Waist-to-weight ratios in pictures: The John Stone transformation

John Stone is a bodybuilder and founder of a bodybuilding and fitness web site (). There he has provided pictures and stats of his remarkable transformation, which were used to prepare the montage below.



John’s height is reported as 5' 11.5". Below the photos are the months in which they were taken, the waist circumferences in inches, the weights in lbs, and the waist-to-weight ratios (WWRs). Abhi was kind enough to provide a more detailed plot of John Stone’s WWRs ().

Assuming that minimizing one’s WWR is healthy, an idea whose rationale was explained here before (), we could say that John was at his most unhealthy in the photo on the left.

The second photo from the left shows a slightly more healthy state, at a reported 8 percent body fat (his lowest). The two photos on the right represent states in which John’s WWR is at its lowest, namely 0.1544. That is, in these two photos John minimized his WWR; at a reported 14 and 13.8 percent body fat, respectively.

When we look at the WWRs in these photos, it seems that he is only marginally healthier in the second photo from the left than in the leftmost photo. In the two photos on the right, the WWRs are much lower (they are the same), suggesting that he was significantly healthier in those photos.

Interestingly, in both photos on the right John reported to have been at the end of bulking periods. Whenever he entered a cutting period his WWR started going up. This suggests that his ratio of lean body mass to total mass started decreasing just as soon as he started cutting. I suspect the same would happen if he continued gaining weight.

Which of the two photos on the right represents the best state? Assuming that both states are sustainable, over the long run I would argue that the best state is the one where the WWR was minimized with the lowest weight. There whole-day joint stress is lower. This corresponds to the photo at the far right.

By sustainable states I mean states that are not reached through approaches that are unhealthy in the long term; e.g., approaches that place organs under such an abnormal stress that they are damaged over time. This kind of damage is essentially what happens when we become obese – i.e., too fat. One can also become too muscular for his or her own good.

How can carrying some extra body fat be healthy?

Most of the empirical investigations into the association between body mass index (BMI) and mortality suggest that the lowest-mortality BMI is approximately on the border between the normal and overweight ranges. Or, as Peter put it (): "Getting fat is good."

As much as one may be tempted to explain this based only on the relative contribution of lean body mass to total weight, the evidence suggests that both body fat and lean body mass contribute to this phenomenon. In fact, the evidence suggests that carrying some extra body fat may be healthy for many.

Yet, the scientific evidence strongly suggests that body fat accumulation beyond a certain point is unhealthy. There seems to be a sweet spot of body fat percentage, and that sweet spot may vary a lot across different individuals.

One interesting aspect of most empirical investigations of the association between BMI and mortality is that the participants live in urban or semi-urban societies. When you look at hunter-gatherer societies, the picture seems to be a bit different. The graph below shows the distribution of BMIs among males in Kitava and Sweden, from a study by Lindeberg and colleagues ().



In Sweden, a lowest mortality BMI of 26 would correspond to a point on the x axis that would rise up approximately to the middle of the distribution of data points from Sweden in the graph. It is reasonable to assume that this would also happen in Kitava, in which case the lowest mortality BMI would be around 20.

One of the key differences between urbanites and hunter-gatherers is the greater energy expenditure among the latter; hunter-gatherers generally move more. This provides a clue as to why some extra body fat may be healthy among urbanites. Hunter-gatherers spend more energy, so they have to consume more “natural” food, and thus more nutrients, to maintain their lean body mass.

A person’s energy expenditure is strongly dependent on a few variables, including body weight and physical activity. Let us assume that a hunter-gatherer, due to a reasonably high level of physical activity, maintains a BMI of 20 while consuming 3,000 kilocalories (a.k.a. calories) per day. An urbanite with the same height, but a lower level of physical activity, may need a higher body weight, and thus a higher BMI, to consume 3,000 calories per day at maintenance.

And why would someone want to consume 3,000 calories per day? Why not 1,500? The reason is nutrient intake, particularly micronutrient intake – intake of vitamins and minerals that are used by the body in various processes. Unfortunately it seems that micronutrient supplementation (e.g., a multivitamin pill) is largely ineffective except in cases of pathological deficiency.

