The holiday season is in full swing, and many people are more focused on cricket than on the state of the economy. Like in all team sports, a favourite pastime of fans is to argue over their choices of the greatest ever team. But there is one person who is an automatic choice. Don Bradman had a test match batting average of 99.94, and the second best average of all-time is just over 60. So just how special was Bradman?
Exceptional events, like Bradman’s average, have been the focus of intensive study in recent years. The financial crisis brought home to everyone the importance of so-called ‘fat tails’ in the distribution of the price changes of financial assets. The scientific methodology used by banks and regulators to assess the risk on portfolios allowed for the theoretical possibility of very large changes. But these were assumed to be so rare that the chances of them happening were in practice zero.
The crisis made it apparent that the science behind the regulators’ models was flawed. Very large price changes were still rare events, but they could certainly happen.
The question of how many large, rare events we can expect to observe has been around for a long time. A century ago, the Italian economist Vilfredo Pareto looked at the question of the distribution of income and wealth. Most people hadn’t got much of either. But, just as today, out there in the ‘tail’, there were a few people with stupendous levels of income and wealth. Pareto focused on this tail.
Mathematically, this tail looks very similar to the way asset price changes can be described. The number of dollar millionaires in the world is currently estimated to be around 12 million. That may seem a lot, but it is mere drop compared to the size of the world’s population. They are already in the ‘tail’. Most of these have ‘just’ a few million, and as the level of wealth increases even more, the numbers drop away sharply.
The same sort of mathematical relationship is found in the sizes of earthquakes and how often they take place. Earthquakes of magnitude 6 on the Richter scale are serious events which can and do kill large numbers of people. Since 1900, there have been around 100 of them every year. But during this period there have only been 5 earthquakes in total of magnitude 9.
In Test cricket, batsmen with career averages of over 45 are the elite of the game. There have only been 95 of them since international cricket began in 1882. 56 of them average between 45 and 50. Only four batsmen average more than 60, and three of them are just over this number. Bradman is 99.94. Even using the maths of the ‘tail’, the probability of observing this number is fantastically low, something like .2, preceded by eleven zeroes! Bradman was a true phenomenon, many, many times less likely than the most powerful earthquake ever seen.
As published in City AM on Wednesday 7th August 2013