In this LAB note
Question · Hypothesis · Method · Results · What Failed · What We Learned · What Changed at MOMS
Question
Our recipe database specifies ingredient weights to a tenth of a gram: 110.7 g of Greek yogurt, 11.7 g of avocado, 0.2 g of turmeric. Which of those decimal places is doing work, and which are digits we have been carrying for no reason?
Hypothesis
We assumed the decimals were specifications. If a recipe reads 110.7 g of Greek yogurt, someone decided on 110.7, and rounding it would move the macros enough that the recipe would stop being the recipe. The competing explanation was that the decimals are residue. Our recipes are built per body type, and a body type enters the formulation as a multiplier. Multiply a round base quantity by a personalization factor and 11.7 and 110.7 are what come out the other side. Under that reading the digits are arithmetic exhaust, not instruction. Either way we expected a uniform answer. Precision would turn out to matter across the database or not matter across the database. We did not expect it to split.
Method
Published research. Gibson and colleagues tested how accurately people quantify food without a scale. Sixty-seven participants estimated the portion sizes of forty-two pre-weighed foods and liquids, whose true weights ran from 9.2 g for a piece of soft cheese to 253.4 g for a beef steak. Using household measures - volumetric cups and spoons - 29 percent of the geometrically shaped items were estimated within 25 percent of their true weight, and 8 percent within 10 percent. A finger-width method the authors developed did better, at 80 percent within 25 percent and 13 percent within 10 percent. For amorphous foods such as rice and mashed potato, the median error with either method sat near 50 percent. The study also measured the hand heuristics themselves: a thumb tip came out slightly under the volume of a teaspoon, 5 ml, despite being widely recommended as a stand-in for a tablespoon. Regulatory context. Nutrition labels are not held to a tight tolerance. Under 21 CFR 101.9(g), a composite sample is misbranded if calories, total sugars, total fat, saturated fat, trans fat, cholesterol or sodium come in more than 20 percent above the declared value, and a naturally occurring vitamin, mineral, protein, total carbohydrate or dietary fiber must be at least 80 percent of the declared value. That is the window our own label has to land inside. Internal analysis. We parsed all six ingredient slots - Liquid, Body, Fruit & Vegetable, Protein, Functional, Flavor - across all 201 recipes, treating 1 ml of liquid as 1 g. That produced 1,714 individual weight entries taking 233 distinct values, from 0.2 g to 334 g, summing to 119,692 g of charged ingredients. We rounded every entry to the nearest 5 g, recomputed each recipe's charged weight, and recorded the percentage shift. Separately we flagged every entry whose rounded value differs from its stated value by more than half of the entry itself.
Results
Most of the precision is already gone. Of the 1,714 entries, 1,275 are whole numbers, 234 end in .5, and 205 carry some other decimal. 1,074 of them - 63 percent - are already exact multiples of 5. But only 5 of the 201 recipes are written entirely in multiples of 5, and 173 contain at least one decimal weight. The precision is sprinkled through the database, not applied to it. Rounding everything to the nearest 5 g barely moves a shake. The median recipe shifts 0.81 percent of its charged weight and the mean shifts 0.87 percent. 129 of 201 recipes move less than 1 percent, and 191 of 201 move less than 2 percent. The worst case in the entire database is WY-W1-DETOX-013-V1 "Clarity Flow," which shifts 15.4 g on 466.4 g, or 3.3 percent. Measured against the tolerance the label itself is judged by, those numbers are small. A 20 percent ceiling on declared calories is roughly twenty-three times our typical 0.87 percent shift and six times our worst case. Then the other half of the result. 167 of the 1,714 entries would change by more than half their own amount, and 103 of them would round to zero: Turmeric 32 times, Monk Fruit 24, Cinnamon 19, Agave 11, Honey 8, Ginger 3, Lemon 3, Ginger (Fresh) 1, Cacao 1, Seaweed 1. Those 103 entries sit inside 79 of our 201 recipes. Rounding the database onto a 5 g grid would silently remove an ingredient from 39 percent of the catalog. The asymmetry is the finding. The 192 entries under 5 g are 11 percent of all entries and 0.30 percent of all mass - 354 g out of 119,692 g. By weight they are nothing. By presence they are the difference between a shake that contains turmeric and a shake that does not. Two recipes make it concrete. MI-W3-VITAL-008-V1 "Bright Vitality" is Rice Milk 140 ml, White Rice 55 g, Papaya 70 g, Lentils 55 g + Egg White 240 g, Agave 10 g, at 387 kcal. Every entry is already a multiple of 5, so rounding it changes nothing at all; it is one of the five. WY-W1-DETOX-013-V1 "Clarity Flow" is Almond Milk 117 ml + Soy Milk 78 ml, Avocado 11.7 g, Black Beans 50 g + Black Sesame 5 g, Egg 27.5 g + Tofu 50 g + Greek Yogurt 110.7 g, Lemon 2.5 g + Cashew 7.5 g, Agave 6.5 g, at 393.3 kcal. Rounding it moves 15.4 g, our largest shift, and still lands well inside label tolerance. The same operation doubles the lemon, from 2.5 g to 5 g. The number that survives rounding comfortably and the number that does not are sitting in the same recipe. Turmeric shows it most plainly. It appears in 34 recipes, and in 17 of them at 0.2 g. No rounding rule built for bulk ingredients leaves 0.2 g standing.
