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 .
The sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares eight different rules, suggested for soccer penalty shootouts, to determine the order of actions . 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 , it remains sufficient to use static rules in order to improve fairness. However, it is worth compensating the second-mover by making it the first-mover in the sudden death stage. Our work has the potential to impact decision-makers who can achieve better outcomes in dynamic tournaments by a carefully chosen sequence of actions .
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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
sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares eight different rules, suggested for soccer penalty shootouts, to determine the order of actions
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considered here
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the
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save valuable resources by choosing only theoretically competitive policy options for field experiments
achieve better outcomes in dynamic tournaments by a carefully chosen sequence of actions