Should Rafa go?

by endlesspsych

Rafael “Rafa” Benítez Maudes find himself in one of the most uncomfortable positions possible for a big four club; outside the big four (at the time of writing Liverpool are seventh with 18 points) predictably this has led to stories circulating that Rafa might not be long in the Liverpool hotseat.

Rafael Benitez has held talks with his Liverpool bosses over the implications if the club fail to reach the last 16 of this season’s Champions League.

Discussions were also held on if the club fail to qualify for next season’s lucrative European competition.

The Liverpool manager revealed today that the club did not budget this term for anything beyond the group stages.

And Benitez insisted he was confident that financial problems next season will be avoided ‘because we will achieve a top four finish’.

In football management ability is judged on the results the manager gets, but only the results in the here and now. Past glories count for nothing and in a sense neither does the managers ability i such decisions. Rafas record at all clubs he has managed is P516 W287 D118 L111 which works out at a 55% record (at Liverpool he has a 57% record). He has been five time recipient of the Premier League manager of the month and twice UEFA manager  of the year and he has won seven trophies with Liverpool.

A 57% record doesn’t sound all that impressive but then again Alex Ferguson only has a 58% record Liverpool legends Bill Shankly and Bob Paisley 51% and 57% respectively, the other big four managers: Arsene Wenger 53% and Carlo Ancelotti 50% (before coming to manage Chelsea).

If we were to treat the result of a football match as akin to the top of a coin then we would expect managers to win about half their matches and loose half their matches. We can call this the expected result and we can use the observed result in a statistical analysis known as a contingency table a form of chi-square. We can then see if a managers performance is better than a coin toss, I’ll only be looking at Rafa but feel free to play around with the data above and other managers stats.

Using this calculation we find that there is no statistically significant difference between the amount of games Rafa has won and lost and the expected results if we had decided a coin toss. He does not appear to perform statistically significantly better then chance alone and yet he has managed to win seven trophies with Liverpool; how is this possible? Well it’s important to remember that statistical significance is not substantive significance: the statistics may say that Rafa has no effect on the team rather then chance but those looking at the trophy cabinet may disagree (or perhaps agree…).

However what this really illustrates is the folly of judging an individuals performance on results, mainly because of aphenomenon discovered by Sir Francis Galton called regression to the mean.

In statistics, regression toward the mean refers to the phenomenon that a variable that is extreme on its first measurement will tend to be closer to the centre of the distribution on a later measurement.

This implies that a managers results will tend towards a figure that represents their actual ability to inspire a team to victory.  In some seasons this will result in anointment – when the team performs above the managers ability and the manager is lauded and in others it will result in regicide – when the team performs beneath the managers ability. It seems likely that Rafa is experiencing a season of regicide and it could well, unfairly to my mind, cost him his job.

All because we don’t really understand statistics…

Although Rafa can perhaps take comfort from the fact that research shows that teams rarely perform better after a change of manager. They are afterall just the same team…