Not long after the news came through that Sam Allardyce was walking off into the sunset, an experienced footballer turned to me and said: “Bolton are in trouble.” And he wasn’t wrong, was he?

Now normally, as you know, I’m not one to take such judgments all that seriously. I think we all tend to overestimate the influence of individuals once they’ve been interviewed on Match of the Day. But Allardyce is a different case. I think the difference he made was critical.

Let’s start with the most direct measure used by the Fink Tank’s Dr Henry Stott and Dr Ian Graham. The statisticians relate the size of club wage bills to the points gained by the team and then plot the numbers on a graph, giving a curve for the expected relationship. Managers whose clubs appear above the curve are winning more points than their owners should expect, given the wage bill, while those below the curve do the opposite.

And Allardyce? He is an “above the curve” manager and that was a consistent feature of his reign at Bolton. Each year the Fink Tank has been picking its manager of the season. Allardyce is the only person to come near the top every time we have done the calculation.

Can we work out why? I think we can. First let’s eliminate a theory that turns out not to work. We wondered if Allardyce’s teams were particularly efficient. In other words, did they turn goals into points better than other teams, winning more narrowly than most teams do, but winning nonetheless? It seems not. When we did the figure work, Bolton turned out to be pretty average.

So what about the transfer market? And here is where we spotted something odd. The Fink Tank player level computer model relates each move on the park, each touch of the ball, to the number of points the move adds. This allows us to rank players. And normally, as the graphic shows, the relationship is predictable. If we know what the players do on the pitch, we can work out the position that the club finish in.

Not for Bolton. As you can see, they are different. With those players doing those things, we would have expected them to finish nineteenth last season. They finished seventh. So what is going on?

The figures suggest that Allardyce was getting his players to adopt a different style, a different route to victory. So the things Bolton players were doing on the pitch to score goals and win points were not the same as the things other clubs were doing to win points.

Just take one example - getting shots on target, a crucial part of scoring. Statistical analysis shows that for most clubs playing well all over the field influences the number of shots on target. For Bolton this is not true. Only the number of shot assists and good crosses appears to have had an influence. For most teams, if they increased the number of good passes in a match, it was a real help. For Bolton it made no difference. This suggests strongly that Allardyce employed a more direct style of play, with much less fannying about with the ball.

Then in came poor old Sammy Lee. The former Liverpool and England midfield player decided that he was going to get the ball to feet and start playing in a more conventional style. Wrong answer. He took players who were not chosen for their skill at standard play and asked them to play in a standard fashion.

Keep Allardyce’s style or get new players. That’s the choice for Bolton. And it’s a tough one.

finktank@thetimes.co.uk

Fink Tank research is fuelled by Lucozade Sport