Mathematical Analysis of Sport

Students attended a lecture at Birmingham University with A Level maths students from other schools around the city. Dr Richard Mycroft discussed many issues surrounding sport such as using the Markov property to analyse the existence of form in sport and a Poisson process to model the progression of a football game to determine the optimum time to commit a foul. We considered the 2010 Luis Suarez red card. We then calculated the time into the game that a player should risk a red card to stop a goal, depending on the probabilities of goals being scored after that point in specific situations. We also considered permutations of teams to decide if a certain ‘unlucky’ draw is rigged. Finally, we discussed Elo ratings and how these can be easily found for players online to statistically  determine the probability of outcomes of matches.

In summary, students saw how even complicated systems with many outcomes, such as football games, can be modeled with anything from only a coin flip to an exponential distribution.