# Is the Body Mass Index Pseudoscience?

## Introduction

Body Mass Index: It sounds so scientific, doesn't it? After all, the expression contains two scientific-sounding buzzwords: "mass" and "index." The originator of the concept was a 19th Century Belgian, named Adolphe Quetelet. Quetelet was interested in averages. Example: For a given height, what is the average weight of a person?

In 1972, Ancel Keys gave the concept its more familiar name, Body Mass Index, or BMI. In the 1980s, JS Garrow and JD Webster suggested arbitrary zones for the BMI--including "overweight" and "obese". And the rest is history.

Without getting too technical, here's the basic concept of BMI: **BMI = c*mass/height^2**

The "**c**" is a proportionality constant, that depends on the units you're using for mass and height. For example, we could use kilograms as the unit of mass. The hat symbol "^" means "to the power of."

That said, there are a few problems with BMI: basic maths, individual variability, and changes of body composition with age. If you're in a hurry, you can skip the Basic Maths section.

## The basic maths

Lets start with an ordinary brick, like the multi-colored one at right. You want to make a small brick pile that has the same proportions as the first brick, but is twice as big in all three dimensions. First you add a brick, in order to double the length. Then alongside that, you add two more bricks to double the width.

Then you add four more bricks on top of the first four to double the height. The total number of bricks is 8.

What have we just done mathematically? We've doubled every dimension. In the process of doing that, we've octupled the number of bricks and octupled the volume of the bricks. The 8 is 2 raised to the third power.

A similar relationship would hold for old and new masses. Now let's apply the concept to people.

Suppose that a tall person has the *same proportions* as a short person. Let their heights be represented as H(t) and H(s), respectively. If the shorter person has mass M(s), then we'd expect the tall person to have mass **M(t) = M(s)*[H(t)/H(s)]^3**

Hey, wait a minute! The magic formula for BMI says that we should use an exponent of 2, rather than 3. What's up with that? Examples 1 and 2 are preliminary feasibility calculations. **Example 1**: A healthy, normally-proportioned 5-foot-tall person weighs 100 pounds. What would we expect a 6-foot-tall person to weigh according to BMI?

The 6-footer should weigh **100*(6/5)^2 = 144 pounds**

That's downright scrawny! **Example 2**. What would we expect the 6-foot-tall person to weigh according to simple mathematical scaling?

In this case, the 6-footer should weigh **100*(6/5)^3 = 173 pounds**

which is within the normal range for healthy people.

Thus the BMI has a built-in bias: It tends to classify taller-than-average people as overweight. This isn't rocket science.

Yes, shorter people tend to be slightly wider in proportion to height, as compared with people of average height. (Head sizes of shorter people also tend to be larger in proportion to height.) You can see that in randomly selected photos of people. What to do about this scaling glitch?

Examples 1 and 2 show that an exponent of **3** is more realistic than **2** for estimating the weight of a person for a given height. With all due modesty, I propose the **Larry Index** **(LI)** as a reasonable compromise, and as a realistic alternative to Ancel Keys' BMI. **LI = c*mass/height^2.7**

Don't worry about the non-integer exponent. Any off-the-shelf scientific calculator can handle it. I would *not* use the LI for clinical purposes--even though it's more reasonable than BMI.

## The obvious question

A high BMI is correlated with increased risk of Type 2 diabetes, heart disease, various cancers, and osteoarthritis. Doesn't that put BMI on a sound scientific footing? Not really. Why not?

Obesity is a major risk factor for these health abnormalities. And BMI is a very crude measure of obesity.

Anyone who's 5 feet tall and 300 pounds is obese. And yes, the BMI would catch that. But do we need a bureaucratic formula to tell us the obvious?

A better test would be to stand parallel to a mirror, turn your head toward the mirror and see if you have a 'beer belly.' Or after you have showered and dried off, stand in front of the bathroom mirror, and jump up and down.

BMI underperforms in the borderline cases.

## BMI and individual differences

Some people have average frames. Others have larger-than-average frames. Still others have smaller-than-average frames.

A person having a large frame and/or a lot of muscle can be flagged by Body Mass Index as being overweight--even when he has low body fat. This was true for disgraced cyclist Lance Armstrong at one point in his athletic career.

On the other hand, a moderately overweight person with a small frame and an average BMI would be classified as normal.

As adults age, our lean muscle mass tends to decrease. If your body fat is borderline normal as a young adult, and your body weight remains constant over time, then you're putting on body fat; it may even increase into the unhealthful range. And no, the BMI will not catch that.

## Who uses BMI?

At best, Body Mass Index tells you what you already know from looking in the mirror. And BMI gives lots of false positives for overweight in tall people. It does not hold up under mathematical scrutiny.

If I had a physician who relied on BMI, I'd be very tempted to find a new doctor.

Personal trainers are qualified to design programs for people with specific exercise related goals--like managing chronic lower back pain. They also teach the proper form for doing various strength training exercises, in order to minimize the risk of injury. A personal trainer, who prattles on about BMI, is just trying to impress you with his 'knowledge'. Be patient.

## The not-so-obvious question

Oh yeah. What about insurance companies? Actuaries are sharp cookies, and they use Body Mass Index. I'm glad that you asked.

First, actuaries work with the information that's available. Since BMI is fashionable, it's what's readily available to actuaries and to other people who work with large collections of data.

Second, tall people are at greater risk of early mortality than people of average height. Since the BMI tends to flag tall people as being overweight, it's more useful in setting life insurance premiums than one would expect at first blush. With BMI as the rationale, insurance companies can charge slightly higher (and more realistic) life insurance premiums for tall people, without appearing to be discriminatory.

## Summary and conclusion

Excessive body fat increases the risks for several major health problems. Body Mass Index is a quick-and-dirty measure of overweight (and underweight). But it's not the best quickie method. The Larry Index is more realistic.

In her article, Hubpages author, Victoria Anne describes some methods that are better than the BMI for quantitating body fat.

The Body Mass Index is somewhat useful for insurance companies. And it's Politically Correct.

In terms of its dodgy mathematics, the BMI is borderline junk science. But in this respect, BMI is less egregious than Global Warming 'studies', in which most of the big-name 'researchers' cherry-pick, hide, or even fabricate data. Click on the link for my long hub on the subject.

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## Comments 8 comments

That's a very good article. Pity it's spoiled (for me) by casting all "global warming" researchers as counterfeiting data - which is an extremely serious allegation for a researcher.

In addition, many of the Global Warming guys are now sheepishly admitting that the recent warming trend was probably caused by increased solar activity, and not puny men.

Good article Larry. We accept far too many 'scientific' claims without doing the math.

(And then, there's that great scientist, Al Gore!)

I have no idea about the maths, but I always thought the bmi was a bit dodgy to say the least. I have no idea how it works when standing on a weighing machine, but to me if its scanning you, how can it tell with clothes on? sorry for being dim about it, but now I know what it means I can ignore it in future! lol! great article, nell

That's an inventive answer to an innseretitg question

8