A post that I read today have made me think – again – about what kind of BS the BMI really is, and how it is just not suitable to apply it to individuals. If a doctor can’t be bothered to use some kind of body-fat measurement device (or even a calliper) then they really just should shut up unless the individual is evidently over or underweight.

So what’s wrong with the BMI? We should probably start with what is right with it, and this is not much, really. The sad thing is, the creators of this index knew this and explicitly stated this, but as it happens so often some other individuals without the necessary insight and brainpower have misused this measure, and now people just use it without thinking.

So what’s right? Well, bigger people are, in average, heavier than smaller people. If you want to do statistics on groups of people this can be a problem. Imagine you want to compare different groups and see whether their body-fat percentage (“BF%”) impacts [insert your favorite health marker here]. Now further assume that you can not measure the BF%, eg because you work on a pre-existing dataset . What do you do? Well, you use weight as a proxy of BF% – if a person is fatter, he or she tends to be heavier. Unless she is smaller of course. According to Wikipedia, it seems that Ancel Keys had this problem in about 1972, and he came up with an ingenious solution: following earlier work of a chap called Quetelet, he postulated that weight / height * height is a good enough proxy for BF% across – and that is important – the population that he was studying. But he understood what he was doing:

BMI was explicitly cited by Keys as being appropriate for population studies, and inappropriate for individual diagnosis.

Then Wikipedia continues

Nevertheless, due to its simplicity, it came to be widely used for individual diagnosis, despite its inappropriateness.

Go figure. Wikipedia is kind enough to provide a graph where we can see how well BMI correlates to BF%

Great fit, isnt it? Well, maybe not. What are the reasons for it. In order to understand this, we need to look at the big ticket items in terms of weight in the human body. First and foremost there is water. I would argue however – and I might be wrong – that in average (across a population, across time, whatever – the water percentage in the tissue is constant, so that we can ignore water. So what else. I’d say, in order of importance for a non-obese individual

  1. muscle
  2. fat
  3. bones
  4. connective tissue
  5. brain and nervous tissue

Whilst possibly important when comparing genetically different populations (or children for that matter) there is not much an individual can do about the weight of 3,4,5 respectively. So what it really comes down to is fat, and muscle. So [drumroll here] BMI is really related to BF% – assuming that neither muscles nor 3,4,5 interfere. But of course they do: I am certainly not the first one to point out that Arnold Schwarzenegger would have been classified as morbidly obese even though he had <10% body fat.

But I also want to make a second point, that is probably a bit less obvious, and that is related to the height of the individual. This also gives me the opportunity to do some recreational physics, which is – as many of you know – is something I like.

Lets first talk about “scaling”: if you increase the size of a three dimensional object, then – by definition – you increase its length, width, and height. If you double each of those measures, then the volume increases by a factor 2*2*2=8. If you increase it with a factor x, the volume increase with a factor x*x*x=x^3 (x to the power of three). As the weight is generally proportional to the volume (ie, density remains the same), the correct scaling for an object is kg/m^3. Note that the BMI has kg/m^2. This is important. It implies that human bodies do not simply get bigger when the individuals get taller, but that they also change shape.

More precisely, an exponent of 2 (as in kg/m^2) assumes that the width and the depth of the human body only scale with the square-root of the height, rather than proportional to height. To put some numbers to it, increasing the height by 10% would only increase the width of the shoulders, and the distance between the pecs and the shoulder blades, by 5% each. As a consequence the taller individual has proportionally narrower shoulders, and a proportionally less “deep” body. Is this true? According to Wikipedia it is, albeit with a bigger coefficient (between 2.2 and 2.7) meaning that the impact is less pronounced.

So does this mean BMI is wrong, but if we use kg/m^2.5 we are alright? Well, no. We might be slightly better, but if you look at the picture above we go from catastrophically wrong to utterly wrong. 2.5 might be the better choice if there is no other choice – ie when looking at a population where BF% is not available – but there is no excuse to use BMI on an individual.

Or to put it slightly different for every health care professional who still does not understand it (some of my otherwise very intelligent doctors for example): Obese is really just a fancy term for fat, as in a certain individual has too much body fat. The correct measure for this is [another drumroll] body-fat-percentage – to use some straw-man numbers 0-5%BF is too lean, 5-10% is lean, 10-20% is normal (albeit potentially on the fat side), and 20% is obese. BF% can be measured very inexpensively, eg with Tanita scales, or some handheld devices, or a calliper (“pinch-an-inch”). BMI is a proxy for BF%, and a very bad one indeed, absolutely unsuitable for individuals, as has been already noted by the person who has introduced this very measure, and there is absolutely no excuse for using it in an individual assessment.


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