Football Leagues

As of the 23rd May 2022 this website is archived and will receive no further updates.

understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

The Premier League is the main English football league, with 20 teams each playing a home and away against each other team making, 38 matches for each team in a season, and 380 matches altogether. Teams are awarded 3 points for a win, 1 for a draw, 0 for losing, and the league position is decided on total points, with equal points decided by goal difference (goals for minus goals against). At the end of the season the bottom 3 teams are relegated.

We can use the history of the Premier League table over the 2006-2007 season to see how the spread of points develops.

The animation below shows how often each of the teams performed up in the 380 games played in the 2006-2007 season. Click on the image to start and click on the fast forward button to speed up the animation. Click on sort to rank the teams by point score.

You need to install the Adobe Flash Player to see the animation.

Click to enlarge the animation

If you click on show histogram, you can see the current distribution of the total points for each team, and how it changes during the season. Check how two teams start to pull away from the rest, while other teams struggle near the bottom. But how much of this spread is due to luck and how much due to skill?

Luck or skill? considers what sort of distribution of counts we would expect if the teams really were all the same, and hence how much of the spread of points in the final league rankings can be explained by chance alone. We shall also assess the probability that the season's winner, Manchester United, really was the best team, and that the teams that were relegated (Watford, Charlton Athletic and Sheffield United) really were the three worst teams.

The 2007-2008 season

Here's an update to the animation showing the 2007-2008 season.

You need to install the Adobe Flash Player to see the animation.

Click to enlarge the animation