AUTUMN is fast approaching, and the focus of the nation’s sporting interest is switching. No sooner have our boys humiliated the Australians at cricket than a new challenge emerges in the shape of two important qualifying games for the football World Cup. The comedian Bob Doolally articulated the views of many when he said: “If courage, endeavour and guts were what counted, England would be world champions. But as long as football games are decided by arbitrary things like skill, what chance have they got?”
The question is perhaps rather deeper than Doolally suspected. Just how far are games in the World Cup decided by skill, rather than by purely random events? An obvious example of the latter would be a referee failing to spot that the ball has crossed the goal line. With a different referee, the score would have been awarded. But the outcome of a game may hinge on a myriad of trivial events. A player may slip on a divot and miss a crucial tackle, while only a few inches away he would have made it, for instance.
One perspective on this is given by the number of goals scored per game in World Cup competitions. A high average suggests that strong teams are beating the weak. Skill therefore shows through. But with a low number per game, random events can easily affect the outcome.
The World Cup started in 1930. There were only 18 games in the finals, no qualifiers being played, with an average of 3.89 goals per game. Next time, in 1934, there were qualifiers, with 5.35 goals scored per game. Teams were slightly more equal in the final stages, though the average here was still 4.12. Averages remained high until the finals of 1962. With 32 games played and 89 goals scored, the average was 2.78.
Over the next 50 years, there have been small fluctuations from competition to competition, but the trend is to an even lower number of goals. In 2010, despite an increase in the number of games played to 64, the average was only 2.25 goals a game. With such a low average, and with penalty shoot outs becoming more frequent, it is clear that the differences in skill between the teams in the final stages are pretty low. This even extends to the qualifying stages. In the 2010 competition, there were no fewer than 200 teams – almost every country in the world took part, some of them tiny. But the average number of goals per game was only 2.71.
A new book, The Numbers Game by Chris Anderson and David Sally, analyses in depth the major national leagues, and in particular the Premier League. Using a mathematical concept known as an “intransitive triple”, a term familiar to economists, they show that the results of almost 50 per cent of games in the Premier League are due to chance rather than skill. Perhaps it is this very uncertainty of outcome which accounts for the enormous fascination with the game. Even England can win the World Cup.
Paul Ormerod is an economist at Volterra Partners, a director of the think-tank Synthesis and author of Positive Linking: How Networks Can Revolutionise the World.