People are 3-dimensional, so it would seem to make sense to cube the height in order to remain proportional.
I looked at the Wiki entry, and this is included as one of the criticisms of the formula. But why would formula have been based on height squared to begin with, and why not just fix it by changing it to height cubed? Must be that it’s not as simple as that.
Because people aren’t proportional. NBA players aren’t just scaled up Pygmies.
Not that I think BMI is a good measure of anything.
Hey, I expected more support from you in particular. 
Not everyone is proportionate to everyone else. But if you’re specifically measuring body fat or the like and comparing people to the world in that regard, then then you’re measuring how far a given person’s proportions differ from that standard.
BMI is purely a propaganda tool with little or no medical value. In 1835 a Belgian mathematician, presented his theory of the average man based upon the measurements of Belgian peasants almost 200 years ago, in a attempt to prove that ‘the weight increases as the square of the height’. Note that the original scale does poorly after 6’ since apparently there were few or no really tall guys in 1830’s Belgium, and at no time did Quetelet think to try to use his “average man” scale to measure obesity or health nor did he consider it useful in that regard. The purpose really was to measure "the average man’ which linked into his criminology studies. Altho quite brilliant in his day, his theories today would be considered “pseudo-science” or badly outdated. Note also that today we are generally taller and healthier than a Belgian from 1830.
*The person who dreamed up the BMI said explicitly that it could not and should not be used to indicate the level of fatness in an individual.2. It is scientifically nonsensical.
There is no physiological reason to square a person’s height (Quetelet had to square the height to get a formula that matched the overall data. If you can’t fix the data, rig the formula!). Moreover, it ignores waist size, which is a clear indicator of obesity level.*
At the center of this debate is the body mass index, a simple equation (your weight in kilograms divided by the square of your height in meters) that has in the last decade claimed a near-monopoly on obesity statistics. Some researchers now argue that this flawed and overly reductive measure is skewing the results of research in public health. For years, critics of the body mass index have griped that it fails to distinguish between lean and fatty mass. (Muscular people are often misclassifed as overweight or obese.) The measure is mum, too, about the distribution of body fat, which makes a big difference when it comes to health risks. And the BMI cutoffs for “underweight,” “normal,” “overweight,” and “obese” have an undeserved air of mathematical authority. … Then, in 1998, the NIH changed the rules: They consolidated the threshold for men and women, even though the relationship between BMI and body fat is different for each sex, and added another category, “overweight.” The new cutoffs—25 for overweight, 30 for obesity—were nice, round numbers that could be easily remembered by doctors and patients.
Keys had never intended for the BMI to be used in this way. His original paper warned against using the body mass index for individual diagnoses, since the equation ignores variables like a patient’s gender or age, which affect how BMI relates to health. It’s one thing to estimate the average percent body fat for large groups with diverse builds, Keys argued, but quite another to slap a number and label on someone without regard for these factors.*
It’s not even a good measurement for potential health risks: wiki:
*A study published by Journal of the American Medical Association (JAMA) in 2005 showed that overweight people had a similar relative risk of mortality to normal weight people as defined by BMI, while underweight and obese people had a higher death rate.[35] High BMI is associated with type 2 diabetes only in persons with high serum gamma-glutamyl transpeptidase.[36]
In an analysis of 40 studies involving 250,000 people, patients with coronary artery disease with normal BMIs were at higher risk of death from cardiovascular disease than people whose BMIs put them in the overweight range (BMI 25–29.9).[37] In the overweight, or intermediate, range of BMI (25–29.9), the study found that BMI failed to discriminate between bodyfat percentage and lean mass. The study concluded that “the accuracy of BMI in diagnosing obesity is limited, particularly for individuals in the intermediate BMI ranges, in men and in the elderly. These results may help to explain the unexpected better survival in overweight/mild obese patients.”[28]
A 2010 study that followed 11,000 subjects for up to eight years concluded that BMI is not a good measure for the risk of heart attack, stroke or death.*
Strangely, that section of the Wikipedia article ends with:
“For US adults, exponent estimates range from 1.92 to 1.96 for males and from 1.45 to 1.95 for females.”
