Baker’s Math Explained
All of bread making revolves around a singular ingredient, namely flour. Baker’s Math uses the total weight of flour used in a bread formula as the basis for deriving all other ingredient weights. It does this mathematically by comparing the ratios of all ingredient weights to the total weight flour used. Bread formula ingredient ratios are expressed as ingredient Baker’s Percentages. The baker’s percentage for any ingredient simply means the ratio of the weight of that ingredient to that of Total Formula Flour, and is expressed as a percentage.
Baker’s Math uses the total weight of all flours used in a formula as the formula basis for determining the other non-flour ingredient weights in the formula. Every ingredient in a bread formula has a Baker’s percentage value. The baker’s percentage of Total Formula Flour is always 100%. It’s the formula basis. The peculiarity of Baker’s Math is that all bread formulae always adds up to more than 100% Total Baker’s Percentage because flour alone is 100%. More complex bread formulae can easily total over 300%. A basic Sourdough or Poolish bread formula (Pain Ordinaire) will likely total no more than 167% to 177% depending upon the degree of hydration (percentage of water) a baker uses.
Understanding the concept of Baker’s Percentage is a mathematical way of understanding a bread formula, and for comparing and analyzing different versions of the same type bread made by different bakers. When the mathematical structure is understood, baker’s can predict certain things about the final product: it’s texture, dough feel, the physical process phenomena that occur during baking, and also how the mixing and handling will change depending upon the recipe hydration (amount of water ratio used), and if other things like eggs, or some type of fat have been added.
To illustrate things, a simple bread formula such as typical French bread, aka Pain Ordinaire, calls for 1000 grams of total flour, 650 grams of water, 20 grams of salt, and 10 grams of yeast. Bearing in mind that Total Flour always has a baker’s percentage of 100%, this formula has a mathematical structure as follows: 100% flour, 65% water, 2% salt, 1% yeast. Added together, there’s a Total Formula Baker’s Percentage of 168%. These ratios comprise the mathematical structure of the formula. The ratios of the ingredients are the recipe. What actual ingredient quantities be required is logically irrelevant, even though it’s a practical necessity to know. We can know them by simply specifying how much Total Dough we desire to make. If the Total Dough Weight desired is 2000 grams, then the amounts of each ingredient can be determined using a simple formula.
Total Formula Weight ÷ Total Formula Baker’s Percentage = Total Flour Weight.
Consequently, all other ingredient weights are simply calculated.
Total Flour Weight x Ingredient Baker’s Percentage = Ingredient Weight.
In the example above the Total Dough Weight desired is 2000 grams, and the Total Formula Baker’s Percentage is 168%. To determine the weight of flour in the above example the calculation is as follows: (2000 ÷ 168) x 100 = 1190.47 grams. You must multiply the value of the parenthetical equation by 100 if you use the number 168, or a mathematically equivalent way of doing it is to change that formula to 2000 ÷ 1.68 = 1190.47. Both methods make the same calculation, but differently, and yield the same value. Calculating the weights of the other ingredients is simply a matter of multiplying the weight of total flour, i.e. 1190.47, times each ingredient baker’s percentage:
water = 1190.47 x .65 = 773.8 salt = 1190.47 x .02 = 23.8 yeast = 1190.47 x .01 = 11.9
Obviously the baker would round the values to 1190 + 774 + 24 + 12 = 2000.
Baker’s Math requires that the Total Baker’s Percentage of all flours called for in the formula always adds up to 100%. If more than one flour is used, then each flour ingredient represents a portion of the 100% of Total Formula Flour. For example, French T55 = 70%, T65 = 25%, Light Rye = 5%.
Baker’s Math is the logical framework of a bread recipe. Ingredient weights are always derivative values, fluctuating according to the Total Dough Weight of the formula that’s specified by the baker. Every day in a bakery, the TDW for the baker’s formulae can change depending on that day’s projected sales volume for each product, or simply by the whim of the baker. The logical structure of the bread recipe is the same until the baker changes the Baker’s Percentage value for any of the ingredients. If you change the baker’s percentage value for any ingredient, you have changed the formula because even a small change to one of the percentage values causes all of the remaining percentage values to change. Baker’s usually think about bread formulae in terms of the Baker’s Percentages, not the ingredient weights. Cooks don’t ever think this way. Recipes are written in ingredient weights, or in volume measures, or both, and Cook’s Percentages are unknowns.
