Was Leicester’s achievement last season unprecedented?

On 25th May 2016, Leicester City were crowned premier league champions for the first time in their 132-year history. A team that had only just escaped relegation the previous year had achieved a seemingly impossible feat. At the start of last season many bookmakers in the UK were offering odds of up to 5000/1 for Leicester to win the league; it’s very hard to find odds longer than 5000-1 offered on anything.

For me, the most striking statistic was that Leicester accumulated 40 more points in the 2015/16 season than the previous season, enough to take them from nearly relegated to champions. How unlikely was this?

The formation of the EPL in 1992 is generally viewed as a watershed moment for top flight football. Billions of pounds in TV money were pumped in, and the image of the sport altered from that of a male-dominated, largely working class pastime to a more family-friendly pursuit for the middle classes. The grittier, more rugged edges of the sport were smoothed away. Out went the terraces and in came plush all-seater stadiums. And up went the prices. A lot.

This injection of finance and general facelift are oft-cited as having made the sport less egalitarian. The conventional wisdom is that, without a substantial influx of cash from a multi-billionaire owner, only a small number of teams have the resources and financial fire-power to make them realistic contenders for the title.

Prior to 1992, England’s top division is thought to have been a more equitable, competitive league. In the 24 years that preceded the formation of the EPL, 21 different teams were able to finish in the top four places; in the EPL era only 14 have managed this.

So, one might think that Leicester’s win was a throwback, an anachronistic return to a bygone era before sporting romanticism was buried under a great big pile of cash. But is this really true? Is Leicester’s win more unusual in this era, or would it have been unusual in any era?

As I have said, for me the key feature of Leicester’s win was their 40-point increase from the previous season. So in order to answer this question, we need to ask another one: in the post-war epoch, on how many occasions has a team managed to improve its previous season’s total by 40 points or more?

Performance improvement over consecutive seasons.

To answer this, I looked at the history of the top division in England since 1945. This amounts to 70 seasons and includes a total of 60 different teams.[1]  

For every season to 2015/16, I compared the number of points obtained by each team in the league that season with the number they obtained the previous season (assuming they hadn’t just been promoted – I only look at points in the top division). All points totals are calculated on a 3 points for a win basis. Over all seasons and teams in my sample, this provided me with 1290 ‘pairs’ of points.

In Figure 1 I plot these pairs of points. Each blue cross shows the number of points obtained by a single team in consecutive seasons, with the first season on the x-axis and the following season on the y-axis. For example, I’ve circled and labeled the cross that indicates the points obtained by Leicester in the 14/15 & 15/16 seasons.

The central dashed line indicates where the same points total was obtained in successive seasons; the upper/lower dotted lines indicate where teams obtained 10 more/less points the following season (which is just under 1 standard deviation).
Figure 1: points obtained in successive seasons for each team in English top division since 1946.

As you’d expect, there is a strong correlation: better teams consistently accumulate more points than weaker teams, season after season. However, there is large amount of scatter, with teams frequently obtaining 10 points more or less than the previous season.[2]

However, it’s immediately clear that Leicester’s performance between the 2014/15 and 2015/16 seasons is highly unusual. In fact, across the 70-year history only one other team has ever matched their 40-point improvement: Arsenal in 1969/70 to 1970/71, and this was in a 22-team league rather than the modern 20-team league (i.e. they played 4, or 10%, more games). In statistical terms, Leicester’s 40 points improvement last season around a 3.6-sigma event. The probability of an improvement of this magnitude occurring turns out to be roughly 1 in 6000.[3,4]

So Leicester’s improvement last season wasn’t just unprecedented in the premier league era, it is arguably unprecedented in the post-war era. Viewed this way, what we should find remarkable is not that Leicester – by premier league standards a relative minnow – won the league, but the speed with which they did it. Other teams have risen from obscurity to prominence, but normally only after being purchased by wealthy owners, and rarely has success been immediate.

Leicester’s transition from relegation fodder to champions is, statistically, one of the greatest rags to riches stories ever told. Will we ever see the like again?

[1] In most professional football leagues in Europe there is promotion and relegation between leagues, with (typically) the 3-4 teams finishing bottom in a season being replaced the following season by the same number of teams finishing at the top of the league below.
[2] Note the y-axis goes to smaller values than the x-axis; this is because teams that were relegated in the first season are not plotted.
[3] Assuming the data is normally distributed: the distribution of the points difference from one year to the next shows that this actually is a reasonable assumption. 
[4] Everton's performance in the opposite direction in 1970/71, when they were a whopping 46 points worse off than the previous season, is even more unlikely. 


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