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Billy Beane has a theory. He has had to hold to it pretty tenaciously because it isn’t a theory most people take to naturally. Here it is — people don’t change.

The general manager of the Oakland Athletics baseball team has achieved great success for his club with very little money. As recorded in Michael Lewis’s book Moneyball (which no Fink Tank reader should miss), one of the reasons for his success is the players he obtains. He waits to see them develop, missing out on hot prospects. And then he signs up only those player who have demonstrated the precise skills he wishes to acquire.

The scouts for the Oakland As were forever trying to get him to sign up players they could work on, players who would grow into the role. But Beane was obstinate. He thought that if a player had a flaw, that flaw would stay with them, it wouldn’t be trained out. Players don’t change.

You can hear the scout view replayed all the time when the Premier League is being discussed. A new player is signed up and doesn’t start well. He will develop, though, the fans comfort themselves. Next season will be better. This theory is at its strongest with foreign imports. The idea is that the Premier League has its own distinctive signature. It takes time to get used to. So you can’t expect a foreign player to be at their best straight away. Give them time, they will play themselves in.

Is this true? Dr Henry Stott, Dr Ian Graham and Richard Berriman have been looking at the stats.

The Fink Tank ranks players each season based on their contribution on the pitch. Our model links every kick to the points those kicks bring. By simulating the competition over and over again with players included and removed, we can see how many points each player adds to their team in a season compared with an average player in their position.

With this work in our database, we were able to pull out those foreign players who had arrived in the past four seasons and had stayed for the succeeding season. Overall we were looking at 63 players. We knew how well they had done in their first season. Did they get better?

When we looked at the data, it seemed at first that the answer was yes. Comparing those who started in 2005-06 with their performance in 2006-07, there was a statistically significant performance. That means that we could be 95 per cent sure that the difference was not just a random fluctuation. So foreign players improve as they get used to the Premier League. (Not all of them, of course, but on average).

Not so fast. When we looked at the next two comparisons — 2006-07 starters and 2007-08 starters — we saw that the opposite held. We found that players got worse on average in their second campaign. What is going on? Well, it seems that being 95 per cent certain that the 2005-06/2006-07 finding was not a random fluctuation wasn’t certain enough.

That first season comparison had tricked us.

Overall, the finding was pretty solid and unyielding. On average in their first season, the foreign players added 0.88 points more than the average player in the same position. And in their second season they added 0.86 points. In other words, the idea of foreigners playing themselves in to our unique Premier League is another of those footballing myths.

And, incidentally, players from these islands who join a club don’t change significantly in their second season either. What you see at first is what you are getting. Billy Beane’s law holds for football.

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