How seriously should we take it? Hull City are third in the Barclays Premier League. Manchester United are eighth. Tottenham Hotspur are bottom. Does this reflect real performance, or is it just caused by the fixture list?

Over at Fink Tank towers, the team have taken their propelling pencils from behind their ears and set to work on an answer. Dr Henry Stott, Dr Mark Latham and Dr Ian Graham have come up with two different ways of looking at the league results.

The problem with the table as it is now is best illustrated by Manchester United. Having played Liverpool and Chelsea away they are at a disadvantage. Fortunately, however, it is possible to make adjustments for this.

The first way is to use the standard Fink Tank model. Using results over two seasons, the Fink Tank weights goals and shots on goal so that the most recent games count most heavily. This allows us to provide the probabilities of different outcomes when any teams meet.

We can therefore simulate the start to the season, showing the number of points that we would expect each side to acquire and comparing it with the number they got. You can then assemble a new league table that measures the quality of their start to the season. Not surprisingly, Hull rank top - they have exceeded expectations by 7.3 points. And, again not surprisingly, Tottenham rank bottom.

They have 9.3 fewer points than we projected they would have at this stage - an extraordinary gap. Liverpool (3.5 points above expectation), Portsmouth (3.2), Aston Villa (2.7) and Chelsea (2.5) have had good starts. Manchester United are pretty much bang on expectations. Everton (3.4 points below expectations), Newcastle United (2.3) and Arsenal (2.1) have done less well than they may have hoped.

It is notable, however, that these are not large figures. A single bit of bad luck could pretty much account for the lot.

There is another way of shedding light on the league so far. And that is to employ our old friend (well, my old friend, anyway) the Perron-Frobenius theorem. Here's how it works. First, you take the league table as it is. Then you include indirect wins. This means adding in all the points of the team you have beaten. So, when Hull beat Arsenal they have attributed to them not only the three points but all of Arsenal's points. If they had drawn, they would have been given one third of Arsenal's total.

You don't do this only once, you do this again and again. So you add to Hull's tally not only all of Arsenal's direct points but all of their indirect points, too (the ones added to Arsenal's tally from other teams they have played).

Then you add in all of the points of the sides beaten by teams beaten by Arsenal, and so on. The Perron-Frobenius theorem says that after you have done this for a while, the league table stops changing. Once it is stable, you can stop.

We did the same for the points lost - that is, we subtracted from a team's total all the points that they lost and all the points that were lost by the teams they lost to.

Confused? All you really need to know is that this exercise weights the league table for the hardness of victories.

The graphic allows you to see the points won and lost in the context of the difficulty of the schedule so far. Hull are not third, but they are not doing badly. Manchester United are right back up. And Tottenham? Still bottom.