At the moment I’m doing a course on stats and it’s got me working out things like standard deviation by hand. If that seems pointless it is because in the age of Excel it is, but I’ve got to memorise it and practice it so what better way than doing this than to get some attendance data and trying to answer the question – which league is, in terms of attendances, the most equal. Just to start with I’ve stuck to the big-5 i.e the Premier League, Bundesliga, Premier Liga, La Liga and Ligue 1 and used attendance data for the 2012/13 season
First up is a rather simple measure of difference, the range. This is the difference between the smallest and largest observation – in this case the difference between the smallest and largest attendances in each league.
From the graph we can see a big difference between the three most unequal; The Bundesliga, La Liga and the Premier League and the more equal Serie A and Ligue 1. In the Bundesliga top club Borussia Dortmund an average attendance at 80 520 compared to SpVgg. Gruether Furth on 16 864, a difference of 63 656. In Ligue 1 by contrast top club Paris St Germain had an average of 43 239 compared to AC Ajaccio who had an average attendance figure of 6 801; a difference of 36 438.
The range is though quite limited and can be swayed by extreme values. Another measure is the interquartile range – that is the difference between the upper and lower quartiles (the lower quartile is the point at which 25% of the observations are equal or less than and the upper quartile is the point at which 75% of observations are equal or less than) . This has the effect of chopping off the extreme values.
This produces a slightly different graph. Notably Spain drops back. This is undoubtedly due to the effect of ignoring Real and Barca who are outliers in terms of attendances. With them out of the picture Spanish clubs are actually a lot closer together in terms of attendances. Serie A though moves in the other direction. This is because Serie A is an oligopoly with several big clubs Inter, AC Milan, Juve, Napoli, Roma and Lazio all drawing bigger crowds whilst at the other end a larger number of clubs draw much lower crowds. Again too it is Ligue 1 which emerges as the most equal with an interquartile range of 9 854.
Another measure still is standard deviation (SD). Easy to work out using a spreadsheet, less so by hand! This shows how clumped around the mean (average) the figures are. A high SD means more spread (and therefore more unequal), whilst a low figure means the numbers are more bunched together (and therefore more equal). The difference from the previous two methods is that SD takes into account the whole distribution.
What we get is a graph which looks quite similar to the first graph, showing the range. Once again Ligue 1 emerges as the most equal. There is one problem with SD however, and that is it can be quite hard to compare when the means are so different; For example the Bundesliga has a standard deviation of 17 039, which is similar to the 17 265 of La Liga, but the mean attendance in the Bundesliga is 46 624, compared to 28 327 for La Liga, so comparatively there is less variation in the Bundesliga.
One way around this is to use a coefficient of variation. This converts SD into a percentage of the mean. If we do this we get the following result.
Strangely the Bundesliga and Premier league now look more equal, the coefficient of variation showing that comparatively there is less variation between attendances than the highly unequal La Liga. Ligue 1 appears more unequal as using the other measures the difference between attendances have appeared lower because the overall numbers are lower for all clubs in the league. Looking at this in proportion shows that attendances are similarly unequal.
Perhaps it is interesting to look at results. The Soccer by Numbers blog looks at the standard deviation of wins for the big five and the Eredivisie for the 2010/11 season and finds that La Liga, the Eredivisie and the Premier League are the most unequal with Ligue 1, Serie A and the Bundesliga being much more equal.
Another stat is to look at the number of different league winners in the ten years between 2003/04 and 2012/13
Even taking into account the dominance of Lyon over the earlier part of the period, Ligue 1 seems the most open with six different winners. In fact since 2007/08 a different club has won the league championship each season.
So is Ligue 1 the most equal league of the big five? Well, it depends how you look at it, but on balance it seems that Ligue 1 is the most equal with the smallest absolute differences in attendances between the clubs. The highest number of different league winners also suggests a more open league, certainly when compared with the highly unequal La Liga.