Probably the reason why Quetelet used an exponent of two rather than something else is that three would have been less correct and a fractional power is hard to calculate by hand.
Also, does it really matter? It’s not like when your BMI goes from 24.9 to 25.1 suddenly you’re a completely different person. However, the difference between 24.9 and 30.1 is significant.
The trouble is, many people like to draw arbitrary lines (like a BMI of 25) and then see how many people cross that line. So if half the population was just under 25, got a tiny bit fatter and is now just over 25, that’s presented as a huge thing, which it isn’t. Show me the scatterplots!
Also see this rant on my blog.
BMI is a measure, just one of many that one should consider when determining their health.
It’s not intended to be a one yardstick determination of one’s health and never was and isn’t amongst most medical professionals.
But to say it is a useless, meaningless measure is foolhardy as well.
Nice blog/rant!
What? If you’re making a predicting model, fitting your formula to your data is exactly what you should do! (And then get some more data to make sure your formula fits that, too, of course).
And – as the Wikipedia article says – the real data says that for adult men, weight is generally proportional to height ^ 1.93, which is really close enough to 2 for this kind of work.
Which isn’t to defend BMI as a good single measure of fitness or obesity, but there’s every reason to use height squared (at least for adult men) if you’re doing a simple formula.
But beyond being a good measure of fitness or obesity, it at least has to be a measure of fitness or obesity.
If you found that “the data” showed that weight was generally proportional to height^1.93, that doesn’t mean that “the data” shows that height^1.93 is any sort of measure of fitness or obesity. That “data” is just a measure of body types that exist, not of fitness or obesity. It’s possible that tall people tend to be thinner. This would not imply that tall people who are not thinner are less fit or obese.
The only thing BMI does is remove the variable height from the equation, so that weight can be compared between all individuals. However, greater than average weight ≠ obese ≠ non-fit. However 2, one doesn’t equal the other, but there’s still a huge correlation, so if you need something that’s quick, easy, cheap and objectively measurable, then BMI is still pretty useful.
Here’s the thing the BMI-function does - it compares thee to a sphere. And the farther thou art from a sphere in thy shape, the better (lower!) will be thy index.
Now, stretch!!
Part of the issue is a mixing up of the history.
Quetelet was not creating a measure of health or of fatness, merely creating a tool that would roughly fit human body mass into a Gaussian normal distribution across heights. Over ht squared just fit the data set better than cubed did. It stayed a pretty much unknown esoteric academic bit of history until the Framingham study and then Ancel Keyes, who renamed the Quetelet Index the BMI.
In point of fact Keyes compared several potential indices for correlation with body fat percent (as per caliper technique) before promoting the Quetelet Index (BMI) including the “Ponderal Index” which is the over height cubed one … over height cubed was thrown out because it performed the worst.
Those studies showed that for populations BMI correlated well with degrees of fatness and heart disease rates. Keyes was very clear that this was a population level tool and that its utility at an individual level was quite limited.
Still it was quick and easy and once people got up into the higher percentiles the correlation with overfat was very high. The first attempt at popularizing the tool used the 85%ile of what was then found as the upper limit of “normal”. For men that was a BMI of 28.0 and let’s leave the oddity of what they did with women alone. By 1985 they decided to use newer data for young adults from NHANES II and labelled “obesity” as the 85%ile and above - BMI ≥ 27.8 for men and BMI ≥ 27.3 for women. 1995 is where the mythic 25 cut off for all as overweight was created, based on what was then the best correlations with mortality data, but with a whole mess of caveats that the increased risk close to 25 was very uncertain.
Short version - the BMI is a very good tool for following similarly composed populations over time. If an individual has a BMI over 30 the odds are pretty high that they have excess adiposity. Some 25 to 30 will be more over fat and some 25 to 30 will actually have little fat. It works modestly well as a screening tool in that labelling all those 25 and over as “overweight” will miss fairly few who have excess fat. Screening tools however always sacrifice some specificity for sensitivity: some without excess adiposity will be overidentified. Perfect it aint. ABSI may be better.
