# European Football - How much is chance?

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

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.

Is football just a matter of luck? Just because a team ends up top of the league, does it really mean it is the best team? We have taken most of the major league football games played in Europe since 1993 and created an animation that shows what happened in each league and how much of the apparent difference between the teams was due to chance alone.

## What does the animation represent?

#### The main bar chart

The main bar chart describes the number of points that each team has after each match of the season. A single step of the animation corresponds to a match between two teams in which a winning team scores three points, a drawing team scores one point, and a losing team scores no points.

By default, teams are listed alphabetically. Clicking on 'Sort' causes the teams to be listed in order of points gained. If two teams have the same number of points then they are ordered first by goal difference, second by goals scored, and third alphabetically.

#### The point distribution graph

Click on the 'Point distribution' button and a grey column chart appears at the bottom of the screen. The horizontal axis of this column chart coincides with the horizontal axis of the bar chart; both measure the number of points scored. The height of a column in the point distribution graph records the number of teams with the corresponding amount of points. Thus a column with horizontal position 22, and height 3, indicates that, at that moment in time, precisely three teams have 22 points.

All leagues award three points for a win, one point for a draw, and zero points for a defeat.

#### The chance distribution graph

Click on the 'Chance distribution' button and a white column chart appears at the bottom of the screen. Again, the horizontal axis of this column chart represents the number of points scored. This time, however, the heights of the columns represent the values we would expect if each game were determined by chance alone.

What do we mean by the 'chance distribution'? Take the English Premier League in the 2008-09 season. if the teams were exactly equal, then each match would end up as a home win, draw, or away win with chances 45%, 26%, or 29% (these are the percentages of home wins, draws, and away wins that occur in the season). By chance alone one team would top the league, another team would be bottom of the league, and, following a simple calculation, we would expect most of the teams to get between 35 and 66 points. The animation's 'chance distribution' shows the expected spread if games were decided randomly using the figures 45%, 26%, and 29%. These percentages would roughly be replicated if, for example, the referee flips a coin and declares a home win if heads turns up, and if it's tails then the referee flips again and declares an away win if heads turns up, and a draw otherwise. This would save a lot of time and money, but it would not be a great spectator sport.

#### The % variance due to chance

The large white number in the bottom right hand corner labelled '% variance due to chance' is a measure of how far the point distribution is from the chance distribution. A small number indicates a large spread in team quality, and a large number indicates that teams are of similar ability.

So in the English Premier League we can say that 21% of the variability is due to chance and 79% due to genuine differences between the teams. This is a low contribution of chance, comparable with that in Greece and Turkey where the leagues contain a wide range of talent. Some leagues, in contrast, have contained teams of essentially equal ability where the league positions at the end of the season could be totally attributable to chance: for example the Scottish 2nd Division in 2002-2003 in which after 36 games each the teams all finished between 36 and 59 points: poor Cowdenbeath were at the bottom but the points show that they were really no worse than any other team, just the unluckiest.

More information on the animation is provided on this page, including the mathematics behind the 'chance distribution' and instructions on how to embed the animation in your own website. In Chance Leagues we have simulated a league based entirely on chance, to help you compare real league tables with chance league tables.

See Premier League for a discussion of luck in the distribution of points in the Premier League, and check out our predictions for the final week of the Premier League 2008-2009 in One game to play!.

Football results have been extracted from Football-Data.co.uk.

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