BMI: Lessons from D&D
By Bryan Caplan
A lot of social scientists are now interested in the effects of the BMI, or Body Mass Index. In the metric system, your BMI is equal to your weight in kg divided by your height in meters squared. If you prefer English units, switch to pounds and inches and multiply by 703. If you’ve got a secure body image, put your own measurements into this BMI calculator and see what it says.
If you think about it, however, there is something strange about this formula. Height is one-dimensional, but mass is three-dimensional. If you double the height of a cube, for example, its mass goes up by a factor of 8. Cubically, in a word. This has been very clear to me since 1984, when I read a fascinating article in Dragon Magazine which helps you, among other things, figure out how much your Hobbit weighs.
Laugh if you must, but this ultra-nerdy article raises serious questions about the BMI. If you really want a benchmark of obesity, weight ought to be cubed, not squared. Otherwise, you can have two identically-proportioned individuals, yet rate one obese and the other under-weight. Example: A 6’8”, 230-pounder gets a BMI of 25.3 – overweight. An identically-proportioned person 4’8” in stature would weigh (56/80)^3=.7^3=.343 times as much, or 79 pounds – and gets a BMI of 17.7 – underweight!
Yes, I had to make my examples awfully tall and awfully short. But the point is that the BMI overstates the obesity of the tall, and understates the obesity of the short. If you buy the argument that the dangers of higher BMI are continuous, there are a lot of tall people we’re needlessly scaring, and a lot of short people we’re giving a false sense of security.
But isn’t it ultimately an empirical question whether (weight squared/height) predicts bad health better than (weight cubed/height)? Sure. But if the first measure wins a statistical horserace against the second, there’s a surprising implication: health nuts need to start watching their height as well as their weight.