A Markovian model for football penalty shootout

This paper introduces a Markov transition model to analyse the kick-first effects on a football penalty shootout. Two different penalty shootout rules are considered, the ABAB rule currently used in football tournaments and the tennis-type tie-break ABBA rule as an alternative which is tested in the lower level football leagues by UEFA. A likelihood inference approach is used in our real data analysis, for the UEFA Euro2020 final penalty shootout. Both the theoretical results and the simulation studies not only confirm that under the ABAB rule the kick-first team has an advantage over the other team, but also find that the advantage can be gained via the leading score advantage. In addition, this paper shows that such kick-first advantage will become more significant for the teams with a higher penalty scoring probability, i.e. for the teams at the higher leagues. Therefore, our results imply that UEFA ABBA type penalty shootout trials in the lower leagues may not be helpful on comparing the two different rules.