Part 4 The Kitchen Formula Calculator v4 & The Logical Structure Of A Recipe

Points Of Distinction, Portions Versus Yield

What distinguishes formulations one encounters in professional settings from popular sources? A recipe’s yield, often popularly conceived as numbers of portions, is of practical importance, but it’s a stipulation that changes day to day. For bread makers, yield is always the same as a formula’s *Total Dough Weight* (TDW), not numbers of portions. This is a chief distinction even between bread bakers and pastry makers. In the pastry shop, formulae will quite often list a variety of different yields for the formula, 4 each 10” pies, or 5 each 9" pies, but doing so is useful for one shop, perhaps some others with similar configurations in equipment, mold shapes, customer expectations for portion size etc, but it’s inexact, and cannot be used to full operational advantage. In addition, many pastry preparations rely upon ingredients, and their measures, the initial volumes for which are far less than their ultimate volumes. For example, one level cup of egg whites (225ml) actually weighs about 8.57 ounces (243grams), but it easily turns into four cups of meringue; one cup of cream becomes two of whipped cream. Therefore, strictly referencing total formula weight has some limitations for predicting ultimate yield. Nevertheless, the volume of a product is not insignificant. For bread bakers, the significance applies more to the actual baking process phenomenon taking place in oven. For pastry chefs, oftentimes volumetric expansion is designed to be held during refrigeration. It is what it is when it goes in the fridge. Not so a baker’s creation. Volumetric expansion is a given during baking. A mousse neither expands, nor contracts in the fridge, and the ultimate geometrical configuration of a Bavarian is determined once it's mixed because it is suspended in a gel. See my previous article (Meditations on Baking) to learn all about the importance of a product’s geometrical configuration, and its relationship to such stuff as density, and thermal conductivity during baking. Volume with respect to most cooking processes does, of course, matter because it’s a sign of proper make up methodology, but it’s not the convenience it appears to be as far as the measuring of ingredients. Formerly, perhaps it was a convenience because most people lacked scales, but this is no longer the case.

If using weight measures has limited utility for anticipating ultimate volumetric (and consequent numbers of portions), how does one get around it? It’s called experience. One understands the nature of ingredients, and also what happens to them when certain forces are applied. Anyone who has ever whipped an egg white understands that the volume of the egg prior to whipping isn’t the same as after. The same relationship between weight and ultimate volume applies. Convert the cup of egg whites to weight measure, it’s still a cup of egg whites, right? But, it is an accurately gauged value that makes more precise sense than saying “cup". As noted previously, “cup” means different things every time someone, or a group of someones has to scoop one full. What does “full” mean anyway? Is it right to the line on the beaker, to the mid point of that line, to the top? Do you always use the same beaker? Different beakers made by different manufacturers may be different. And, how can we know…by using another cup to fill it? Everyone gauges “full” differently. Every “cup” is therefore, inevitably, even if marginally different. Is it of formula-invalidating significance? Not necessarily, but why not use a measuring standard that eliminates the variance entirely? Especially considering the other practical benefits of doing so, and how easy it is to do it.

Note that I am not proposing all cooks scale all ingredients at all times. In a busy kitchen this is not practicable. What I am proposing is to write recipes/formulae using weights, and for cooks to get the same feel for what 15 grams of diced onions looks like, just as they gauge what two tablespoons of it looks like. In the course of learning a new recipe all good cooks will take pains to measure the ingredients according to the recipe, then, rendering this to memory, a cook’s margin of variance (within Chef’s specifications) to achieve the target organoleptic profile, or due to changes to the raw materials allows for spoons to be set aside. In other words, after doing the recipe a couple times, cook’s get the hang of it, and have to increase their pace because there’s much to do to set up one’s station. Doing that, and also executing recipes well is not easy. Cook’s are nervous creatures. Always edgy because Chef’s expectations are high, and there’s never enough time. Practice, practice, practice and learn. Assimilate the feel for what is 15 grams of onions and go! Except for specific critical ingredients, whether it’s 15g or 18g doesn’t make a distinct difference, and as the saying goes, “a difference that makes no difference is no difference”. This agility to maneuver within a recipe’s confines applies much more to the kitchen than the bake shop of course, but the basic point is that recipes should begin with as much accuracy as possible, which means that measures refer to units that are precise every time the item is measured. Weights are. Spoonfuls of stuff are not.

The same laws of physics apply to 243 grams of egg whites as to one “cup” of it. If I whip a cup of egg whites, I can end up with 4 cups of meringue. How so? Because I put a lot of air into it. The ability of an egg white to form a meringue, and to retain that vastly expanded geometric configuration afterwards, and whether or not that foam begins to weep it's water content (syneresis) depends upon its chemical composition (egg white, sugar, sugar syrup, glucose, or acid used), the proportions of ingredients used, whether these were heated (and if so, to what degree), ingredient freshness, the amount of force applied, perhaps even the type of bowl used to mix it up. All things being equal, if I double the weight of egg whites used, I will double the subsequent volume yield provided I can execute the process properly. I can express the quantity of egg white required as 1 cup, or as its equivalent, 243 grams. Therefore, what is the advantage of specifying a *volume* of whites in the formula, especially considering that different sources claim a “cup” weighs different amounts, versus simply scaling a “cup” of whites, and using the gram weight instead? There is none, unless you believe teaspoons, tablespoons and beakers are magic. A volume measure is forever going to be inexact, the weight measure forever precise. The fact that we have to start by attempting to accurately fill a “cup”, before obtaining the precise gram weight value of that particular fill is absurd. It’s mere habit that we persist in using volume measures. There certainly are advantages to specifying ingredient weights.

