Small advantages show up in the extremes

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.

5 thoughts on “Small advantages show up in the extremes

  1. Tomato Addict (Dan)

    “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.”

    I confess my knowledge of Canadian hockey is several standard deviations below the mean, but there might be other explanations that are equally meaningful. For instance, an older player is more developed and therefore more likely to be drafted (do they do that?). The implication is that there are younger players, equally good, who never got noticed.
    Reading this again, my explanation might fall under “getting more attention”.

  2. A cousin of mine has a racehorse farm in Arizona. We stayed there in February and a foal was born. It turns out that almost all racehorses are born as soon as possible after January 1. Just as in Canadian hockey, racehorses’ ages for competition groupings are based on the calendar year in which they were born, regardless of when they were born in that year. The way it was explained to me was that officially all racehorses are born on January 1.

    Thus it is a big advantage for a racehorse to be born just after New Year’s. Racehorses are a big investment so considerable care is taken to time the births. I wonder if Canadian hockey fans do so, too?

    If so, the disproportionate number of players who are born in the first quarter could by itself explain a disproportionate number of top players who were born then, too. Of course it matters what you mean by disproportionate.

    A similar calculation surprised the heck out of a colleague of mine. He had just gotten the SEER cancer database and was looking at the lung cancer data and noticed that birth dates were included. Just for grins he decided to test whether a person’s astrological (zodiac) sign had a significant effect on their chances of getting lung cancer.

    Imagine his amazement when he discovered that they had a significant effect! Well, eventually he discovered that humans, like most mammals, do not give birth at a uniform rate over the calendar year. If I recall correctly he said there are something like 30% more births in the summer months. In fact astrological sign does not affect one’s cancer risk, but when the cases are divided up into groups by astrological signs the signs under which more people are born will have more lung cancer cases. If you assume that the birth rates are the same for the different signs, you will discover a significant astrological effect.

  3. I think that this correlates to the education of children also. I was born on October 30th and just barely made the cutoff date to enter Kindergarten at 5 years old. Most of my classmates were six to eight months older than I was. When talking to other people of the same situation it seems that there is a collective sense of struggling to keep up. I wonder if there are any definitive studies on this.

  4. I haven’t read Outliers, but I have heard of similar studies on hockey players. More professional hockey players (NHL) are born in the first half of the year, as you mention. Interestingly, top draft picks tend to be born later in the year. The theory is that, as kids, they were younger and smaller, so they had to be that much better (or work that much harder) to compete with their older, bigger, stronger peers.

  5. If most professionals are born early in the year but the top draft picks are born later in the year, does that suggest that top draft picks don’t last long in the NHL? It’s not a direct comparison since we’re talking about all NHL players but only the top recruits.

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