Currently, with nine games remaining my football team, Aston Villa, are bottom of the Priemiership.
They seemed doomed for regulations. Now almost every week, the local Radio Station DJ, Radio WM Paul Franks ask the depressed Villa fans – what is the probability of Aston Villa staying up? Now depending on how Aston Villa play in their last game, the answers ranges from 0 to 20%.
However, how did they come up with such a figure? Is a pure emotional response, football experience of previous club in the same situation or just good old gut feel?
Well, as we are talking about probability surely there is a mathematical way of finding the probability.
Now football is a funny old game, the closer we get to the business end of the season the more the form book is thrown out of the window. Let us look at the table as it stands on the 6th March 2016
By using the simplifying assumption (the form book is thrown out of the window) and the mathematical method – The Random Walk, one can calculate the probability of Aston Villa remaining in the Priemiership.
A random walk is a mathematical formalisation of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modelled as random walks, although they may not be truly random in reality.
By considering the bottom seven teams, a simulation of each team’s random walk to the end of the season is calculated. To every game to the end of the season, the random event of a win, draw or lost is allocated to the team. This is repeated over and over again to see how many times Aston Villa finishes outside the bottom three. The answer is 0.6%.
Everybody knows Aston Villa chances are slim, but with mathematics we can qualify our feelings.