## On parity in the Premiership

There seems to be a near continual background discussion as to the level of parity in the Premiership. Whilst there have been various big fours around for the majority of the Premiership era, or at least since the turn of the century,the exponential improvement in Man City, coupled with upticks from both Spurs and Liverpool over the past couple of seasons have expanded this group, leading to Simon Gleave christening the top group of ‘Superior 7’ teams at the top of the league, sitting above a ‘Threatened 13’, whose aim each season is simply to avoid relegation. With that in mind I wanted to take a numerical look at the level of parity in the Premiership, and whether that level of parity is changing over time.

There are a few metrics that occur to me as good ways to express the spread of team talent in a given Premiership season. The first is points, the second is goal difference, and the third is the rating I calculate for each team (a rough outline of the calculation of which may be found here and here). The larger the spread of each of these metrics, the less parity there is in the league.

I’ve taken each of the 14 seasons beginning with 2000-01 and ending with 2013-14, and looked at the spread of their values (where the spread is simply defined as the standard deviation). First I’ll show the three plots, and then discuss what they show beneath. The plots are already pretty large, but full size versions can be viewed by clicking on them.

Lets begin with the things that the plots have in common. First of all, each of the slopes are positive, which suggests that the level of parity in the league is decreasing over time. Secondly, if we take the line of best fit for each plot, both points and ratings suggest have standard deviations 18% higher, when x=14 than when x=1, whilst for goal difference the value at x=14 is 28% higher than the value at x=1 (for more on the value of goals over time see appendix 1).

Further detail becomes much easier to visualise if I normalise the values for each metric. Basically what I’m doing is saying ‘in the study the average stdev of points was 16.9 points. If I divide each of the numbers from the points plot above by 16.9 then a season with a stdev of 16.9 points would have a normalised value of 1.00, which represents an average level of parity. A season with a stdev of 15.2 points would have a normalised value of 0.90, whilst a season with a stdev of 18.6 would have a normalised value of 1.10. And, as before, the higher the normalised value, the less parity was in the season. I’ve done this for each of the three metrics and plotted them together below.

So for any given season we have a pretty good agreement between the three models. For example there’s a consensus that ’00-01, ’03-04, ’05-06, and ’10-11, were all all seasons that exhibited a lot of parity, and that ’07-08, ’09-10, and ’13-14 were seasons in which there was a pretty disparate spread of talent.

The rating seems to differ a little from the others around the middle of the century, particularly in ’04-05. Over the 14 seasons in the sample the ’04-05 versions of Chelsea, Arsenal, and Man United are rated in the top 15 teams. Of the 12 other teams that complete the top 15, 7 won titles, 4 failed to win the title but that seasons title was won by a fellow top 15 ranked team, and one team failed to win the title in the year that the title was won by a non top 15 ranked team. In short, being rated as highly as AFC, CFC, and MUFC were in ’04-05 is a rare feat. The discrepancy between the rating and points/goal difference was somewhat expected – goals translate directly to points, but they are only included as a relatively minor part of the calculation of a teams rating. In all the ratings line up well with the points, and if we consider the differences between their normalised values the standard deviation is <9%, which I'm actually pretty happy with.

Finally, lets split the sample in two even parts – the first seven seasons ('00-01 – '06-07) and the last seven seasons ('07-08 – '13-14). In the first seven seasons 16 points lie below the line of y = 1, whilst only 5 lie above it. In the latter seven seasons there are 16 points that lay above the line and only 5 below. What this suggests is that there has been less parity in the league the last seven seasons than there were in the seven seasons before that. Basically, the R^2 values for a given metric are low enough that I'm not happy saying the effect is sure to continue, but I think we can at least tentatively say that there appears to the level of parity in the Premiership appears to be on the decline.

Appendix 1. There’s a weak correlation between the value of a goal and time. It turns out that a goal was worth about 0.73 points over the course of the 2000-01 – 2004-05 seasons, but only 0.70 points over the course of the 2009-10 – 2013-14 seasons.