From one to 403 - the full listings

Five of the best and worst

So here you have it. Every Premiership player’s season, ranked. How did Fink Tank do it? We used a multivariate Poisson log-normal model. I hope you find that information helpful.

Dr Ian Graham and Dr Henry Stott used the model to allow us to identify the relationship between goals scored and every kick of the ball made by every player for every club. Once this was done, they simulated the league season over and over again, removing players one by one and replacing them with an average player in his position.

This allowed them to see whether a player added or subtracted points from his team compared to an average replacement. The best player this season would be the one who added the most points.

But this process did not yield us the player of the year automatically. There were a couple of dilemmas to overcome.

The first was whether to take into account periods out with injury or not being played. Robbie Keane, for instance, is a fabulous player, but for one reason or another he spent only 47 per cent of the season’s playing time on the pitch for Tottenham Hotspur. Should we just ignore this?

We decided not to. Players were penalised for being out of the team. We multiplied the points added in our simulation by the proportion of time on the pitch. This produces one controversial feature of our ranking. If a player adds points compared to the average, they rise up the table the more they play. But if they subtract points, then the more they play the lower they are in the rankings. We take the view that they are making their team worse the more they play.

The other dilemma was more complicated. Gilberto Silva added more points to Arsenal than any player did to any team in England. Should he be the player of the year? The case for him is simply his importance to his team. But the case against him is that he was boosted by the fact that there were fewer impressive Arsenal players during this campaign for him to share the points with. A Manchester United player might have been better but had to split his contribution with four of five other stars.

So we hit on another way of calculating the player of the year. We looked at how many points a player would add to an average team, giving us an even playing field. This is not the perfect solution – Wayne Rooney may score more than a Sheffield United player simply because of the quality of Manchester United’s passing – but we thought that it was fair.

So what was the outcome? Here are a few headline points. Cristiano Ronaldo deserved to be crowned player of the year. The data confirms that judgment.

Also, Frank Lampard is fabulous. The common view is that Steven Gerrard is better than Lampard. Well, we cannot pass comment on basic skills. We are ranking the contributions made by players this season, not ranking abstract talent. Perhaps Liverpool do not let him breathe. Or something. But Fink Tank is absolutely clear that the free-scoring, great-passing Lampard is a towering figure. And Gerrard? He came 80th.

Finally, England and Tottenham have a goalkeeping problem. We rank 403 players and Paul Robinson came 402nd.

Now feel free to roam our rankings yourself.

HOW IT WORKS

The Fink Tank Predictor provides forecasts and ranking systems for English and European club football, based on a statistical model of matches based on more than five years of football scores.

In looking at player rankings for this season, the phrase “time-adjusted points” means the number of points the player would have added to an average team in the full season, compared with an average replacement. The points are then adjusted to reflect the amount of time spent on the pitch – minimum 400 minutes.

THE TOP 10

KEY: Player, club, position, pitch time, time-adjusted points

1 C Ronaldo Manchester United Midfield 85.12% 19.12

Voted player of the year by his fellow professionals and by football writers, the 22-year-old Portugal winger is our man of the season as well

2 F Lampard Chelsea M 97.31% 16.24

An ordinary season for Lampard? The statistics say otherwise

3 Gilberto Arsenal M 88.14% 16.01 P

Ten league goals was a remarkable return for the midfield man

4 Cech Chelsea G 50.15% 14.41

Chelsea missed their ’keeper desperately when he was injured

5 J Lehmann Arsenal G 97.30% 13.94

He may be 37 but the German is still among the league’s elite

6 P Scholes Man Utd M 79.10% 13.50

Enjoyed spectacular return to form after last season’s eye injury

7 T Howard Everton G 94.59% 12.96

Failed to make the grade at Old Trafford but a Goodison star

8 N Vidic Man Utd D 66.11% 10.48

The centre back was rock-solid in his first full season in England

9 B McCarthy Blackburn F 88.98% 9.91

Eighteen goals in 36 starts proves McCarthy is a lethal predator

10 A Hleb Arsenal M 68.14% 9.87

Not as flashy as some of his teammates, but highly effective