In this LAB note
Question · Hypothesis · Method · Results · What Failed · What We Learned · What Changed at MOMS
Question
If you multiply a shake's listed protein, carbohydrate and fat by 4, 4 and 9, the answer lands above its listed calories in 178 of our 201 recipes. How much of that gap is fiber?
Hypothesis
We expected the listed calories to follow the textbook arithmetic closely, with the shortfall concentrated in high-fiber shakes. Fiber is counted inside total carbohydrate but is only partly digested, and the Atwater general factors were built from average mixed diets, not from shakes made of beans, kale and dates. So the more fiber a recipe carries, the further its listed calories should sit below the 4-4-9 figure.
Method
Published work: Southgate and Durnin (1970) fed young and elderly adults controlled mixed diets, measured faecal losses and heats of combustion, and found that the classical Atwater factors estimate metabolizable energy reasonably well when available carbohydrate is counted at 3.75 kcal per gram. In their diets, more unavailable carbohydrate increased faecal energy loss. Internal data: for each of our 201 recipes we computed 4 x protein + 4 x carbohydrate + 9 x fat from the listed grams and subtracted it from the listed Kcal. A negative gap means the listed figure is lower than the arithmetic. We compared the gap with fiber grams, split the recipes into fiber quartiles, and fitted listed Kcal against protein, carbohydrate, fat and fiber by least squares. We do not have the formula behind the Kcal column in front of us, so the fit describes the pattern; it does not reveal the method.
Results
178 of 201 recipes (89%) list fewer calories than 4-4-9 gives. The average gap is -6.7 kcal, the range runs from -31.0 to +5.7, and only 64 recipes sit within 5 kcal of the arithmetic. Fiber and the gap correlate at r = -0.48, which works out to roughly 1.1 kcal lower for each additional gram of fiber. Across fiber quartiles (2.5 to 5.8, 5.8 to 7.6, 7.6 to 9.4 and 9.4 to 14.4 g) the average gap is -3.3, -6.5, -7.3 and -9.5 kcal. The extreme case is EY-W1-ENERGY-012-V1, Blazing Dawn (Oat Milk 176.8 ml, Avocado 35.8 g, Dates 21.1 g, Kale 25 g, Black Beans 60 g, Egg White 195 g, Cocoa 8 g). Its 32.1 g protein, 52.3 g carbohydrate and 10.1 g fat give 428.5 kcal by 4-4-9, but it lists 397.5, a 31-calorie gap, with 14.4 g of fiber. At the other end, MY-W3-GUT-005-V1, Anchored Calm (Rice Milk 120 ml, Cauliflower 45 g, Blueberry 70 g, Dates 13.7 g, Egg 50 g, Egg White 240 g, Tofu 6.3 g), has 3.6 g of fiber and lists 350.9 kcal against 350.6 from the arithmetic. The least-squares fit gives about 4.4 kcal per gram of protein, 3.8 per gram of carbohydrate, 8.4 per gram of fat and -0.7 per gram of fiber. Read that way, fiber is counted at about 3.1 kcal per gram instead of 4: partly discounted, not removed. A flat 2 kcal per gram for fiber overshoots in the other direction and flips the average gap to +8.5.
What Failed
Fiber is not the whole story. It explains about 23% of the variation in the gap (r-squared of 0.23), so roughly three-quarters of it comes from something else. Eight recipes with under 6 g of fiber still list more than 10 kcal below the arithmetic. WY-W3-BALANCE-004-V1, Whole Harmony (Soy Milk 220 ml, Banana 80 g, Pumpkin 65 g, Papaya 70 g, Dates 21.1 g, Greek Yogurt 220 g), has 31.5 g protein, 56.3 g carbohydrate, 5 g fat and 5.9 g fiber. The arithmetic gives 396.2 kcal; it lists 379.1, a 17-calorie gap with almost no fiber to blame. We have not identified the cause. Two other things did not work out. Neither textbook version matches the column: 4-4-9 runs high by 6.7 on average, and a 2 kcal-per-gram fiber correction runs low by 8.5. And our internal Score is uncorrelated with the gap (r = 0.03), so it neither rewards nor penalizes recipes whose listed calories diverge from the arithmetic.
What We Learned
The 4-4-9 rule is an approximation, not a measurement, and for our whole-food shakes it overstates energy by about 7 calories on average and by as much as 31. The error is largest where fiber is highest, and fiber accounts for part of it but not most of it. A reader who adds up the printed macros will not reproduce the printed calories, and the difference is not random.
What Changed at MOMS
We are adding a short note to each recipe page saying that listed calories are not the sum of 4-4-9 applied to the printed macros. We are also auditing the 52 recipes whose gap exceeds 10 kcal, starting with the high-fiber ones, to find where the difference enters the calculation before we decide whether the calories, the macros or the note should change.
References
Southgate DAT, Durnin JVGA. Calorie conversion factors: an experimental reassessment of the factors used in the calculation of the energy value of human diets. British Journal of Nutrition. 1970;24(2):517-535. doi:10.1079/BJN19700050
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