Though we think in terms of making X number of portions, portions are not fundamental to a formula, they are derivative, variable, and reflect a particular baker’s notion of appropriate portion size suitable for a particular use. As we know, “appropriate” is subjective and relative. Portions are practically significant, but logically immaterial to the formula. From a given formula for Cheesecake batter I can make 25cm diameter cakes, or 20cm ones, and so, more or less units of cheesecake. A Cheesecake can be sliced into 12 portions or 10, or 8, or the batter can make many many little tartlets.

In place of “portions”, professionals substitute Total Formula Weight, or in the case of bread makers, Total Dough Weight. No one makes 30 portions of baguette dough, they make a Total Dough Weight (TDW) of basic French bread dough, Pain Ordinaire, and whatever portions are derived from that TDW is determined according to the shop’s style, specific business demands, cost considerations, market acceptable price points, guest preferences, sometimes by legal decree, and often also by tradition. Formula yield in the bread shop is Total Dough Weight, not numbers of portions. In the kitchen, traditionally, it has been volume yield, but using *The Kitchen Formula Calculator* it is a more precise value, Total Formula Weight.

Some might quibble, noting that it makes more difficult predicting portions if total formula weight is in its place. How can I know expected portions a Savoiardi formula will likely yield? The weight of egg whites and egg yolks doesn’t shed light on the subsequent volume; therefore knowing total formula weight isn’t so helpful. This misses the point that very few formula such as for Savoiardi mention either a total volume yield for the very good reason that every time a pastry maker prepares Savoiardi the volume yield is indeterminate, maybe more, maybe less depending on the precision of the execution, not just of ingredient measurement, but also adherence to proper mixing methodology. How does your baker feel today? Nor does it really make sense to say a Savoiardi formula yields 36 pieces, since each shop makes a “piece” according to its own standard. If I desired to write a formula for Savoiardi that is useful to any cook, any shop, then Total Formula Weight is the only metric that makes sense. Each shop can interpret such stuff as “portion size”, or “piece” according its own standard. In essence then, neither volume yield, nor portion yield is any more helpful. Additionally, this quibble ignores the basic fact that a cook can easily extrapolate from the Total Formula Weight to appropriate numbers of expected portions based on the house standard. Make the formula once or twice, and understanding expected yield in portions is not difficult, but Total Formula Weight also carries valuable practical value which “portion yield” lacks.

What then is “yield”?

Formula yield is a measure of the total weight of all ingredients in a formula. In *The Kitchen Formula Calculator*, “yield” is called *Total Formula Weight*. It is equal to the sum of all ingredient weights. Individual ingredient weights for bread crafting are derived from the desired TDW, Total Dough Weight. Total Formula Weight, is a condition, or put another way, an assumption, that will drive the calculations of ingredient weight, but it does so according to the specified baker’s percentages for each ingredient. Ingredient weights are derivative, not given. In this sense it is fundamental, and differs from the notion of “portions” as a recipe yield because numbers of portions one can hope for has nothing at all to do with determining ingredient weights. Portions don’t drive any sort of formulaic calculation. Baker’s Math is different from Martha Stewart Math. Cook’s Percentages can do the same thing in the kitchen, but it is a slightly different “math” than Baker’s Math. We shall soon see how.

While the sum of all ingredient weights for any formula (bake shop, bread shop or kitchen) will certainly equal the specified Total Formula Weight, they are determined by the Total Formula Weight, and not the other way around. Just as ingredient weights do not determine Total Formula Weight, neither is the formula itself determined by the total yield desired. This is a distinction born of the definition of “formula”. For bread baker’s the formula is nothing but the ingredients list, and their assigned baker’s percentages. Baker’s percentages are the heart of the formula because it is the mathematical expression of ingredient ratios. Total Dough Weight is a changeable condition that applies, and when taken together, these comprise the two data points required to calculate individual ingredient weights. The desired Total Dough Weight represents a baker's best guesstimate regarding how much is required to satisfy a one-day demand without either under or over producing. As seen in the section about formulae as argument form, it is a premise. Bakers increase or decrease the TDW of a formula to accommodate the expected demand, but the formula, i.e the ratios, do not change unless the day arrives that Chef decides to reformulate the Pain Ordinaire, and if that day comes, what then changes? The ratios change.

I do not propose that cooks begin to write recipes starting from ingredients Cook's Percentage values. That would not be helpful. And it is true that I can derive the Cook's Percentages from the ingredient weights. That's precisely what The Kitchen Formula Calculator does, but by doing so a mathematical basis is determined that can be useful for other important things. Re-scaling a recipe is no longer time consuming or error prone, and performing recipe costing is done much more efficiently.

This is not to say that a change in yield doesn’t affect the process at all. It certainly will, but what changes when the formula yield is changed? What changes are all the individual ingredient weights. The basic logic of a bread formulae is Baker’s Percentages, and of a kitchen formula, the Cook's Percentages. Percentages of a formula don’t change unless the Baker or Chef decides to change them. But any change to a single ingredient weight has no effect upon the others. What this singular change has done is to alter all the formula's ingredient ratios as percentage of the whole.

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