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. 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 consider the probability of reaching the sudden death stage, as well as the complexity and strategy-proofness of the rules. Some designs are found to be inferior because they do not lead to a substantial gain in fairness compared to simpler mechanisms. Changing the standard rule by reversing the shooting order in the sudden death stage improves fairness, while it remains less complicated than the regulation of field hockey shootouts . Our work has the potential to impact decision-makers who can save  resources by choosing only theoretically competitive policy options for field experiments.
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.
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Some designs are found to be inferior because they do not lead to a substantial gain in fairness compared to simpler mechanisms. Changing the standard rule by reversing the shooting order
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
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improves fairness, while it remains less complicated than the regulation of field hockey shootouts
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valuable