Baker's percentages and how not to explain them

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Tags: baking, math, oops

I like to bake, and I work in a professional kitchen from time to time, so I picked up The Baker’s Manual, 5th ed., hoping to carry it in my kitchen bag as a quick reference for large-scale recipes.

Before going further, you need to know two things about professional bakers. First, they measure dry ingredients not by volume, the way home bakers do, but by weight, which is both faster and more precise for the large quantities frequently used in professional kitchens. Second, when the pros write bread recipes, they express quantities in relative terms called “baker’s percentages.” Each ingredient’s quantity is given as a percentage of the recipe’s total flour weight. For example, the book provides the following recipe, referred to as a “formula,” in the section on baker’s percentages:

80.0% bread flour
20.0% whole wheat flour
66.0% water
2.0% salt
1.2% yeast

As you would expect, the percentages for bread flour and whole wheat flour add to 100 percent.

Now, here’s where the book goes down in flames. It attempts to explain how baker’s percentages let you easily scale recipes to any desired batch size, but it fails. Utterly. Here’s the book’s explanation for how to scale the above recipe to 300 pounds:

[T]o calculate the weight of each ingredient in the [300-pound] recipe, you add up all of the percentages in the above formula. This total percentage value is 169.2. Divide this number by the desired dough weight, 300 pounds, to get .564. Round this number up to get .6. Then multiply the percentage amount for each ingredient in the above recipe by .6 to obtain the larger weight required by the larger recipe. (Emphasis mine.)

When I read that explanation, I thought, Multiply? That’s the exact opposite of what you ought to do. And, sure enough, the book went on to prove its own explanation completely wrong:

80% bread flour * .6 = 48 pounds
20% whole wheat flour * .6 = 12 pounds
66% water * .6 = 39.6 pounds
2% salt * .6 = 1.2 pounds
1.2% yeast * .6 = .7 pounds

Note: the above is quoted verbatim from the book.

Does the “scaled-up” recipe yield 300 pounds? Nope. Add up the resulting weights and you get 101.5 pounds. Oops.

Is it really that hard to see that the correct method is simply to multiply each percentage by the desired batch size and then divide by the sum of percentages? In the case of the book’s 300-pound example, we would multiply each percentage in the recipe by the following factor:

300 pounds / 169 percent = 177.5 pounds

Let’s try it out:

80% bread flour * 177.5 pounds = 142 pounds
20% whole wheat flour * 177.5 pounds = 35.5 pounds
66% water * 177.5 pounds = 117.2 pounds
2% salt * 177.5 pounds = 3.55 pounds
1.2% yeast * 177.5 pounds = 2.13 pounds
Total 300 pounds

Now if you add up the resulting weights, you get the desired total of 300 pounds.

That the book not only gets the scaling method completely backward but then goes on to prove itself wrong is amazing. Didn’t anybody at John Wiley & Sons proofread the math?

Not exactly a confidence-builder for the rest of the book.