After reading around a bit, my understanding is that the height exponent was derived empirically – the height exponent was chosen to maximise the fit to the data (of weight vs height in lean subjects). (Here’s a retrospective article from the Wikipedia citations.)
The guy who developed the index did this in the 19th century, so it may well be the case that we’d find a different exponent given modern data – but e.g. this study finds an exponent of 1.96 for males and 1.95 for females, suggesting it isn’t all that dumb. (This study finds lower exponents – bad for BMI but still not supporting a weight/height³ relationship.)
I don’t find this too surprising – allometry is complicated and often deviates from what a naive dimensional analysis would suggest. A weight/height³ relationship would only hold if tall people were isometrically scaled-up versions of short people; a different exponent implies that tall and short people have systematically different body shapes, which matches my experience.
In any case, my claim above is based on empirical evidence, comparing obesity as identified with BMI to obesity identified by other, believed-to-be-more-reliable metrics – those studies find that false positives are rare. Examine.com is a good source, and its conclusions roughly match my impressions from earlier reading, albeit with rather higher rates of false negatives than I’d thought.
After reading around a bit, my understanding is that the height exponent was derived empirically – the height exponent was chosen to maximise the fit to the data (of weight vs height in lean subjects). (Here’s a retrospective article from the Wikipedia citations.)
The guy who developed the index did this in the 19th century, so it may well be the case that we’d find a different exponent given modern data – but e.g. this study finds an exponent of 1.96 for males and 1.95 for females, suggesting it isn’t all that dumb. (This study finds lower exponents – bad for BMI but still not supporting a weight/height³ relationship.)
I don’t find this too surprising – allometry is complicated and often deviates from what a naive dimensional analysis would suggest. A weight/height³ relationship would only hold if tall people were isometrically scaled-up versions of short people; a different exponent implies that tall and short people have systematically different body shapes, which matches my experience.
In any case, my claim above is based on empirical evidence, comparing obesity as identified with BMI to obesity identified by other, believed-to-be-more-reliable metrics – those studies find that false positives are rare. Examine.com is a good source, and its conclusions roughly match my impressions from earlier reading, albeit with rather higher rates of false negatives than I’d thought.