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Life’s a beach ball, and then you die. After the freak goal by Darren Bent brought defeat by Sunderland, one or two pundits wondered if Liverpool fans were too accepting of the injustice. Perhaps, they speculated, the Kop has finally tired of Rafael Benítez. Perhaps they were looking for a chance to get rid of him. And the beach ball provides a chance.

But if that is what they are thinking, then I believe they are making a mistake.

Dr Henry Stott, Dr Ian Graham, and Dr Mark Latham have been untangling a tale of two seasons. Liverpool did so well last season, staying in the title race until it was nearly over. But now our progress chart suggests that they are already down to little more than a 3 per cent chance of lifting the trophy. Manchester United have won (in 2002/3, Fink Tank’s first season) after having a 4 per cent chance in mid November. But there is, well, a 97 per cent chance that this won’t happen to Liverpool this season.

What is going on? And should it be laid at Benítez’s door?

The simple answer, at least as far as it is possible to answer it this early in the season, is that nothing much is going on. But to see what I mean you have to understand the last campaign.

A team such as Liverpool begin the season with a range of places they can finish in given their quality. Luck and the variable performance of other sides might change the place the side finish in even if their performance doesn’t vary. So we know the probability that they will finish in a certain place, without, naturally, being able to offer any certainty.

For this reason, a team has a chance of winning the Barclays Premier League even if they aren’t the best side. The table, in other words, does lie. The best side might be defined as the one that would be the favourite on a neutral ground against any opposition from the Premier League. And you can determine this, as we do, by a model employing a weighted measure of goals and shots on goal.

The longer the season lasts, the more chance there is that the best team will win the title. But in a 38-game season, reasonably short from a statistical standpoint, even the third and fourth ranked sides have an appreciable chance of winning the title, while still remaining third or fourth best.

And this, pretty much, is what happened to Liverpool. They started last season ranked in third equal place with Arsenal and with only a 10 per cent chance of winning the title. In the middle of the season their chance peaked at 20 per cent, before dropping off again. In other words, we were always pretty confident that Liverpool wouldn’t win the Premier League.

Nevertheless, by coming second, Liverpool exceeded our expectations for a team of their quality. And it is not surprising at all that they have dropped back off again this season. Their start to this season is more what we would expect of them.

So what is behind it? Three things seem worth mentioning. First, they have stayed steady in quality but have changed with their defence getting weaker and their attack getting stronger. They are letting in a large proportion of the shots on goal. They need to put this right.

Second, Xabi Alonso was, next only to Steven Gerrard, their best player. It was a disaster to lose him to Real Madrid.

But most importantly — the money. Our figures show that Benítez outperforms the wage bill. Blame the Americans. Not Rafa.