Calculating

Express anything as a number, a statistic, and it takes on the air of authority. The more apparently precise that number, the more digits after the decimal point, the more substantial it seems to people -- even if that very precise figure was arrived at through a speculative and arbitrary set of calculations.

Take, for example, "BMI" -- the body mass index. The paper ran a story on obesity yesterday, including a sidebar explaining how to calculate your BMI.

If your BMI is between 18.5 and 24.9, the article said, you are "normal." If your BMI is above 30, you are considered obese. But 18.5 or 30 whats? What are the units here? And how do you arrive at the figure that represents your figure?

To calculate your BMI, first take your weight in pounds and divide it by your height in inches, squared.

Already I'm skeptical -- dividing pounds by inches seems like an odd muddying of different measures. And why is your height squared? Height, after all, is a single dimension. I kind of thought that height, by definition, can't be squared. You start squaring things and you're no longer just talking about height, you're talking height x width.

Anyway, take this number, this plum-pudding of inches and pounds, and multiply it by 703. That's your BMI.

What explains the use of 703 as our constant here?

Why not use a good old, woven-into-the-mysteries-of-the-universe constant like pi? One arbitrary constant is as good as another isn't it? So why not use the time-tested ratio of the circumference to the diameter of a circle instead of the area code for northern Virginia?

The number 703 apparently gets plugged in just to make the final range of figures more manageable. Replacing it with pi would give everybody a BMI of less than one. But we can fix that by no longer squaring everybody's height all willy nilly, thus reducing the denominator in our equation.

So, using this new calculation, I find I have an ABMI (adjusted body mass index) of 7.85. Which means ...

It doesn't mean anything. Arbitrary nonsense with three digits after the decimal point is still arbitrary nonsense.

We ought to know whether we are skinny or fat without depending on some faux-authoritative bit of quantification. The current enthusiasm for calculating BMI is mostly harmless, but our gullibility for misplaced concreteness is a dangerous thing.

Comments

[JoXn Costello]

Any time you see a magic constant like "703" it's reasonable to wonder what's going on. In this case, it's a conversion factor, because the BMI is defined in terms of the SI units kg/m2.

The BMI is a useful tool -- for statisticians who are trying to estimate the general nutrition of a population. This is because population data sets are much more likely to contain individual height and weight measurements than they are to contain the electrical impedence measurements you'd need for a clinical diagnosis of obesity. It seems that there is a statistical correlation between BMI and the harder-to-obtain bioelectrical impedence which is good enough to give a valid, if vague statistical overview of a population's general nutrition status.

Your objections in the main still stand. BMI is a statistical tool. Applying it in any individual circumstance is very problematic.

See this wikipedia article on the BMI for a more detailed overview, of which my above remarks are just a summary.

[Richard A. Lovett]

Fred,

I'll second the above, but more strongly. My perspective is that I'm a science (and science fiction) writer by profession. What you've run into is a poor piece of science writing by someone who underestimated the intelligence of the average reader (a common failing in health stories).

JoXn correctly states that the 703 is a units coversion: it's a weird number because the scientists who developed the BMI concept worked in metric units. On a global scale, it's not they who are weird, but us for working in ancient units like inches, pounds, etc. When I've written about BMI, I've always given the formula in metric units, then said, something on the order of "if you do it in inches and pounds, you have to multiply the result by 703." Obviously, we could just have separate scales for scientists and the lay public, but that would be another source of confusion.

What BMI is, basically, is a measure of the "roundness" of your body. That's why height comes in squared, though explaining why is a bit difficult. BMI actually conveys this information quite well. A low BMI means you're a string bean. A high BMI signifies an NFL lineman. As those examples indicate, it's not the same thing as fatness. Large boned muscular people will have higher BMIs than fine-boned people like Kenyan distance runners, even if they have the same percentage body fat. But there's a subtantial correlation. If your BMI's below 18 or so, the word "anorexic" is very, very likely to describe you. If you're above 25, "overweight" is likely to apply.

Basically, BMI figures are the ones used to construct the weight ranges in the body weight tables that used to be more popular. BMI is more in the vogue today, but it's exactly the same thing as the "normal weight" range you can find in lots of tables, on line or elsewhere.

So, the problem here isn't the BMI concept. It's sloppy journalism by a reporter who either didn't understand it, presumed that the reader was too stupid or lazy to care, or didn't take the time to present it more carefully.

Any of those is worth exposing, and as a general matter, I love you posts. This time you fell victim to the sloppy science writing that gave you just enough to know that something was wrong, but not enough, without a nutrition or coaching background, to know what!