Urbanites may need to carry a bit of extra body fat to be able to have an appropriate intake of micronutrients to maintain their lean body structures in a healthy state. Obviously the type of food eaten matters a lot. A high nutrient-to-calorie ratio is generally desirable. However, we cannot forget that we also need to eat fat, in part because without it we cannot properly absorb the all-important fat-soluble vitamins. And dietary fat is the most calorie-dense nutrient of all.

Why not putting on extra muscle instead of carrying the extra fat? For one, that is not easy when you are a sedentary urbanite. Particularly after a certain age, if you try too hard you end up getting injured. But there is another interesting angle to consider. Humans, like many other animals, have genetic “protections” against high muscularity, such as the protein myostatin. Myostatin is produced mostly in muscle cells; it acts on muscle, by inhibiting its growth.

Say what? Why would evolution favor something like myostatin? Big, muscular humans could be at the top of the food chain by physical strength alone; they could kill a lion with their bare hands. Well, it is possible. (Many men like to think of themselves as warriors, probably because most of them are not.) But evolution favors what works best given the ecological niches available. In our case, it favored bigger and more plastic brains to occupy what Steve Pinker called a “cognitive niche”.

Even though fat mass is not inert, secreting a number of hormones into the bloodstream, the micronutrient “need” of fat mass is likely much lower than the micronutrient need of non-fat mass. That is, a kilogram of lean mass likely puts a higher demand on micronutrients than a kilogram of fat mass. This should be particularly the case for organs, such as the liver, but also applies to muscle tissue.

While gaining muscle mass through moderate exercise is extremely healthy, bulking up beyond one’s natural limitations may actually backfire. It could increase the demand for micronutrients above what a person can actually consume and absorb through a healthy nutritious diet. Some extra fat mass allows for a higher level of micronutrient intake at weight maintenance, with a lower demand for micronutrients than the same amount of extra lean mass.

Some people are naturally more muscular. Their frame and underlying organ-based capabilities probably support that. It is often visibly noticeable when they go beyond their organ-based capabilities. A common trait among many professional bodybuilders, who usually go beyond the genetic gifts that they naturally have, is an abnormal swelling of internal organs.

What complicates this discussion is that all of this seems to vary from individual to individual. People have to find their sweet spots, and doing that may not be the simplest of tasks. For example, even measuring body fat percentage with some precision is difficult and costly. Also, certain types of fat are less desirable than others – visceral versus subcutaneous body fat. It is not easy differentiating one from the other ().

How do you find your sweet spot in terms of body fat percentage? One of the most promising approaches is to find the point at which your waist-to-weight ratio is minimized ().

An illustration of the waist-to-weight ratio theory: The fit2fat2fit experiment

In my previous blog post, I argued that one’s optimal weight may be the one that minimizes one’s waist-to-weight ratio. I built this argument based on the fact that body fat percentage is associated with lean body mass (and also weight) in a nonlinear way.

The fit2fat2fit experiment (), provides what seems to be an interestingly way to put this optimal waist-to-weight ratio theory to test. This is due to a fortuitous event, as I explain in this post.

In this experiment, Drew Manning, a personal trainer, decided to undergo a transformation where he went from what he argued was his fittest level, all the way to obese, and then back to fit again. He said that he wanted to do that so that he could better understand his clients’ struggles. This may be true, but it looks like he planned very well his experiment from a marketing perspective.

His fittest level was at the start, with a weight of 193 lbs, at a height of 6 ft 2 in. That was his fittest level according to his own opinion. At that point, he had a waist of 34.5 in, and looked indeed very fit (). At his fattest level, he reached the weight of 264.8 pounds, with a 47.5 waist.

As he moved back to fit, one interesting thing happened. Toward the end of this journey back to fit, he moved past the level that he felt was his optimal. He dropped down to 190.1 lbs, and a 34 in waist; which he perceived as too skinny. He talks about this in a video ().

As a self-defined “fanatic” personal trainer, I figured that he knew when he had gone too far. That is, he is probably as qualified as one can get to identify the point at which he moved past his optimal. So I thought that this would be an interesting way of putting my optimal waist-to-weight ratio theory to the test.

Below is a bar chart showing variations in waist-to-weight ratio against weight for Drew Manning during his fit2fat2fit experiment. I included only three data points in this chart because I would have to view all of his video clips to get all of the data points.



