The decline of luck in football

Recently I wrote about the gradual increase in inequality when looking at Premier League clubs number of wins per season. To recap – over time there has been a long-term tendency for the number of wins to be shared less equitably among the competing teams.

One explanation I offered for this was luck and as luck would have it as I was pondering this I came across Ed Smith’s book Luck.

In this Smith makes the argument that football is, by its nature, determined significantly by luck

The huge size of football’s currency unit – the goal – makes luck a far greater force in football than in other sports. A net cord, we already know, can randomly determine a single tennis point. But it would be staggeringly unlikely that one player could get enough lucky net cords in one match to change the result. In football, by contrast, one lucky score is all you need.

Citing Stefan Szymanski he adds however, that the Premier league and its brand of financial inequality have acted to reduce the role of luck over a season, with the number of wins correlated with a clubs financial muscle – though he does maintain that when it comes to individual games there is still a role for luck to play.

One way of visualising the degree of luck in football (in Luck Smith points to a similar exercise involving American Football) is to observe the distribution of wins. The more luck (which is random) plays a part in determining the results the more the chart will represent a normal distribution – or to use its other name the bell-curve – which is the sort of distribution you’d end up with if results were determined by flipping a coin, or rolling a dice.

bell curve

Taking the 1929-30 season we can see that the distribution of wins is distinctly bell-curve like. In other words what we’d expect with a random distribution.

2930 season graph

Moving forward to the last full season in 2013-14 however, the distribution of wins over the season looks much less like a bell-curve with a breakaway number of clubs clumped at the far end; Man City, Liverpool, Chelsea and Arsenal.

1314 season graph

This is, of course just a snapshot, but below is a few more charts which suggest that over time the distribution has changed

5960 graph

7980 graph

8990 graph

9900 graph

0910 graph

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