Sincerely,
Richard A. Lovett, Ph.D., J.D

[Beth]

Thanks Joxn and Richard, for explaining it all so well. All of this goes to the biggest problem with statistics: trying to apply them to individuals is often worse than useless. (I wonder, for example, how many perfectly capable students have abandoned their academic ambitions because they were told their IQ scores made success unlikely.) For tracking weight trends of nations, BMI is probably useful. For determining an individual's distance from their ideal weight, I suspect that looking in a mirror would be a much more accurate test.

[Danyel]

Beth,

I'd almost agree with you about the lack of necessity for applying statistics to individuals, if it weren't for the fact that people are pretty bad at calibrating themselves. If you live in a population of fat people, you might be the skinny kid at a mere 200 pounds for your five and a half feet.

You could be incapable of seeing your skin and bones under your imagined weight, as seems to be the distressing case with anorexia.

In either case, skimming a Cosmo column, or a newspaper article, on the topic isn't going to rock your world. But it might let you realize that something -- maybe your calibration, maybe the article -- is way off.

[Peatey]

The real question should be why Fred hates the BMI... Is he a "30+?" :)

[Adam]

The real question should be why Fred hates the BMI... Is he a "30+?" :)

By my workings, not unless he's about 4'8". (I know, too much time on my hands).

[Pat Vogel]

All of this is well and good, but let's get to the political part of Fred's post (with me, it's all political). I'm talking about that intriguing last phrase, "our gullibility for misplaced concreteness is a dangerous thing". In a post purportedly about BMI, Fred has illustrated a key difference between those on the left and those on the right in this particular political season. Those on the right are all about received wisdom. If the President says it's so, by golly, then it's so. This is their Truth, and nothing will shake them. Those on the left have more inquiring minds. They have a more analytical approach to truth. They ask questions, and shape their opinions according to the facts as they can best be understood. War in Iraq? Social Security? The right is standing behind their man, no questions asked. The left prefers to take a good look at the issue so that important decisions will be in synch with reality.

I'm pretty sure about this, but please don't take this as received wisdom. Think it over a little; ask a few questions. We'd all be better off if more of us got in the habit.

[Donald Johnson]

I've been curious about why it is height squared rather than height cubed. If tall people of healthy weight were geometrically similar to short people of healthy weight, it would be height cubed. That is, a 6 foot tall man who was geometrically similar to a 5 foot tall man (I'll ignore differing genders, since it's come to my attention that men and women have different shapes) would be 6/5 as tall, 6/5 as wide, and 6/5 as thick. So assuming identical body composition, he'd weigh 216/125 as much. But the BMI calculation says that the healthy 6 footer should only be 6/5 times 6/5 as heavy.

So according to the BMI approach, tall people of healthy weight should appear quite thin compared to short people of healthy weight. They'd be thicker in the two horizontal dimensions, but not by the same factor as they are taller. I could accept that this is true for some reason, but if that's the case why is the exponent exactly 2? An exponent of 3 would make sense for the reason given above, but toss that out and why shouldn't it be 2.5 or 1.9 or something else? Somehow I doubt there was a linear regression that gave exactly 2 as the answer when the original inventors of the BMI compared the logarithms of healthy weights to the logarithm of height.

I'm pretty sure about this, but please don't take this as received wisdom. Think it over a little; ask a few questions.

Why should I?

[eristick]

"If your BMI's below 18 or so, the word "anorexic" is very, very likely to describe you."

In an otherwise great post, this is off-base. Small-boned women who don't have an eating disorder frequently come up with very low BMIs. I know it's a shocker in our diet-obsessed culture, but some women are skinny without starving themselves, particularly those of us with very small frames.

[Jack]

Danyel said, "I'd almost agree with you about the lack of necessity for applying statistics to individuals, if it weren't for the fact that people are pretty bad at calibrating themselves. If you live in a population of fat people, you might be the skinny kid at a mere 200 pounds for your five and a half feet."

Well... Sort of. The problem here is that this *isn't* an accurate measurement when applied to a single individual. Individual builds vary too much; the BMI is only useful as an aggregate measure. Also, there's an even more basic problem: the BMI equates 'weight' with 'fat,' which simply isn't valid.

According to every height/weight chart I've ever seen, I'm overweight, but I'm closer to my ideal weight *now* than I was back when I fifteen and working out three times a week. In reality (by contrast), the opposite is true - I'm carrying notably more body fat now than I was then. To get down to my 'ideal' *weight*, I'd have to lose about ten pounds more than would be healthy, whereas if I started working out again I'd probably lose fat but *gain* weight.

[Beth]

Danyel's right. Body image can be way off, and a 'double-check' may be helpful. Still, simply scaling down a statistical tool is a pretty poor way to accomplish that. I'm sure there are simple tests that would much more accurately determine obesity or anorexia, something along the lines of 'Does your belly hide your belt?' or 'How many ribs can you see?'

