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Do people and companies choose optimal strategies under various situations? If not so, why not? Pursuing the reason for this helps to understand individuals and companies. In addition, game theory has been heavily involved in the understanding of sports, economics and other social sciences. In this study, we focused on football’s penalty shootout where data is relatively easy to collect, mixed strategy can be applied and making a pay-off matrix considering our own probability is possible. Using the pay-off matrix, we obtained optimal strategy of the kicker in the penalty shootout and revealed the gap between the optimal strategy and actual action taken by players. We compared the probability distribution for each data attribute in the dataset in order to obtain the cause of the gap. We use 100 professional penalty shootouts (total 1032 kicks) which were collected from internet video site during the period from 2001-2016. Experimental results showed that there was a gap between the optimal strategy and the actual action taken by players and that it also suggested the position and team attributes and temporary scores of the shootout and kicking order involved in the gap. Considering them we made the hypothesis and estimated the cause of the gap. We hope this method can apply to other fields than sports.

Do Professional Football Players Follow the Optimal Strategies in Penalty Shootout?