Baker's percentages and how not to explain them

Tom Moertel — Sat, 16 Sep 2006 02:11:00 -0400

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 pound

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 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

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.

Math makes tea taste better

Tom Moertel — Mon, 11 Jul 2005 12:00:00 -0400

I enjoy tea, especially green varieties, which taste best when infused at less-than-boiling temperatures. The problem is that my electric water kettle can reach only one temperature reliably: a full-boiling 212 degF. To infuse my tea, then, I have devised a simple, reliable way of heating water to other temperatures.

I start by boiling three cups of water in the kettle. (I know that I need at least that much to warm my cup and infuse my tea.) Then I cool the boiling water to the desired temperature by adding just the right amount of tap water.

The trick, of course, is determining the right amount of tap water to add. In my house the tap water is about 80 degF. Thus to infuse at a green-tea-friendly 180 degF, I must solve the following equation:

3 cups · 212 degF + x cups · 80 degF = (3 + x) cups · 180 degF

Solving, I get x = 0.96, and so I draw just shy of a cup from the tap.

This boil-and-cool method is easy and effective. And it costs less than buying a temperature-adjustable water kettle, which would probably be inaccurate anyway.

Just one more example of how math makes life better.

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

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 pound

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

Tom Moertel's Weblog: Category math

Baker's percentages and how not to explain them

Math makes tea taste better