Bryan Caplan  

BMI: Lessons from D&D

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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.


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TRACKBACKS (1 to date)
TrackBack URL: http://econlog.econlib.org/mt/mt-tb.cgi/575
The author at johnopedia in a related article titled BMI Farce writes:
    OK, so ever since the government introduced the Body Mass Index (BMI for short), I’ve hated the thing. It became quite obvious to me that tall people are penalized for being tall due to the poorly thought out formula. The fact that the governmen... [Tracked on October 4, 2006 9:33 PM]
COMMENTS (14 to date)

Having read that article many years ago, I occasionally inform people in the appropriate context (how much people weigh, or would weigh) that a cubic foot of human flesh weighs 47 pounds. This generally draws concerned stares and the comment that they really do not want to know how I determined this.

Max writes:

If you read the whole article about how the BMI came about, you'd be dumb-founded and it is still cited as major science on obesity. Many professional movie actors and models have been tested with the BMI, where the doctor said they have perfect health and (f.e. Johnny Depp) the BMI said they were overweight.

Also, when you do your turn and apply it to "short" people, it also gets out of the scale.

However, as an engineer, I am very cautious about this formula, because it doesn't even resemble basic physics, as you noted (mass per area). I mean, they conclude that mass equally distributed on a box, where the edges are of your body size, represents whether you are obese or not?
Well, what about differences in muscularity and true fat? What about heavier and lighter bones?

It is too simplistic to represent what "obese" means.

KipEsquire writes:

One of the most oft-repeated warnings back when the BMI was first introduced was that it was wholly inappropriate for children.

Fast-forward a few years, and we see calls for putting the number on students' report cards.

Splendid.

liberty writes:

As Max pointed out above, the problem extends beyond the basic math/physics, because the measurements are inappropriate even when calculated properly. Many athletes are "overweight" according to the measure though they may be the healthiest among us, simply because they have a lot of muscle and sometimes a naturally sturdy build. There are so many body types that do not conform to the BMI standard. I have a friend who is 5'11" and about 190; according to the BMI overweight (perhaps in part due to the height error) but 5'11" is not at the tail end of the height distribution covered, in any case she is actually very skinny. She has big hips, big bones in general and breasts - other than that she probably has very little fat on her body. The volume based body mass test, or a test that could actually determine muscle from fat would tell you she has very little actual fat.
http://www.new-fitness.com/body_fat_analyzing.html

Independent George writes:

I first learned about this in an evolutionary biology class. I remember one of the questions on the final was to explain why Godzilla would have trouble standing, much less destroying Tokyo, if it stood 400 feet tall. Good times.

Dr. T writes:

People aren't cubes. The relationship between mass and height in us non-cubic beings is not cubic. *Example: Typical weight for a 65" tall healthy, medium-frame man is 140 pounds. Typical weight for a 75" tall (1.154 times taller) healthy, medium-frame man is 174 pounds (1.243 times heavier). If there was a cubic relationship between height an weight, the 75" tall man should weigh 215 pounds (1.154^3=1.537; 1.537*140=215).

Using squared mass in the BMI calculation already overemphasizes weight. Using cubed mass would be much worse.

The BMI was not designed to assess degree of obesity or thinness. It was a 19th century construct used to assess fitness of average-sized individuals. In the past, health care professionals used height and weight tables adjusted for sex, frame, and muscularity to assess whether someone was too thin or too fat. But, the CDC and other government agencies decided that those tables are just too damn complicated. We will use one measure and one scoring system. Sex doesn't matter, frame doesn't matter, muscularity doesn't matter: BMI is the be all and end all of body habitus assessment. Grrr.

*Data from 1999 Metropolitan Height and Weight Tables for Men and Women According to Frame, Ages 25-59 with corrections for shoe height (1") and clothing weight (5 lb.).

Brandon Berg writes:

Typical weight for a 75" tall (1.154 times taller) healthy, medium-frame man is 174 pounds (1.243 times heavier). If there was a cubic relationship between height an weight, the 75" tall man should weigh 215 pounds (1.154^3=1.537; 1.537*140=215).

At six feet and 200 pounds myself, and not unusually fat or muscular, I see 215 pounds as a much more reasonable weight for a 6'3" man than 174.

Karl writes:

The medical community is moving away from BMI, slowly. See this article http://www.msnbc.msn.com/id/14483512/

meep writes:

FWIW, my husband is 6'3" and overweight when 174 pounds... for him. He's a really lightly built guy. If he gets over 175 or so, I start seeing a roll of fat around his gut.

Obviously, what one cares about is overfat, not overweight. You can have two people with same height, sex, and body fat %age, but very different weights due to muscularity. But body fat %age is difficult to measure, as I found out after a coach bruised my leg trying to pinch fat off of it (sorry, all muscle.) There's lots of different ways to try to measure fat, and the most accurate involve a lot of work (and money).

Swimmy writes:

According to the indicator I'm slightly underweight at 17.9. This would explain the number of women in my life telling me how much I need to gain weight. Well I don't need them and I don't need poor scientific calculators! Scrawny nerds for life!

Heather writes:

Well thats an interesting thype of measurement. But, honestly those charts are so ridiculous anyways. Whats the use of having them when nothing is every accounted for like body types (stocky, muscular, fat, short). Nothing is ever going to really prove statistically what is "overweight" "underweight" except society's ovearll perception of you...not squared or cubed.

aaron writes:

175#
5'8"
BMI 26.6
Overweight.

I have an athletic build. BMI seems to have for flaws than lack of dimension.

pelkabo writes:

Bryan, I looked at some data from the NHANES study to see if weight/height^3 gives a better fit to the data than BMI. See this post. The results may surprise you.

Bob Dobalina writes:

Having read that article many years ago, I occasionally inform people in the appropriate context (how much people weigh, or would weigh) that a cubic foot of human flesh weighs 47 pounds. This generally draws concerned stares and the comment that they really do not want to know how I determined this.

A cubic foot of water weighs 62.4 lbs, and a cubic foot of fat weighs 57.3 lbs. So how does human flesh weigh so little? Are you counting bones, or are organs made of really undense stuff?

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