The standard design of soccer penalty shootouts has received serious criticism due to its bias towards the team that kicks the first penalty  . The rule-making body of the sport has decided in 2017 to try an alternative mechanism. Although the adoption of the new policy has stalled, academic researchers have recently suggested some other designsto improve fairness . This paper offers an extensive overview of seven such soccer penalty shootout mechanisms, one of them first defined here. Their fairness are analysed in three different 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 designs. Some rules are found to be inferior as they do not lead to a substantial gain in fairness compared to simpler mechanisms.  Our work has the potential to impact decision-makers who can save resources by choosing only theoretically competitive designs 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 . 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.
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an alternative mechanism. Although the adoption of the new policy has stalled, academic researchers have recently suggested some other designsto improve fairness
alternative designs
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seven such soccer
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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.
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