Chance has a genius for disguise. Frequently it appears in numbers that seem to form a pattern. People feel an overwhelming temptation to deduce that there is more to the events they witness than chance alone. Sometimes we are right. Often, though, we are suckered, and the apparent order merely resembles one.
To see why, take a bag of rice and chuck the contents straight into the air.
Observe the way the rice is scattered on the carpet at your feet. What you have done is create a chance distribution of rice grains. There will be thin patches here, thicker ones there, and every so often a much larger and distinct pile of rice. It has clustered.
Now imagine each grain of rice as a cancer case falling across a map of the United States.
Wherever cases of cancer bunch, people demand an explanation. The rice patterns, however, don’t need an explanation. The rice shows that clustering, as the result of chance alone, is to be expected. The truly weird result would be if the rice had spread itself in a smooth, regular layer. Similarly, the genuinely odd pattern of illness would be an even spread of cases across the population.
This analogy draws no moral equivalence between cancer and rice patterns. Sometimes, certainly, a cancer cluster will point to a shared local cause. Often, though, the explanation lies in the complicated and myriad causes of disease, mingled with the complicated and myriad influences on where we choose to live, combined with accidents of timing, all in a collision of endless possibilities that, just like the endless collisions of those flying rice grains, come together to produce a cluster.
Michael Blastland and Andrew Dilnot, The Numbers Game