As you can see, at the point at which he felt he was too thin, his waist-to-weight ratio clearly started going up from what seems to have been its optimal at 34.5 in / 193 lbs. This is exactly what you would expect based on my optimal waist-to-weight ratio theory. You probably can’t tell that something was not right at that point, because he looked very fit.

But apparently he felt that something was not entirely right. And that is consistent with the idea that he had passed his optimal waist-to-weight ratio, and became too lean for his own good. Note that his waist decreased, and probably could go down even further, even though that was no longer optimal.

What is your optimal weight? Maybe it is the one that minimizes your waist-to-weight ratio

There is a significant amount of empirical evidence suggesting that, for a given individual and under normal circumstances, the optimal weight is the one that maximizes the ratio below, where: L = lean body mass, and T = total mass.

L / T

L is difficult and often costly to measure. T can be measured easily, as one’s total weight.

Through some simple algebraic manipulations, you can see below that the ratio above can be rewritten in terms of one’s body fat mass (F).

L / T = (T – F) / T = 1 – F / T

Therefore, in order to maximize L / T, one should maximize 1 – F / T. This essentially means that one should minimize the second term, or the ratio below, which is one’s body fat mass (F) divided by one’s weight (T).

F / T

So, you may say, all I have to do is to minimize my body fat percentage. The problem with this is that body fat percentage is very difficult to measure with precision, and, perhaps more importantly, body fat percentage is associated with lean body mass (and also weight) in a nonlinear way.

In English, it becomes increasingly difficult to retain lean body mass as one's body fat percentage goes down. Mathematically, body fat percentage (F / T) is a nonlinear function of T, where this function has the shape of a J curve.

This is what complicates matters, making the issue somewhat counterintuitive. Six-pack abs may look good, but many people would have to sacrifice too much lean body mass for their own good to get there. Genetics definitely plays a role here, as well as other factors such as age.

Keep in mind that this (i.e., F / T) is a ratio, not an absolute measure. Given this, and to facilitate measurement, we can replace F with a variable that is highly correlated with it, and that captures one or more important dimensions particularly well. This new variable would be a proxy for F. One the most widely used proxies in this type of context is waist circumference. We’ll refer to it as W.

W may well be a very good proxy, because it is a measure that is particularly sensitive to visceral body fat mass, an important dimension of body fat mass. W likely captures variations in visceral body fat mass at the levels where this type of body fat accumulation seems to cause health problems.

Therefore, the ratio that most of us would probably want to minimize is the following, where W is one’s waist circumference, and T is one’s weight.

W / T = waist / weight

Based on the experience of HCE () users, variations in this ratio are likely to be small and require 4-decimals or more to be captured. If you want to avoid having so many decimals, you can multiply the ratio by 1000. This will have no effect on the use of the ratio to find your optimal weight; it is analogous to multiplying a ratio by 100 to express it as a percentage.

Also based on the experience of HCE users, there are fluctuations that make the ratio look like it is changing direction when it is not actually doing that. Many of these fluctuations may be due to measurement error.

If you are obese, as you lose weight through dieting, the waist / weight ratio should go down, because you will be losing more body fat mass than lean body mass, in proportion to your total body mass.

It would arguably be wise to stop losing weight when the waist / weight ratio starts going up, because at that point you will be losing more lean body mass than body fat mass, in proportion to your total body mass.

One’s lowest waist / weight ratio at a given point in time should vary depending on a number of factors, including: diet, exercise, general lifestyle, and age. This lowest ratio will also be dependent on one’s height and genetic makeup.

Mathematically, this lowest ratio is the ratio at which d(W / T) / dT = 0 and d(d(W / T) / dT) / dT > 0. That is, the first derivative of W / T with respect to T equals zero, and the second derivative is greater than zero.

The lowest waist / weight ratio is unique to each individual, and can go up and down over time (e.g., resistance exercise will push it down). Here I am talking about one's lowest waist / weight ratio at a given point in time, not one's waist / weight ratio at a given point in time.

This optimal waist / weight ratio theory is one of the most compatible with evidence regarding the lowest mortality body mass index (, ). Nevertheless, it is another ratio that gets a lot of attention in the health-related literature. I am talking about the waist / hip ratio (). In this literature, waist circumference is often used alone, not as part of a ratio.