Football tactics helped by maths formulae

On the eve of the World Cup, scientists Mike Wright and Nobuyshi Hirotsu from the department of Management Science, have used software based on formulae devised by a Russian mathematician to help to predict the best time during the game to make a substitute, the optimum time to switch from defence to attack, and even to judge the probability of scoring in the time left.

In the calculations, based on an analysis of data from Premiership games, the researchers developed a series of equations to deal with variables and probabilities.

The formulae also includes data on how the team performed in the past, and when individual players had been put on or taken off. All this is fed into a computer. At least in theory, outcomes the kind of answers that premiership managers are paid millions to make.

"It is at an early stage, and there are always going to be limitations because you have to make assumptions and you would need to account for players getting tired, or not playing as well as usual," said Mike Wright, whose research appears in the Journal of the operational Research Society. "It could one day be used at the pitchside, more as a guide than a precise rule. But we are not at that stage yet. We need to include more analysis, more on players and formations and so on. Whether or not it does eventually get used will depend on football's culture.

"If you look at American football or baseball, they have people analysing things to death before, during and after a game. Some of the top sides have their own full-time analysts. When a baseball manager is thinking of substituting a pitcher, as well as considering how the player is playing, he will also chat to the analyst sitting next to him".