality difference.