Applied Mathematics Commons^™

Football: An Intransitive Endeavour, Joe Walsh, Ian Timothy Heazlewood

Joe Walsh

It has long been established that competitions should be structured to give each team a fair chance of winning. The aim of this research paper was, considering similarities of shared parameters between codes, to investigate intransitivity in football codes. Variables effecting probabilistic outcomes of games were identified for the football codes: soccer, gridiron, rugby union, rugby league and touch football. An algebraic probabilistic model for obtaining tactical advantage in individual transition states was developed. Hypothetical teams were constructed in order to test the possibility of intransitive games states. It was clear that intransitivity could logically exist for a variety of …