MyScience.ie

There has been plenty of debate here in Ireland recently about Roy Keane’s decision to resign as manager of Sunderland. Keane has always been a figure you either love or hate and the weekend papers swung either way in their analysis. One viewpoint was that he simply didn’t want to make up the numbers in the Premiership and struggle to make up the numbers each season. The alternative was that when Keane doesn’t get his way, he simply walks.

Something which caught our attention over the weekend on a semi related note was Dr Chris Hope’s paper on ‘Measuring the vulnerability of managers in the English Premiership.’ Hope’s formula (pdf) sets out to investigate the strategy a football club should adopt when deciding whether to sack its manager. Interestingly when Hope originally set out his formula Peter Reid was manager of Sunderland and he was deemed most likely to be given the sack.

In the original model, the club’s strategy consists of three choices:

• The length of the honeymoon period during which it will not consider sacking a new manager,
• The level of the trapdoor, the average number of points scored per game; if the manager’s performance falls below this, he will get the sack,
• The weight that it gives to more recent games compared to earlier ones when calculating the manager’s performance.

There are five types of manager: poor, fair, good, excellent and world class. A club with a poor manager will on average be in the bottom three positions, a good manager will on average equal the mean performance of the 20 clubs in the league, and a team with a world class manager will on average be in the top three. Fair managers are in between poor and good, and excellent ones are between good and world class. But the club cannot observe the quality of its manager directly. Instead it looks at results on the pitch.

After his first game in charge the performance of the manager is given by perf(1) = result(1) where result(m) = 0 if the game was lost, 1 if the game was drawn, ad 3 if the game was won.

After any subsequent game his performance is given by an exponentially weighted average of his results to date:

perf(m) = smooth * result(m) + (1 – smooth) * perf(m-1)

We haven’t had the time to look up Keane’s performance to date to see whether Keane was right to quit or whether it was only a matter of time before he had to walk the plank given the recent run of games. However we may drop Chris Hope a line and see if he will shed some light on the subject.