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The accepted wisdom for converting a daily calorie deficit to resulting weight loss is roughly 3500 kcal to half a kg, with the amount of weight loss getting smaller with body weight.

However, I'm curious if any more accurate models have ever been created, specifically based on empirical evidence. The 3500 kcal figure seems to be based on a rough estimate of the calorie content of body fat, and not on actual observed weight loss.

It shouldn't be that difficult to do a simple study where a diverse sample of people follow a calorie deficit diet and do some exercise, and to fit a model from the basic variables (age, wieght, height, starting weight, calorie deficit) to the weight loss on a given day.

It would seem to me that such studies have most certainly been done, but unfortunately the internet is not giving me anything more that the figure above. Can anyone provide more in-depth research?

I should perhaps stress that I'm not doing this to set out a diet plan or to calculate my own weight loss. I know there's no predicting personal weight loss to this level of accuracy. I'm just curious.

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I don't believe that you'll find better research on the subject currently. Here's why:

  • Until very recently, there was such a strong taboo in the medical community against acknowledging hormonal impacts (other than thyroid hormone deficit or overproduction) on basal metabolic rate (BMR) that nobody could get studies funded on it. People like me with hormone disorders that impact our BMR are still to this day often told by more "old school" doctors that we are simply lying about our food intake or activity levels rather than treated for those disorders. The problem is changing...slowly...but the associated social taboos have impacted research funding as well as clinical practice.

  • The US government has been weirdly focused in recent decades on weight loss rather than fat loss. Most of the research money they pump into health studies has focused on weighing people rather than doing serious study of body composition, so muscle gain, water retention changes, and so on have messed with results. Some studies do track fat rather than weight (or in addition to weight), but not the majority.

  • The obsession with weight means that the impact of muscle on BMR is also ignored in many of the studies I've seen. I.e. a 5'10" tall, 26yo male who is a 230 lb. weightlifter is assumed to have the same BMR as a man of the same height, weight, and age who is a chubby desk jockey carrying minimal muscle.

  • The study would have to be done and re-done for a number of different scenarios to be generally useful. Due to impacts on insulin production and uptake, as well as other hormonal systems, a calorie isn't just a calorie. The balance of macronutrients and micronutrients in a diet can have a noticeable impact on fat gain/loss, even with all else being equal. As an extreme example, if I eat 1600kcal/day in cookies I'll gain fat while being miserable and hungry and maintaining or losing muscle, but if I eat 1600 kcal/day in eggs I'll lose fat while gaining muscle and feeling overfull. (This is not an endorsement of an all-egg diet; I said it was an extreme example.)

  • Similarly, a minute of activity is not a minute of activity. We'd need a great deal more studies to improve our estimation of caloric burn based on activity level and relative body composition vs. age and other factors to know what people are actually burning before calculating deficits.

In the end, I'm not too worried about not having the data you are looking for. We have enough data for people to know what variables to experiment with in tuning their individual diets, and given the number of variables in play, no straightforward calorie-to-activity accounting is possible. To get more data than we have now, a huge swath of individuals would have to do years of tightly-controlled studies isolating each of those variables...and all we would get for the money, time, stress, and hassle would be slightly better predictive models that still need experimentation to tweak for the individual.

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