Penalty shootout in soccer is recognized to be unfair because the team kicking first in all rounds enjoys a significant advantage. The so-called Catch-Up Rule has been suggested recently to solve this problem but is shown here not to be fairer than the simpler deterministic Alternating (ABBA) Rule that has already been tried. We introduce the Adjusted Catch-Up Rule by guaranteeing the first penalty of the possible sudden death stage to the team disadvantaged in the first round. It outperforms the Catch-Up and Alternating Rules, while remains straightforward to implement. A general measure of complexity for penalty shootout mechanisms is also provided as the minimal number of binary questions required to decide the first-mover in a given round without knowing the history of the penalty shootout. This quantification permits a two-dimensional evaluation of any mechanism proposed in the future.

中文翻译：

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足球点球大战设计的比较

足球中的点球大战被认为是不公平的，因为在所有回合中首先踢球的球队享有显着的优势。最近有人建议使用所谓的 Catch-Up Rule 来解决这个问题，但这里显示的并不比已经尝试过的更简单的确定性交替 (ABBA) 规则更公平。我们引入了调整后的追赶规则，保证在第一轮处于劣势的球队在可能的猝死阶段获得首罚。它优于 Catch-Up 和 Alternating 规则，同时仍然易于实施。还提供了点球机制复杂性的一般度量，作为在不知道点球大战历史的情况下决定给定回合中的先发者所需的最少二元问题数量。