Losing weight doesn’t need magic—just keeping the energy balance equation in mind: energy intake=energy expenditure. When energy intake is less than energy expenditure, you will gradually lose weight by principle of physics.

Estimating energy intake is straightforward. As I have demonstrated in the Oct. 2 post, you carefully record what you eat during the day and you will know exactly how much your energy intake is. However, estimating energy expenditure is tricky. It takes common sense and some physiology knowledge.

Total energy expenditure has three components: basal metabolic rate (BMR), thermic effect of feeding, and physical activity. Briefly, BMR is the energy expenditure when you lie in the bed doing nothing; thermic effect of feeding is the mysterious energy expenditure when you eat foods; and for physical activity, we all know what it is.

Among these three expenditures, for a sedentary person, BMR can account for 70-75% of total energy expenditure, the thermic effect of foods accounts for 8%, and the daily activity accounts for 17-22%. Therefore, accurately estimating BMR serves a correct base for estimating the total energy expenditure.

Strictly speaking, BMR should be measured after 12 hours of fasting and 8 hours of sleep (basically in the morning before breakfast). Nevertheless, we can use several equations and some approximations to estimate it. The most notabe one is the Harris-Benedict equations:

For men, 66.4730 + (13.7516 * weight) + (5.0033 * height) − (6.7550 * age)
For women, 655.0955 + (9.5634 * weight) + (1.8496 * height) − (4.6756 * age)
Where weight = weight in kilograms, height = stature in centimeters, and age = age in years.

The math is quite simple. But from the statistical point of view, this set of equations lacks one key ingredient: the prediction error. Say when you get an estimation of 1700 kcal BMR, is this the real number or not?

This question is raised because these two equations were derived from regression methods based on hundreds of people in 1918 (! How many overweight and obese people were there then?). This can be illustrated in the following figure, body weight vs. total heat production in men:

The estimated BMR from the equation is on the regression line. But the actual value can range from 1490 kcal to 1890 kcal for the body weight of 70 kg. The difference is 400 kcal, equivalent to the energy from a light meal.

I am not aware of the actual prediction error for the original H-B equations, as they were detailed in an obscure monograph. However, some articles reported an 80 kcal of prediction error. For a common overweight or obese people, I would suggest subtracting 100 kcal from the predicted BMR as the actual BMR because overweight or obese people are more likely to have a lower metabolic rate than those muscular people with the same weight, that is, their actual dots lie under the regression line.

I haven’t seen any online guideline that considered the prediction error (maybe most of them are not statistically oriented anyway). Nonetheless, this relatively conservative estimation is critical. Because all other energy expenditures (thermic effect of feeding and daily activity) are calculated based on BMR, we don’t want to overestimate the BMR to inflate the total energy expenditure, thus misoverestimating (!) the required energy intake.

Physiologically, BMR is the energy expenditure for all sorts of essential biochemical process to keep our alive. Organs such as liver (27%), brain (19%), heart (7%), and kidneys (10%) are big energy consumers in our body but we can do nothing about it. Luckily, the skeletal muscle accounts for 18% of BMR. More muscles mean higher BMR. But during weight loss, we not only lose fat and water but also lose muscles. Thus, BMR decreases with the decrease of weight, also indicated in the equation and figure.

Anyway, except for the fun of number tweaking, getting an estimation of BMR won’t help us losing weight. Among the three energy expenditures, only physical activity is at our disposal. For a short period, we can only increase physical activity to increase the total energy expenditure.

Spending energy by physical activity is hard and often yields moderate energy expenditure. For example, running 3 miles at 12min/mile speed, a 170 lb people may spend about 400 kcal. This is not a lot considering one cup of milk has 100 kcal of energy. But this level of exercise is the maximum of torment and commitment most people can bear.

The real contribution to weight loss, sadly, has to be the calorie restriction, i.e. sacrificing all delicious foods and the associated pleasure.