Cite? Now sure, being very overweight with lots of body fat does correlate with heart disease rates. But BMI does not correlate directly with either.
see my wiki cite:
*A study published by Journal of the American Medical Association (JAMA) in 2005 showed that overweight people had a similar relative risk of mortality to normal weight people as defined by BMI, while underweight and obese people had a higher death rate.[35] High BMI is associated with type 2 diabetes only in persons with high serum gamma-glutamyl transpeptidase.[36]
In an analysis of 40 studies involving 250,000 people, patients with coronary artery disease with normal BMIs were at higher risk of death from cardiovascular disease than people whose BMIs put them in the overweight range (BMI 25–29.9).[37] In the overweight, or intermediate, range of BMI (25–29.9), the study found that BMI failed to discriminate between bodyfat percentage and lean mass. The study concluded that "the accuracy of BMI in diagnosing obesity is limited, *
Do you read what you post?
Defining “obese” by BMI criteria.
The study of people who are identified as having coronary artery disease (defined as defined as already having a history of percutaneous coronary intervention, coronary artery bypass graft, or myocardial infarction)? Not sure what that is supposed to say relevant to any other population or what their BMI was before they got ill (I am sure it would shock you to find out that someone with a bad course loses more weight when ill) and given that the study did not measure body fat percent hard to know how they concluded anything about BMI’s value in identifying obesity.
Here however is some data on the correlation between BMI and body fat %. The problem with using a BMI of 30 as the definition of obesity is not that it overcalls some who are not overfat as obese but that it misses too many of the overfat.
If you have a BMI of 30 or higher the odds are very high that you are overfat. If you are less than a BMI of 30 you still may be overfat … or not.
AGAIN “overweight” by BMI always included such a large portion as to not be too useful. The group includes those with more fat and worse fat (visceral) than many of those categorized as Grade 1 obese and those with a fair amount of muscle mass and not only fairly little fat but in particular extremely little fat that is viscerally located. The lowest mortality rates vary according to the study but are actually generally come out right around where the 50%ile was back in the 1988 to 1994 NHANES III data, just above and below (depending on the exact study) a BMI of 25. By 27 they go up in all studies that do not arbitrarily shove all of 25 to 29.9 into one grouping.
Why would you use height cubed? My height is my longest measurement. If you want my volume, you need my length, width, and height. Height cubed is going to go over by at least an order of magnitude.
Essentially, what happens with BMI is that the other dimensions are assumed to be basically consistent given the other two (weight and height).
Because it’s a ratio and the OP assumes small humans are scaled down large humans or vice versa.
Since this has already been explained earlier in the thread I’ll include an example. Let’s say I have two boxes each mass of 1, and one is twice as large as the other. Let’s say 10x10x20 and 20x20x40. I’m only interested in comparing the densities of the two, i.e. the ratio of mass to volume, not in the units used.
System one uses all the measurments and I get densitites of 1/2000 and 1/16000, so the larger box has a density one eight of the larger.
System two just looks at “height” and, unsurprising to the OP, since it’s the premise of the question, you get “densitites” of 1/8000 and 1/64000, so the larger box also has a “density” one eight of the larger.
It works by assuming the objects scale isometrically, which isn’t true for humans, but wasn’t that far fetched a starting point.
Actually, that’s a pretty good idea. I we know your volume and your mass, then we have a pretty good idea about how much fat you contain.
The trouble of course is that even three dimensions isn’t enough: your volume would be very different if you were more round vs more rectangular. But a good way to determine your volume is to dunk you in a liquid and see how much of that liquid is displaced.
Not sure if your doctor can be bothered to do that every time you come in, though.
Very simple to do with a log-log slide rule, (invented 1815) before scientific calculators came along.
Data point: Mrs Nobbins works in the eating disorder field (anorexia etc) and they use BMI because it is a) simple, and b) good enough.
No, it could be solid muscle. Bodybuilders usually get into “Obese” despite their very low body fat %.
Yes.
Your objection is valid against the BMI, but not against volume /mass = density. As fat weighs less than muscle, you can get a very reasonable body fat percentage estimation from a person’s density. (I guess it’s a bit more complex in practice to get a good guess of bones and other relatively fixed stuff.)
I.e., a fat guy with a BMI of 30 floats (density < 1), a body builder with a BMI of 30 sinks (density > 1).