The trivial game
The gap between good and bad teams at the World Cup finals has narrowed dramatically over time. One measure of this is the average number of goals scored each game. Large differences in ability will be reflected in games in which teams are defeated by many goals. The average was 3.89 in the first competition in 1930, rising to a record 5.38 in 1954. There was then a sharp fall to 2.78 in 1962, and ever since it has fluctuated around 2.5. This is despite a big expansion in the number of teams in the finals from 13 to 32. Many matches are decided by one goal, even between teams many places apart in the world rankings. This narrow gap implies a big element of randomness in success or failure. Perhaps this is part of the persistent appeal of an essentially trivial game which has few possibilities for innovation.
The foreign prisoners fiasco has revealed just how little information we have on the number of crimes an individual commits over a lifetime. The best source in Britain is still the 1961 Cambridge Study in Delinquent Development, a survey of 411 males in a working-class area of London over 20 years. A third got at least one conviction over this period—49 got just one, 21 got two and so on up to the two individuals with 14 convictions. The Pittsburgh Youth Study, which began in the mid-1980s, recorded not convictions, but self-reported acts of delinquency. The average number of boys in the sample was 421. Amazingly, almost exactly a third report delinquent activity—the same proportion as in the Cambridge study—and the number of boys associated with each number of crimes falls away in almost exactly the same way.