I’ve been reading Malcolm Gladwell’s book Outliers: The Story of Success. One of the examples he gives early in his book studies the best Canadian hockey players. A disproportionate number of the top players were born in the first quarter of the year.
The eligibility cutoff for age-class hockey league assignments is January 1. Those with birthdays early in the year will be older when they are first eligible to play for a given age group. On average, these children will be larger and more skilled than those born later in the year. Being a few months older is initially an advantage, but It would seem that it should wear off over time. It doesn’t. Those who had an age advantage, coupled with talent, developed a little more confidence and received a little more attention than those who did not. The advantages of extra confidence and attention carried on after the direct advantage of age disappeared.
I wrote a post a while back that looks at this sort of situation in some mathematical detail. Suppose the abilities of two groups are normally distributed with the same variance but the mean of one group is shifted just slightly. (The post I referred to looks at male and female Olympic athletes, but we could as easily think about Canadian hockey players born in December and January.) The further you go out in the extremes, the more significant that shift becomes.
For another example, think of how heights are distributed. Men are taller than women on average, but it’s not unheard of for the tallest person in a small group to be a woman. However, as the group gets larger, the odds that the tallest person in the group is male increase exponentially. As it turns out, average heights of men and women differ by about six inches. But even if average heights differed by the slightest amount, the odds in favor of the tallest person in a group being male would still increase exponentially as the group size increases.