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.
[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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