Football managers get sacked all the time. There’s near-constant speculation in the media about which manager will be the next to go. Bookies even run an annual “sack race”, with punters betting on which Premier League manager will get sacked first in the season. It’s difficult to think of a profession with worse job security.

Right now, Sam Allardyce’s job at Newcastle is looking vulnerable. He’s only been at the club for seven months, but the team are playing ugly football and losing, so there are calls for his head.

One of his senior players, Nicky Butt, has backed him using an argument that always comes up on these occasions: stability leads to success.

If you look at all the big teams, like United and Arsenal, they’re the clubs that have stood by managers for a long time. If we do that, I’m sure we’ll do it right.

[Source: BBC Sport: Allardyce has to stay, says Butt]

So the argument is that the big clubs have stood by their managers for a long time, so standing by their managers must be what made them successful.

The first concern with this argument is that it there may be some selective sampling going on. Man Utd and Arsenal may have had the same manager for years, but Chelsea have done fairly well recently despite sacking two successful managers since Abramovich bought the club a few years ago: Ranieri and Mourinho. Not all the big clubs have had stability. That’s a minor quibble though.

The real problem with the argument is that it seems to get the causal order wrong. Plausibly, it’s not standing by your manager that makes you successful; it’s being successful that makes you (more likely to) stand by your manager.

Sure, a few managers have been sacked when things have been going well on the pitch, but it’s much more normal for managers to get sacked when things are going badly. Even if stability didn’t lead to success, then, we would expect to see a correlation between teams doing well and their managers keeping their jobs.

Perhaps Man Utd and Arsenal don’t keep on winning because they’ve stuck by their managers; perhaps they’ve stuck by their managers because they keep on winning.