There seems to be an underlying assumption that because 'science' uses BMI it must be accurate. There are a couple of problems with that. First, science doesn't use BMI; scientists do, and unlike science, scientists can be stubborn, prejudiced, or just plain wrong. Fred -- and Donald -- are certainly right to question their pronouncements. Second, you can't just take a tool from one context, and assume it will work in another (e.g. applying statistical measurses to individuals). When the public simply accepts whatever newspapers say that scientists say as gospel, there's bound to be trouble.

Donald, I don't know much about anatomy, but I doubt that a 6-footer's heart, intestines, etc. are 6/5 larger than a 5-footers, or that their skin, bones, and veins are 6/5 thicker. So the ratio of height to girth or weight wouldn't be a straight line. It's probably more of a parabolic curve (of the sort you get when you graph an equation involving squares). You're right of course that we're not 2-dimensional, but that doesn't mean that sqaring height won't produce a sufficiently accurate graph of the proper ratio of weight to height.

[Richard A. Lovett]

<>--Jack

Yes and no. Yes, a person can have a high BMI and not be fat. Conversely, you can have a perfectly median BMI and be all flab and therefore too fat. So the number's not the definitive answer, but it's a strong real-world feedback to whether you should check more deeply.

>>"If your BMI's below 18 or so, the word "anorexic" is very, very likely to describe you."

In an otherwise great post, this is off-base. Small-boned women who don't have an eating disorder frequently come up with very low BMIs. I know it's a shocker in our diet-obsessed culture, but some women are skinny without starving themselves, particularly those of us with very small frames. --eristick<<

I should have used fewer "very's," and said "too thin" because there are penty of causes for excessive thinness other than an eating disorder. a tapeworm would do it, too!!! The point is that, a BMI of 18 is very thin. To put this in perspective, that's 5'9" and 124 pounds.

There are a few fine-boned women for whom this is probably optimal, but there are a lot of others for which it is not. This is a level at which (one of my sidelines is coaching distance runners) I'd be saying "prove to me you're not to thin" with an underwater weighing. Even if a woman is naturally thin, at a low body fat women start missing menstrual cycles, and that starts thinning bone density, leading to stress fractures. Fred's article put the warning threshold at a BMI of 18.5. I used 18 in my prior post. I've also seen 17.5. This, among runners, is the biggest risk I know of from a borderline too-low BMI, and it's ended many, many college running careers.

[Anne M.]

My BMI is under 18, I've never been anorexic or bulimic, and while I am skinny, I have never been so thin as to have it affect my menstrual cycle. I'd like to weigh more, but my metabolism right now is just not working that way (since I'm entering my late 20s, that may change soon).

[Anarch]

I mucked around with one of those online BMI calculators and found that I had a BMI of around 17 when I was in high school. It was just a freakily high metabolism, though; I've had far more health problems since (with a BMI that's around 20-22 nowadays) than I did at the time.

[eristick]

"5'9" and 124 pounds" may sound shockingly thin, reminding one of emaciated supermodels, but again, the calculations can bring to mind another image. A 5'1", 95 lb woman is very petite, but not unusual (I immediately recall the tiny Chinese woman who I see at the bus stop every day.) And remember that the statistically smaller number of people with that sort of build are a still thousands of people in this country. This math falls apart at the low end the same way it does at the high end.

In taller, larger-boned people, extra weight in the form of muscle skews the calculation. In fine-boned, shorter people, especially those who are not athletic, the calculation is also skewed. I *just* crossed the "healthy weight" threshold at 31 years old, and I'm not particularly scrawny. In college, my BMI was under 17, and I was still no-where near missing periods and fracturing bones (I'm a klutz, so if my bones had thinned, I'd have found out the hard way.)

To Fred's original point, all of this hyper-calculating in place of common sense drives me nuts. (And it seeps into medical practice, too, which drives me even nuts-er.) I think it's part of the larger malaise of thinking if we could just follow the magic formula, we'll be healthy/happy/thin/sexy, and anyone bursting the fantasy bubble with common sense should be shouted down with pseudo-science.

[The Navigator]

So, the upshot is:
Fred, eat something!
No, seriously, it's good to have an honest analysis of the limits of BMI, but it still sounds like our proprietor is on the thin side.
Although he refers to it as his "adjusted" BMI. I don't see anything on the CDC page about "adjusted" - am I missing something? It's just regular 'BMI' as far as I can see.

For those who could do with a hearty lunch, I recommend the Italian roast pork at Tony Luke's, Front and Oregon in bee-yootiful South Philly. Pork, provolone, and broccoli rabe. Mmm, mmm, that's good eats.

[chuck]

Fred might be a little thin, but he does eat. I once saw him eat a hotdog cooked on the exaust manifold of a 2000 Chrysler Mini van. Tony Luke's can't make anything that tastes like that!