Confusion about the "Law of Large Numbers"

An important concept in the theory of risk that seems to confuse a lot of people (journalists in particular) is the law of large numbers. The law of large numbers is a statistical law which implies that the average value of a randomly selected sample is likely to be close to the average value of the population from which the sample is drawn. The law of large numbers makes important risk pooling mechanisms such as insurance economically feasible. For more information on the law of large numbers, see the Wikipedia entry on this topic, entitled “Law of large numbers”.

Lately in the media, I have heard numerous (incorrect) references to examples of the “law of large numbers” at work. For example, this morning on Bloomberg Radio, an analyst was droning on about how the “law of large numbers” works to the “disadvantage” of large companies like Walmart. This analyst correctly observed that as large firms such as Walmart grow even larger, their opportunities for further growth in the future diminishes. This is an example of the “law of diminishing returns”, not the law of large numbers.

Fooled by Randomness quote

I really like the following quote from Fooled by Randomness (pp. 55-56): “Things are always obvious after the fact… It has to do with the way that our mind handles historical information. When you look at the past, the past will always be deterministic, since only one single observation took place.”

This describes well a common error that is made all too often, by the news media in particular. News reporting often involves studying risky phenomena after the fact; i.e., after a disaster has already occurred. Journalists are highly susceptible to this particular aspect of being fooled by randomness. Often their analysis only makes sense if one had the luxury of perfect foresight.