Pulis sacking shows owners' failure to grasp probability

George Bernard Shaw said in 1944 that nobody should become a politician unless they understood probability. It was a good suggestion but 73 years later there is no indication that anybody listened.

And that is not surprising. Almost nobody understands probability in any walk of life. Not politicians. Not the people I know, not the people you know. Not football club owners.

Last Monday West Brom sacked manager Tony Pulis after ten Premier League games without a win. Even such a long run of bad results can occur naturally without the manager or players being at fault.

We may have reached the point where managers can be fired for sequences of results that will occur in the normal course of events. Not because the manager did anything wrong, not because the players did anything wrong, but because every now and again such things will happen.

Let me make a comparison. Suppose somebody employed me to play for them in a coin-tossing competition. I am trying to throw heads but eventually I throw tails ten times in a row. My employer sacks me and replaces me with someone else. But I have not done anything wrong. Any sequence of throws is possible. Sooner or later my successor will also throw tails ten times in a row.

Of course there are differences between tossing coins and playing football – but there are also similarities, enough for it to be a valid starting point in our discussion.

In August West Brom extended Pulis’s contract. So they were happy with him then. He won the first two games of the season. So they were still happy with him, we must assume. And then he went ten games without a win.

After West Brom had won their first two games, what was the chance that they would not win any of the next ten? I mean what was the chance that they would not win any of the next ten if Pulis and his players still worked at the same level that had been commended before? I reckon it was about one in 32 – quite small, but not vanishingly small.

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Before explaining how I got that figure let me give you some context. I looked at Premier League results from the last 20 seasons, 1997-98 to 2016-17. In that time there were 239 sequences of ten games without a win out of a total of 11,600 sequences of ten games. I will do the maths for you. About one in every 50 sequences of ten games contained no wins.

For elite clubs with big budgets the number would have been bigger, which means that for other clubs it would have been smaller.

Owners are entitled to expect what they pay for. In recent seasons West Brom’s payroll has represented between 3.3 and 3.4 per cent of the Premier League total. Over nearly 20 seasons other clubs with payrolls in that range averaged between 44 and 45 points. For WBA Pulis averaged 1.16 points per game, equivalent to 44 points over a season. In his two full seasons he provided 43 and 45 points.

What is the chance that a team playing well enough to feel they would be entitled to 44 or 45 points over a season will nonetheless not win any of their next ten games? I calculate that on average it is about one in 32.

Obviously the precise number will vary with opponents and venues. I went back over my ratings for Pulis’s last ten West Brom games to work out in this way the chance of them not having won any. I came up with a similar ratio: one in 35.

Johan Cruyff complained that most club owners know nothing about football so they are not qualified to hire and fire coaches, or for that matter decide which players should be bought or sold.

The situation is even worse than Cruyff thought, though. Not only do owners generally know nothing about football – they also generally know nothing about probability, which would help them understand how often bad things can happen without anybody being at fault.

Teams with reasonable expectations of 44 or 45 points over a season will average 14 points from their first 12 games. West Brom had ten points from 12 games when Pulis was sacked – just four below reasonable expectations, despite going ten games without a win. Four points can be lost with two touches of the ball.

Disappointed that prediction came true

In my last column of last season I wrote:

“I worry for Tony Pulis… He achieved his best Premier League finish of tenth in his first season for West Brom’s new owner. If Guochuan Lai is like many other owners he will expect an even better finish next season. But another rise is less likely than a fall, and if that happens Lai could turn on Pulis.

“Everything in Pulis’s garden looks rosy, which is when an admirer peeking over the hedge should wonder what might lurk unseen in the flowerbeds.

“There is little to choose between most teams in the Premier League. One can finish above another without being better, just because results broke more kindly for them. Next season, as likely as not, positions will be reversed. But when that happens owners and fans can get cross.”

Most unusually, I am disappointed to have predicted something that happened.

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