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A Sergio Aguero shot heading toward goal is like a dice rolling out of a tumbler

Football stats and philosophy from Kevin Pullein

Man City's Sergio Aguero and Raheem Sterling
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One of the reasons we can be wrong about what will happen next is that we were wrong about what happened last. Or rather we misinterpreted what happened before.

When a football team win we assume they did something good that made them win, and when they lose we assume they did something bad that made them lose.

We might disagree about what those things were, but not that there were such things. We accept the score as an unimpeachable truth, for which we then seek an explanation. In some matches, though, the score gives a false impression of the play.

Last Tuesday I watched Newcastle v Burnley on television. I had company so, unusually for me, the sound was on. Newcastle scored in the 24th and 38th minutes and won 2-0. The commentators praised Newcastle and criticised Burnley. They said Newcastle had played well and Burnley had played badly.

I was confused. This was not what I had seen. I saw each team have a similar number of shots with Burnley’s coming from better positions.

Newcastle’s first goal came when defender Fabian Schar shot from almost 30 yards. One commentator said it was a wonder goal. Ninety-seven times out of a hundred after such an attempt a commentator will ask incredulously: “Why did they shoot from there?”

Burnley defender James Tarkowski missed from five yards. Perhaps four times out of ten in similar circumstances a player will score.

Given the quantity and quality of opportunities created by each side, I thought, the fairest score might have been a 1-1 draw or a 2-1 win for Burnley.

Often I turn on the sound after a match and hear descriptions of a contest I do not recognise. They seem to me to be mostly rationalisations of the score.

Who am I, you might ask, to say this? It is a fair question. Obviously the studio guests know a lot more about football than I do. They are former players and managers who have participated in hundreds of matches.

I would accept that my way of watching matches is as inaccurate as most shots from distance were it not for one thing. These rationalisations of the score in the last match become the build-up story for the next match, and many times what it leads us to anticipate does not occur. Last Saturday Newcastle lost 2-0 at West Ham.

And there is more, as the comedian Jimmy Cricket used to say. Football professionals think like I do when they are working for a club and preparing for the next game. A manager does not ask his analysts for the opposition’s recent results. He asks them how the opposition played in previous games.

When Ruud Gullit managed Chelsea he asked little-known European opponents for some tapes of past matches. They sent the tapes but with their goals erased. Gullit laughed. To plan how Chelsea should play, he did not need to know how their opponents had scored but how they had tried to score. This would give him a much better idea of what Chelsea might have to cope with.

In technical language, goals are a randomly distributed function of attempts.

Sergio Aguero has averaged one goal every five or six shots for Manchester City. He is much better than an ordinary Premier League player, who will score once every ten shots. Let us, though, do Aguero a slight injustice and say that he averages only one goal every six shots. It will make for a neat comparison.

Aguero shooting a ball then will be like you rolling a dice. Suppose that every time you roll a six you will get what you want and every time you roll any other number you will not get what you want.

Keep rolling that dice. After you have rolled it many times you should find that in about one-sixth of the rolls you got a six – probably not in exactly one-sixth but something close to. Why, though, did you get a six this time and not that time? There is no way of telling. It is like this with Aguero’s shots and goals.

Let us imagine now that in each of a long series of games Aguero has six shots. He will average a goal per game. But he will not score one goal in every game. Sometimes he will not score. Other times he will score two goals or more. In about a third of all games he will not score. In about one out of every 15 games he will score three goals or more.

When Aguero gets a hat-trick or better and goes home with the match ball he will be described as clinical. When he does not score he will be described as uncharacteristically wasteful.

But Aguero will not be aware of doing anything different when the ball goes in than when it does not. And we will not see anything different. Stop film of each shot at the moment Aguero kicks the ball and nobody will be able to distinguish the ones that go in from the ones that do not.

Hopefully Aguero has realised that he plays pretty much as well in every match, regardless of how many shots he has or whether any go in. And if he has not, hopefully his manager, Pep Guardiola, will tell him. Opponents should have the same expectation of him no matter what has happened in the past few matches.

What we see next, from any player or from any team, may not be what we saw last because what we saw last may not be what we should have seen.

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When a football team win we assume they did something good that made them win
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