Weight Loss Math Uproar: Sorting it out!
Wednesday, September 28, 2011 at 1:41PM 
An article recently published in the medical journal Lancet,[i] authored by Kevin Hall PhD, a biophysicist at the National Institutes of Health set off some erroneous news coverage on the effect of calorie-restriction on weight loss.
Since there is too much misinformation from the “reporting” on this research paper to try to set straight in a single blog, I’m going to devote my next few blogs to clearing up one piece of confusion at a time.
I’ll start with Jane Brody’s recent column (veteran food columnist for the New York Times). Brody tells us that, “It turns out that a long-used rule of weight loss—reduce 3,500 calories (or burn an extra 3,500) to lose one pound of body fat—is incorrect and can ultimately doom determined dieters.”
Not exactly.
To be fair to Ms. Brody, Hall’s paper has more than its share of abstruse statements. But remember, his audience is other research scientists, not journalists! Hall’s actual point has three parts:
1) Since weight loss lowers both your resting metabolic rate and energy expenditure from activity/exercise, that estimates of continued projected weight loss will be wrong IF they are not adjusted to your CURRENT weight (each week). And with continued weight loss they will get progressively more and more inaccurate. [Ideally, your body composition needs to be tracked, not just your weight; see point #3. But the majority of the "error" is managed by adjusting to your current weight.]
2) Hall asserts that “widespread official recommendations” are misleading, basically because people (including some professionals) don’t understand the above.
While I have no idea how many “professionals” in the weight loss field aren't aware of these facts, there are plenty that are. For instance, I was trained (in 1994) to calculate “predicted weekly weight loss” based on current scale weight (from the weekly weigh in).
To be clear, that training came from a hospital-based outpatient weight management program that had—at that time—20 years of treating obesity already under it’s belt. It wasn’t information that either my undergrad or masters dietetics course work covered, but in my opinion it's also common sense!
The fact is that there are plenty of professionals and programs that have long taken Hall’s concern about adjusting for changes in body weight into account. The point is ensuring that you are actually incurring the TARGET calorie deficit. Actually, you will find manual record keeping forms, including what I call a "Weekly Summary" form in my book, The Healthy Eating & Weight Management Guide; where I teach a simple but reasonably accurate way to track your weight loss, and yes I have you adjust your calculations to your current weight each week. (And also explain the excess water loss that always occurs secondary to restricting calorie intake.)
Additionally, there are various web-based programs and cell phone applications that track and predict weight loss trajectories based on your resting metabolic rate, food diaries, and physical activity. If they also adjust to changes in body weight (by adjusting your "calorie-intake target" down as your energy needs decrease) they will keep you reasonably on track for the one or two pound weight loss you're after. While I haven't personally used any of these programs, these are the programs that I hear colleagues say are most popular: LoseIt!, myfitnesspal.com, and fitday.com.
That said, we still have the third part of Hall’s actual point to cover:
3) The type of weight people lose (fat versus muscle) varies significantly between individuals, and therefor the caloric cost of the “pound” varies. This means that a 3,500 CALORIE deficit doesn’t always mean a pound of weight loss.
To explain this, a little background is required; 3,500-calories is NOT the energy in a pound of body fat (as Brody states). It’s the caloric equivalent of the “average” pound of “body weight” lost, which consists of 75% fat and 25% muscle. (This ratio is based on lots of data tracking changes in body composition as weight is lost, but it's "thumbnail average". The greater one's initial body fat, the higher the percent lost as fat will be.)[i],[ii]
Here’s the math behind the 3500-calorie-per-pound “rule of thumb”:
A pound of lean body mass (normally hydrated muscle tissue) = 825-calories
A pound of fat mass (adipose tissue) = 4,291-calories
So, for the “average pound of body weight” lost (based on 75% fat, and 25% LBM) we have:
[Fat: 4291 x 75% = 3218] + [LBM: 825 x 25% = 206] = 3,424 calories![iii]
The origin of the 3,500-calories-per-pound “thumbnail” can be traced back to a calculation that assumes exclusive loss of adipose tissue (which is 87% fat; Wishnofsky 1958 AJCN).
To be completely clear the relationship between lean body mass (muscle) and fat mass is NOT linear, so the 75/25 ratio is another thumbnail average! Regardless, the lean and fat compartments of your body are linked and dietary alterations (positive or negative energy balance) induce simultaneous changes in BOTH compartments in the SAME direction.[iv] (This means that you can't gain muscle while losing any significant amount of body weight. The best you can do is minimize the loss of LBM.)
The loss of lean body mass (muscle) is an inverse function of body fat content, up to about 50-kg of body fat. In other words, obese persons preferentially lose fat mass and preserve muscle.(iv)
Takeaway #1: This means that obese persons actually have to deficit more than 3,500 calories to lose a pound because more of that weight will be coming from body fat. For example, if they are losing 85% from fat, the actual cost of that pound is 3,771-calories.
That variance (3,500 versus 3,771-calories in the above example) is Hall’s concern, and why he’s been working on a complete mathematical model of weight loss that is fine tuned to the intricacies of accurately predicting an individuals’ weight loss trajectory.
Keep in mind, that underreporting of energy intake is a far larger problem than this variance in the actual energy cost of the weight lost over the week. As Hall also notes, the so-called plateau that people seem to hit at 6 months isn't a plateau at all. Instead, their energy intake has simply reached (increased to) the point where they are in energy balance (not creating an energy deficit).
Takeaway #2: For those persons only in the overweight range the old 3,500-calorie thumbnail is “close enough” as long as you remember point number one (above).[iii]
Finally, the most important thing for everybody to remember is that while weight loss is still a numbers game, the biggest challenge isn't math! It's having our behaviors align with our health objectives in a culture that makes healthy habits hard!
So there you have what I hope was a clear and concise explanation of just one of the points of misinformation—on the “Weight Loss Math Uproar!”
My next blog will tackle the confusion over what Hall calls the "energy gap" and the "maintenance gap".
Best,
-Dorene
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- If this is the kind of information you appreciate, you may also like my book: The NEW Healthy Eating & Weight Management Guide.
Related articles:
How to Lose Weight 101: Understanding Energy Balance
What do You Really Know about Your Metabolism?
Weight Loss Plateaus: How to reignite your weight loss
[i] Hall, KD, et al. Quantification of the effect of energy imbalance on body weight. Lancet 2011;378:826-37.
[iii] Hall, KD. What is the Required Energy Deficit per unit Weight Lost? Int J Obes 2008;32(3):573-576.
[iv] Yang M, VanItallie TB. Effect of energy restriction on body composition and nitrogen balance in obese individuals. In: Wadden TA, VanItallie TB, eds. Treatment of the Seriously Obese Patient. New York: Guilford Press; 1992;83-106.
[v] Forbes GB. Lean Body Mass-Body Fat Interrelationships in Humans. Nutrition Reviews 1987;45(8):225-231.
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