English Premier League Scoreline Analysis: A Stochastic and Game Theory Approach

Abstract

Making an appropriate decision in the selection of sustainable club from other clubs studied involves the use of right statistical approach, hence the need for stochastic and game theory analysis of English premier league scoreline. The following clubs Manchester United (MU), Chelsea (C), Arsenal (A), Manchester City (MC), Liverpool (LP), Tottenham (T) and Everton (E) were studied for both home and away matches for the period of 2010/2011 to 2019/2020 season. The optimal strategy and overall optimal strategy for MR G and MR B were obtained for each season and the 10 seasons respectively. The result showed that Manchester United has the highest probability (0.29) of being selected by MR B and Liverpool has the probability of 0.27 of being selected by MR G. The matrix of flow was also obtained when Manchester United played against Liverpool, given that Manchester United is home, as WWWLWWDWDD, and when Manchester United is away and Liverpool home, as WDLWLLDDWW. The two and four step transition matrix was also used to predict the future matches and their probabilities obtained given the probabilities of the previous game. The limiting distribution of the transition probability matrix obtained showed that Manchester United has a 67% chance of winning Liverpool while Liverpool has a 33% chance of winning Manchester United, this shows that Manchester United is stronger at home. Thus, the two most sustainable clubs out of the seven clubs studied are Manchester United and Liverpool.