In this LAB note
Question · Hypothesis · Method · Results · What Failed · What We Learned · What Changed at MOMS
Question
When someone excludes two allergens instead of one, does the MOMS recipe library shrink twice as much, or more than twice as much?
Hypothesis
We expected the loss to be close to additive. Our two most common allergen flags each sit on a little over 40 percent of recipes, so excluding both should leave roughly a third of the library standing. We also assumed the survivors would stay spread thinly but evenly, so that every body type and every program week kept at least a few options. The number we planned to watch was how many recipes survived.
Method
Published work framed the question. Gupta and colleagues surveyed more than 40,000 US adults and found that 10.8 percent had a convincing food allergy, and that 45.3 percent of those adults were allergic to more than one food. A customer excluding two things at once is therefore close to half of the allergic population, not an edge case. Meyer and colleagues followed 130 children through an elimination diet and found that the elimination itself did not improve growth parameters; what predicted improvement was whether energy and protein targets were still being met afterward. Read together, the two papers say the question is not how much a customer removes, but whether what remains still does the job. Internally we took all 201 production recipes and read the Allergens column, which carries five distinct flags. We counted flagged recipes for each allergen alone, then for each pair, then re-ran the identical counts as coverage of the 32 personalization cells in the program, eight body types (EY, EI, WY, WI, MY, MI, WAY, WAI) times four weeks, rather than as a share of the library.
Results
Tree Nuts is flagged on 89 of 201 recipes and Soy on 87. Gluten sits on 62, Egg on 52, Sesame on 2. Only 21 recipes carry no flag at all. Taken one at a time, neither exclusion hurts. Removing every tree-nut recipe leaves 112 recipes and all 32 cells still filled. Removing every soy recipe leaves 114 recipes and, again, all 32 cells filled. Only two cells drop to a single option. Taken together, 57 recipes survive. That is 144 recipes gone, 71.6 percent of the library. If the two flags were independent we would expect 63 survivors (0.557 x 0.567 x 201). We get 57, because only 32 recipes carry both flags where chance predicts 38.5. The two flags partly avoid each other, which widens their union and makes the pair cost more than the arithmetic suggests. The count is not the damage. Four cells are now empty: WY week 3, MY week 2, WAY week 2, and WAY week 3. Of the 28 cells that survive, 12 hold exactly one recipe. MY week 1 is down to Crisp Reset (MY-W1-COOL-009-V1: Coconut Milk 300ml, Egg White 240g). WAY week 4 is down to Petal Renewal (WAY-W4-RENEWAL-002-V1: Coconut Milk 150ml, Chicken 130g). Half the grid, 16 cells of 32, has no choice left in it. Adding gluten as a third exclusion leaves 27 recipes across 20 cells, 15 of which hold a single recipe. The flags trace back to single ingredients, which is why they are so expensive. Soy Milk appears in 65 recipes and flags soy in all 65. Almond Milk flags tree nuts in 28 of the 29 recipes it appears in, Cashew in 34 of 35, Walnut in 12 of 12.
What Failed
Our headline prediction was close enough. We guessed about a third would survive, and 28.4 percent did. The hypothesis that actually failed was the unstated one: that recipe count measures the harm. It does not. The first exclusion deletes 89 recipes and costs zero cells. The second deletes 55 more and costs four cells plus twelve choices. The same size of deletion does very different amounts of damage depending on where it lands. The more uncomfortable finding is in the column itself. Coconut appears in 74 recipes, and 52 of those are not flagged for tree nuts. The FDA lists coconut as a tree nut; our sheet does not. Every tree-nut-free number above therefore quietly assumes a customer who is fine with coconut. For a customer who is not, tree-nut-free drops from 112 recipes to 60, and tree-nut-plus-soy-free drops from 57 to 27 spread across only 18 of 32 cells, which is worse than the three-allergen case above. We are publishing both the 112 figure and the 60 figure because the column as written cannot tell you which one applies to you. Separately, 8 recipes are flagged for tree nuts with no nut-family ingredient listed anywhere in them, and 4 are flagged for soy with no soy ingredient. Small numbers, but they confirm the column is partly hand-entered rather than derived from the ingredient list.
What We Learned
In a personalized system, the cost of a restriction is not the recipes it deletes. It is the cells it empties. Personalization multiplies constraints while a catalog only adds recipes one at a time, so a second restriction is reliably more expensive than the first even when it removes fewer items. A library-wide percentage hides this completely: 28 percent of 201 recipes sounds like plenty until you find out that half the weeks it has to cover contain exactly one option, or none.
What Changed at MOMS
We stopped reporting allergen coverage as a share of the library and started reporting it as cells filled out of 32, with a floor of two recipes per cell for any exclusion combination we offer at checkout. Combinations that fall below that floor are now a formulation backlog item rather than a silent gap, and the four cells that go empty at nut-free plus soy-free are the first four recipes in the queue. We are also splitting coconut out of the tree-nut flag into a column of its own, because as written that flag answers a different question than the one the customer is asking.
References
Gupta RS, Warren CM, Smith BM, et al. Prevalence and Severity of Food Allergies Among US Adults. JAMA Network Open, 2(1):e185630, 2019. | Meyer R, De Koker C, Dziubak R, et al. The impact of the elimination diet on growth and nutrient intake in children with food protein induced gastrointestinal allergies. Clinical and Translational Allergy, 6:25, 2016.
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