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Do Small Reductions in Caloric Intake add up to Big Changes in Weight?

The answer is: probably not.

This is important question because there are many studies finding that various interventions (from fat taxes to menu labels) have very (though sometimes statistically significant) small effects on caloric intake.  Proponents of the policies are often undeterred - and say things like "well, a 20 kcal reduction every day can really add up to big weight loss over time."

As I've already discussed, some of this sort of analysis is based on the faulty logic that 3500kcal = 1lb.  But, as was mentioned in that post, our body does not react linearly to caloric changes in the fashion implied by this formula.  

Now, there's more on this topic by Trevor Butterworth in a well-written and catchy-titled post Sex And Lies! The Iffy Science Of Measuring Calories.  Here is a key excerpt:  

Hall was responsible for filling in the crucial measurements that elucidated one of the most widespread myths highlighted by Allison et al.: the idea that small, consistent changes in energy intake or expenditure will, over time, lead to large changes in weight. The assumption appears to have been based on the 1958 calculation by Max Wishnofsky that one pound of body fat gained or lost is equal to 3,500 kilocalories. This seemed to give people a convenient way to estimate weight loss through diet or exercise, while promising extremely convenient results. If you simply knocked off a 100 kilocalories from your energy intake each day—a ten-minute jog, or a mile walk—you'd end up losing over 50 pounds in five years. Little wonder that early proposals for soda and fat taxes promised to save Americans from themselves: pay a little more, consume a little less, watch a lot of weight disappear in a few years.
Hall first heard the claim listening to a dietician make a calculation for an obese patient. His intuition told him that this calculation was incorrect and would lead to exaggerated weight loss predictions. When he asked for a reference, he was pointed to a nutrition and dietetics textbook. "I subsequently found the mistake everywhere I looked." People weren't stopping to think "about the dynamic interaction between energy intake and expenditure, which is complicated," he says. What they failed to take into account was that "the rate of weight loss changes over time and is primarily determined by the imbalance between energy intake and expenditure—a value that also changes over time." To radically simplify his model, this means that cutting calories in your diet leads to a decreasing calorie expenditure, which in turn slows weight loss until weight eventually plateaus after a few years. "Of course," says Hall, "cheating on your diet will cause your weight to plateau much sooner." In the case of soda taxes, Hall and researchers at the US Department of Agriculture showed how static modeling overstated weight loss by 346 percent after five years.