Global goal frenzy

It’s official: English football teams score fewer goals.

Soccer teams worldwide are scoring more goals than they ought to be, whereas English teams seem to follow statistical expectations. The news may delight fans outside England, but it is puzzling the physicists who have found that the chance of a high-scoring game is significantly greater than it may first appear¹.

John Greenhough and colleagues at Warwick University in Coventry, England, analysed the scores of over 135,000 football (soccer) games in the domestic leagues of 169 countries, played between and 1999 and 2001.

They found that games with a total of more than 10 goals occur only once in 10,000 English top division matches (about once every 30 years), whereas they make up about one in every 300 games worldwide – which means that there is roughly one per day.

Low scoring games seem to follow a random probability distribution: the chance of a particular score is more-or-less what one would expect if there is a constant, random probability of a goal at any moment throughout the game.

In such a random process, bigger scores become increasingly unlikely. There are more 1-1 draws or 2-0 victories than there are 6-1 victories, for example. According to the rules of statistics, the chance of a high score should become less and less likely, the higher the scores become – something called a Poisson distribution.

But physicists have known for several decades that football games are far from normal. The chance of goal scoring doesn’t stay even throughout a match, but depends on the previous number of near-goals. The Poisson distribution can be modified to allow for this, resulting in a ’negative binomial probability distribution’.

In a further analysis Greenhough and colleagues find that for English league and championship matches for the seasons 1970-1971 and 2000-2001 the total scores of all matches fit a negative binomial distribution well. In contrast, domestic matches worldwide produce many more ’extreme events’ (high scores) than predicted by this statistical distribution.

Why the difference? Does it mean that the English defence or goalkeepers are unusually good, or the strikers are unusually poor? Possibly, but there may be a statistical explanation: in terms of probability, football games may behave more like the stock market or earthquakes.

In recent years, statistical physicists have realized that probabilistic processes underlying these complex phenomena show something called strong correlations.

Correlations arise when the behaviour of one part of a system is strongly influenced by the behaviour of other parts. In football, this suggests that goals become increasingly likely as their number mounts up. Fans and players will already have an intuitive notion of the effect. When trailing by 5-0, say, a defence is more likely to ’crack’ than when the score is 2-0. Even if the teams are well matched, the game becomes more ’volatile’ if it reaches, say, 4-4: goals then begin to flow more readily.

Why English teams don’t show this effect so strongly is a question sure to provoke endless debate among armchair strategists.

References

1. Greenhough, J., Birch, P. C., Chapman, S. C.& Rowlands, G. Football goal distributions and extremal statistics. Preprint, (2001).