The Betfair Prof / Leighton Vaughan Williams / 08 July 2008 /

The Betfair Prof, Leighton Vaughan Williams, looks at how to judge the impact of a change of manager and how prediction markets can add to the insight...

As Luiz Felipe Scolari takes over the reins at Chelsea, I'm reminded of Prime Minister Harold Wilson's dictum that there are few jobs more stressful and more precarious than that of a front-bench politician but the post of football manager is certainly one of them. Well, opinions are divided about the benefits of sacking those who run the country, and it is difficult to devise a measure which all would agree upon, but there is a great deal of published analysis available which allows us to judge the effect of a change of management in other fields.

This literature can broadly be sub-divided into three distinct theories. According to the "common sense" theory, when a team is under-performing the manager is replaced, and if a better manager takes over, performance should improve. In the "vicious circle" theory, poor performance tends to trigger managerial change, but the disruption caused tends to make things worse. Then there is the "ritual scapegoating" theory, in which the appointment of a new manager makes no difference, on average, to team performance.

Rick Audas, Stephen Dobson and John Goddard sought to disentangle the competing theories, for the case of English football, in an article published in the Journal of Economics and Business. In that study, they conclude that a within-season change of manager tends, on average, to have an adverse effect on the results of matches played by that team during the remainder of the season.

To be precise, a typical game between two teams that had not changed their manager for the previous 20 games had match outcome probabilities of 46.3% for a home win, 24.7% for the draw, and 29% for an away win. For the first match following a change of the home team's manager, the chance of the win declined to just 42.5%.

For the second match following the change of home team manager, the probability of a home win was 44.7%, up on the probability for the first game but still significantly down on the situation before the new manager arrived. Eventually, the probabilities reverted to where they were before the change of management. The findings were little changed whether the changes of manager were voluntary or involuntary.

In light of these findings, is it possible to offer a rational explanation for existing attitudes to management change? The answer to this question is yes, and it lies in a thing called "variance", which is the dispersion of results about the average. A change of manager may not improve performance on average but it does shake things up a bit. In other words, it's a bit like a throw of the dice, with the odds in favour of the house.

It's dangerous to apply a general rule to any specific case, but to the extent that we can this means that we might be able to emulate the house by opposing Chelsea in the markets, especially for the opening few matches. Then again, this is no ordinary management change and it is not taking place mid-season. So is it worth that throw of the dice? You decide!

Professor Leighton Vaughan Williams is the Director of the Political Forecasting Unit and Betting Research Unit of Nottingham Business School, Nottingham Trent University, and Editor of the Journal of Prediction Markets

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