The standard rule of soccer penalty shootouts has received serious criticism
due to its bias towards the team kicking the first penalty in each round.
Therefore, the rule-making body of the sport has decided in 2017 to try
alternative designs. This paper offers an extensive overview of eight penalty
shootout mechanisms, one of them first introduced here. Their fairness is
analysed under three possible mathematical models of psychological pressure. We
also discuss the probability of reaching the sudden death stage, as well as the
complexity and strategy-proofness of the rules. In the case of stationary
scoring probabilities considered here, it remains sufficient to use static
rules in order to improve fairness. However, it is worth compensating the
second-mover by making it first-mover in the sudden death stage. Our work has
the potential to impact decision-makers who can save valuable resources by
choosing only theoretically competitive policy options for field experiments.Comment: 23 pages, 3 figures, 4 table
