Sacking your manager is pointless and a result of bad luck and the stats prove it

It feels a little like Agatha Christie’s And Then There Were None, adapted for the Premier League. A quarter of the way through the season, four managers have already been sacked.

Booting out managers does work - just not for the reasons people think. Teams who sack their managers do enjoy a short-term uplift in their results. But this doesn’t have anything to do with the new managers.

Managers are not only sacked when their teams are at a low-ebb. They also tend to be sacked when their teams are being extraordinarily unlucky. The football consultancy 21st Club analysed the points earned by teams in the big five European leagues in the eight games before and after sacking a manager. In the eight games before a manager leaves, the team averages 0.8 points per game. In the eight subsequent matches, they average 1.2 points per game - a clear improvement. But based on expected goals - the quality and quantity of chances created and conceded - the team actually ‘deserved’ 1.2 points per game in the eight points before the manager left, exactly the same as they actually got under their new boss.

So what really changes with the new manager isn’t their new tactics or motivational team talks. It’s simply that they don’t suffer from the old manager’s bad luck.

Except, if a struggling manager is persisted with, the team’s luck improves anyway - and their results improve by as much as if they had been sacked. That’s why, on average, Premier League sackings make no difference at all to a team’s performance, as a study of Premier League sackings from 2000-2015 found. Comparing underperforming teams who sacked their managers after a terrible run to those clubs who kept their managers after the same dire form, the group of Dutch academics showed that results improve, and by the same amount, regardless of whether or not the manager is sacked. Studies of other leagues have shown the same.

The ‘managerial bounce’ is a chimera: this phantom bounce is nothing more than regression to the mean. On average, an in-season replacement of the manager has zero effect on performances, either during the season or in the long run.

This isn’t to say that managers can’t make a difference at all. It’s just that you have to be an exceptionally good or bad manager to do so, and the overwhelming majority of managers are bunched in the middle, where replacing one with another will statistically have no more impact than fans starting to go to games in a pair of lucky socks. In English football from 1973 to 2010, Stefan Szymanski found, only 10 per cent of top-flight managers consistently overachieved when wages were taken into account.

And panic-stricken teams who sack their managers after a couple of dodgy deflections in mid-season hardly have their pick of the elite 10 per cent. Instead, unless they are prepared to spend a lot poaching another club’s manager - and most teams either aren’t, or don’t have the means to - they are left fishing in the pool of unemployed managers.

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Most are unemployed for a very good reason: they are not elite. New research from Szymanski and a team of economists finds that, in English football, clubs who have just sacked a manager tend to replace them with a “low talented, experienced” replacement. In a quarter of cases, the new manager actually has a lower estimated ability than their predecessors. So much managerial tinkering is churn for churn’s sake, without clubs giving any proper regard to whether the new boss will genuinely be any better than the old boss. Sometimes a club’s manager may indeed be mediocre; sometimes they should still be retained, for all the plausible alternatives are even worse.

Why, then, does the never-ending cycle continue? The reasons go well beyond football.

90 per cent of drivers believe they are above average: humans are not very good at realistic self-assessment. This illusory superiority permeates football too: owners and fans are often incapable of seeing where their team really stands, rather than where they would like it to. The sobering truth is that, as Soccernomics shows, there is a 90 per cent correlation between teams’ wages and their results.

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Clubs also misinterpret randomness. Because football is a low-scoring game, results hinge more on chance than other sports. Who wins a football game is determined by 50 per cent skill and 50 per cent luck, Chris Anderson and David Sally explain in The Numbers Game, largely because about half of all goals occur after a moment of fortune - ball deflections, lucky bounces, a bad decision from a referee, or even the impact of a stray balloon left on the pitch. And the football season also has comparatively few games - each Premier League teams plays under half as many league games as NBA teams and under a quarter as many as MLB teams - so judgements are made on a comparatively small sample size. Add in the grave financial consequences of relegation from the Premier League, and you have a cocktail of endless, debilitating short-termism.

None of this is to suggest that all managers should be bullet-proof. Some sackings really are justified. West Ham, for instance, are 18th on 21st Club’s expected goals model this year, after an underwhelming 2016/17 season, suggesting that sympathy for Slaven Bilic should be limited.

Yet the broader point remains. The median length of an English football manager is only a year. Most of these sackings “are undeserved - they are overrated solutions” as Omar Chaudhuri, head of football intelligence at 21st Club, observes. Working as a consultant to clubs, 21st Club have helped stop managers getting the chop unfairly, by showing that poor results were down to bad luck, not a dramatic decline in underlying performances.

Where there is market inefficiency so there lies opportunity for those who recognise it. Rather than be seduced by the Fool’s Gold of incessantly changing their manager, clubs who splurge so much cash on sackings would be better off instead investing in areas - scouting, youth coaching or improving facilities - where it could actually make a difference.