What Failed
Our hypothesis was wrong in the least convenient way. We expected a uniform answer and got a split one: roughly 90 percent of entries where the precision is inert, and 10 percent where it is the entire ingredient. We cannot tell the kitchen that the decimals do not matter, and we cannot tell them to measure everything to a tenth. Both instructions are wrong for a large part of the database. We measured mass, not macros. This database does not carry a per-ingredient nutrient table, so we could not recompute calories or protein from the rounded weights. We measured the shift in charged weight and we are reporting it as a shift in charged weight. That is a proxy, and it is not a neutral one. If a recipe's rounding error lands on a cashew or a flaxseed it will move calories more than it moves mass; if it lands on cucumber it will move them less. A 0.87 percent mass shift is not a claim of a 0.87 percent calorie shift, and we are not making that claim. Charged weight is also not finished volume. Every recipe is recorded as a 16 oz serving and the ingredient sums do not fit inside 473 ml. We can compare recipes against each other on charged weight; we cannot say what arrives in the cup. We found a defect in our own data while counting. Seven of the 201 recipes list the same ingredient in two different slots - eight such pairs. WAY-W2-COOL-001-V1 "Cool Cleanse" carries Sweet Potato 38 g and Taro 21.1 g in both the Body field and the Fruit & Vegetable field. We could not tell from the sheet whether that is a duplicated field or a genuinely split portion, so we counted both, which means our entry count is accurate to about half a percent rather than exactly. That is a database defect, not a result about precision, and it needs fixing independently of anything else in this note. Our Score does not track any of this. Across all 201 recipes, Score correlates +0.14 with a recipe's sensitivity to rounding and +0.19 with how many sub-5-gram entries it carries. Both are weak enough to be nothing. "Clarity Flow," our worst-case recipe, scores 13. "Bright Vitality," which rounds perfectly, scores 14. "Cool Cleanse," another high-error recipe, scores 18. Whatever the Score is measuring, it is not this, and we are not going to imply otherwise. And Gibson is not a study of our kitchen. Sixty-seven people, mostly young, mostly female, mostly university-affiliated, estimating portions by eye without a scale. It establishes how much error enters when a weight is guessed rather than weighed. It says nothing about the error in our own bench process, which we have not measured. Nothing in this note tells us how accurately our recipes are actually executed - only how much accuracy the specification is asking for.
What We Learned
Precision in a recipe spec is not one property. It is two properties sharing a notation. For the 1,522 entries at or above 5 g, the decimal is inherited arithmetic. Rounding them onto a 5 g grid moves a shake by about eight tenths of a percent, inside a label tolerance twenty points wide. Those digits were never a decision anyone made. They are what came out when a base quantity was multiplied by a body-type factor and the result was written down unrounded. For the 192 entries below 5 g, and especially the 103 that round to zero, the digit is the ingredient. Rounding 0.2 g of turmeric to the nearest 5 g is not an approximation of turmeric. There is no tolerance band inside which deleting an ingredient is a small error. So the question was never how precise our recipes ought to be. It was what they ought to be precise about. One standard of care applied across entries that differ by three orders of magnitude will be too loose at one end and pure ceremony at the other.
What Changed at MOMS
We split the build sheet into two measuring regimes. Everything at or above 5 g is specified and weighed to the nearest gram on a bench scale. Everything below 5 g moves to a 0.1 g scale, and where a sub-gram ingredient repeats across a week of builds it gets pre-portioned in advance rather than measured at assembly. Gibson's thumb tip is why we will not accept a spoon heuristic for this tier: a thumb tip is a teaspoon, not the tablespoon it is widely sold as, and most of the entries in this tier are smaller than either. We are rounding the database on purpose, and in one direction only. Every entry at or above 5 g gets rewritten to the nearest gram, and onto the 5 g grid wherever the recipe tolerates it. The decimals we keep are the ones below 5 g, and they now carry a flag so a future recipe edit cannot quietly round them away. 103 entries are protected by that flag. The duplicate-slot check goes into the same pass. The seven recipes that list an ingredient twice get resolved to a single field before any of this is rewritten, because you cannot round a number correctly when you do not know whether it is one portion or two. And we stopped treating measurement time as free. This one comes out of running the kitchen rather than out of the sheet, and we will hold it as a hypothesis rather than a result. A specification that asks for a tenth of a gram on every line looks costless on paper, because the cost does not arrive as an ingredient price - it arrives as handling time at the bench, which we had never counted. Because we had not counted it, uniform precision looked like the careful choice. Once we counted the handling rather than only the grams, the two-regime version looked both more accurate where accuracy changes the shake and less work where it does not. We have not run it long enough to call that settled.
References
Gibson AA, Hsu MSH, Rangan AM, Seimon RV, Lee CMY, Das A, Finch CH, Sainsbury A. Accuracy of hands v. household measures as portion size estimation aids. Journal of Nutritional Science, 5:e29, 2016. | US Food and Drug Administration. Nutrition labeling of food, compliance provisions. 21 CFR 101.9(g)(4)-(5), Code of Federal Regulations, Title 21.
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