A string of defeats often leads to the early departure of a football team’s manager. Such a decision can sometimes seem an arbitrary one, when factors beyond the manager’s control - player injury and suspensions can all contribute to the team losing.

Now a model developed by academics at the ICMA Centre at Henley Business School at the University of Reading in the UK takes much of the guesswork out of these decisions and could provide directors with the data they need when deciding on their manager’s future career.

Using a financial model known as bootstrapping, researchers Chris Brooks, a professor of finance, Adrian Bell professor in the history of finance and school director of teaching and learning, and PhD candidate Tom Markham looked at whether the performance of football club managers can be attributed to skill or luck. They stripped out factors such as transfer spending, wages and player absence and awarded managers points for each game, thus allowing them to assess the manager’s performance based on ability alone. Their model allows a comparison between the manager’s actual performance over a period of time against a model predicting what the team’s performance should have been.

The trio used data from the seasons from 2004/05 to 2008/09. Whilst in some cases the data supported the view of experts, in others it suggested an alternative view: for example the model supports experts’ opinions that Everton manager David Moyes was over-performing in his role, but based on match performances the model suggests that Sven-Göran Eriksson, whose role as manager at Manchester City was terminated at the end of the 07/08 season was in fact outperforming 95 per cent of results forecast.

Mr Markham says that there is a belief that wealthy teams can buy success. “However, our method is a big step forward as for the first time we are able to identify whether the number of points per game secured by the manager is due to the characteristics of the team or managerial skill.”

The performance of football club managers: skill or luck? was published last month on the Social Science Research Network.

● And still in the realm of mathematical models, an economist from the Kellogg School of Management at Northwestern University has used numerical models to examine decision making in consumer buying-selling scenarios.

When buying a car, a computer or even a house the customer relies on the knowledge of the salesperson or estate agent. Before parting with thousands of pounds a customer will first want to know as much as possible about a potential purchase and will look to the expert for answers.

In looking at such scenarios, Wioletta Dziuda, an assistant professor of managerial and decision sciences at Kellogg, says that although the salesperson or estate agent might point out a flaw - the previous models of the car were criticised for excessive fuel consumption, though this had now been corrected, or the house had recently had a crack in one room repaired - such information rarely puts off a potential purchaser.

Prof Dziuda points out that the expert may well present “a limited amount of negative information, bulking up his or her credibility by appearing honest”. However this is then often followed by considerable amounts of more positive information, which frequently sways the customer in favour of making the purchase. Prof Dziuda warns that the purchaser must be aware of the subcontext of the expert and recognise that there may well be further pieces of negative information which are being withheld. Purchasers, she says, often feel that because a negative piece of information has been revealed this must mean that the expert is more likely to be honest and so the negative information is therefore discounted when making the purchasing decision.

The buyer must not take the information at face value warns Prof Dziuda and must instead consider why this information was revealed and what possible information is being withheld.

The paper, Selling with selective disclosure, is published in The Journal of Economic Theory.

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