It is commonly understood that a recipe is simply a list of ingredients and their quantities, plus a specified method of putting it together. “Quantity” can be variously expressed either in volumes required (teaspoons, tablespoons, cups,) or by their weights (ounces, pounds, grams, kilograms). This common perception is not correct. In fact, the ratios of ingredients is the recipe, and it's more easy to understand conceptually if, instead of using the word "recipe", formula is used. Ratios of ingredients in a formula comprise the logical structure of the "recipe".
Ingredients must be expressed as weights in order to use Baker’s Math (and to provide the mathematical basis for The Unabaker’s Kitchen Formula Calculator, which is described in detail in sevarlo previous posts. Ingredient weights are always merely derivative values, fluctuating depending upon the total yield (Total Dough Weight) specified for the formula. The ratios, however, remain the same, until they are changed by the baker. When the ratios, i.e. the Baker’s Percentages change, the formula changes.
These ratios are the underlying logic, the mathematical basis of the baker’s formula. If understanding this, then it becomes a fairly simple task to write a new formula based upon changed ratios, and a stipulated Total Dough Weight desired. This is a very common daily production management scenario in professional shops. Determine how much of each of the bakery’s offerings is required to meet the day’s expected sales, and scale the total yield up or down accordingly. Baker’s Math and Baker’s Percentages are a special way of designing formulae. Total Dough Weight, and Ingredient Baker’s Percentages are the foundational data required.
A Final Word
Imagine this! A baker writes a formula that specifies 100% flour, 85% water, 2% salt, 1% yeast and 5% oil. Can you guess what he is making? Most bakers can tell you it’s Focaccia bread. That’s how burrowed in is the concept of Baker’s Percentages in the brains of bakers.
If using The Unabaker’s Master Formula Calculator, the baker can plug these percentages into the table, and type in a Total Formula Weight. Doing so the baker will get an immediate report about the precise ingredient weights to use. How much to yield depends on how much baker expects to sell, but the value for yield, i.e. Total Formula Weight could be something silly like 103.347 grams for a single Focaccia roll, or it could be silly in the other direction, 10,285.37 grams. Either way the Master Formula Calculator will precisely calculate all ingredient weights to whatever decimal point is desired. In either case the total gram weight of the two formulae will be reported at the bottom of the grams column in the tables, and it would be exactly 103.347 and 10285.37.
Now imagine this! A cook writes a recipe for Pork Green Chile. The cook has not the slightest clue about Cook’s Percentages, so of course, cook specifies something like this:
5# pork shoulder, cut in large chunks
3/8 cup garlic, chopped
3 large yellow onions, chopped
6-8 pc dried green chili, seeds removed
1 tbsp crushed roasted coriander seed
1 tbsp crushed roasted cumin seed
2 or 3 sprigs Mexican oregano
1 or 2 sprigs epazote
2 tsp ground black pepper
1 small chunk of piloncillo
1/2 cup roasted Masa Harina
5 btl Tecate Beer
4 qts water
1 big bunch of cilantro, chopped
salt to taste
Can you figure out the mathematical profile for this recipe? What are the Cook’s Percentages? No, of course you can’t. Can you upscale it in your head by a factor of 2.3? Probably not. That’s why you need The Kitchen Formula Calculator's spinoff for Cooks and all recipes other than bread. What most cooks can do is to figure out a methodology for cooking it based on their experience. Most cooks could identify this as some type of stew, a spicy one, probably Chile, and they could make a representative rendition.
After reading this entire article, if you are not injured sufficiently already, you can harm yourself more by checking out the YouTube channel The Unabaker. I am not advising anything, I’m merely reporting.
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