One of the most embarrassing moments of my life involves baking muffins for a visitor in my apartment back in April of 2007. At a little before 8 in the morning I had flour, oil, and eggs but no milk. I knocked on the door of my neighbor - who I'd seen only twice before and luckily she was home and let me borrow some milk. Like the good ol' days, huh?

One problem was averted yet another arose. These "muffins" I was making actually had to be good, not the barely eatable non-sense I usually made. Having no other game plan I threw something together, prayed, and dished out my questionable muffins to my guest. What a bad host I am!
That day, I thought really hard... so what exactly are baked goods? We say "pie crust, muffin, cupcake, coffee cake, puff pastry, and croissant", but do we know what they actually mean?

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I used to dismiss baking as making goo or sugar covered pillow-like bread, but this is not entirely true. Yes, the essence of baking can be hidden behind all the goo, but this is obscenity encroaching on the fine art of baked goods and unfortunately unless one is a connoisseur the fundamental distinctions are not noted very well. So I spent some time - a really long time - baking, serving, and eating cakes, cookies, coffee cakes, etc. trying to figure out what fundamentally defines baked goods. I finally came up with an answer which was naturally due to my initial false assumptions and failures.
I tried using a numerical range, but after following this method and getting unsatisfactory results I knew there was still room for culinary error, something that was unacceptable. I envisioned having a few criteria one could follow and from there spontaneously throw in random ingredients like a flux capacitor to get a satisfactory batter or dough for a baked good.

After pouring through countless recipes I finally created a procedure to accurately characterize baked goods, in it, we must employ three calculated values. These values are the moistness value, butter(oil) content, and the egg content; all obtained from a recipe.
Of course, a recipe provides a list of ingredients and measurements, which includes instructions for combining the ingredients. Each ingredient can be considered either a wet or a dry ingredient. In the following procedure, most wet ingredients are given constant values (see Table1.), while flavorings, leavenings (baking powder, baking soda, yeast, etc.), seasonings (e.g. salt), and food pieces (shredded coconut, walnut pieces, blueberries, etc.) are omitted. The constant values are multiplied by their respective quantities (in cups) yielding a product. The products are summed and finally divided by the dry ingredient product (obtained from Table 2.) to yield a solution called the moistness value.

I know... "How can you possibly use volume (cups)?" Either volume or mass can be used assuming standard mass/volume conversions, but I found using volume greatly simplifies the calculations.

But what is this beast of a procedure? Does it design baked goods? Does it analyze baked goods? After years of reinventing itself, the procedure has settled in the role of a design tool which aides in creating new recipes, an analysis tool for reviewing recipes with no need for baking, and a characterization tool which attempts to define all possible baked goods. Immense, yet its most useful role is likely in allowing one to substitute ingredients.

Wet Ingredient	Value/cup
banana (mashed)	0.375
butter, oil, shortening	0.5
buttermilk	1
cream cheese	0.35
cooked (sweet) potatoes	0.5
cranberries mashed/pulsed with sugar	0.2
grated carrots	1/3
jumbo eggs	1/4
extra-large eggs	1/5
large eggs	1/6
large egg yolk	1/8
large egg white	1/24
honey, milk, molasses, orange juice, water	1
sour cream, yogurt, whipping, heavy cream	0.7
applesauce	0.6

Table 1. Values for some common wet ingredients

Dry Ingredient	Value/cup
almond paste	1
finely ground pecans, walnuts, almonds	1/3
flour (cocoa powder, whole wheat, all-purpose, etc.)	1
old fashioned rolled oats	0.5
melted chocolate (non-dark)	0.5
peanut butter	2/3

Table 2. Values for some common dry ingredients

All values in Table 1 and Table 2 are "per cup" except for eggs which is "per egg". Let's look at an excerpt from an example recipe.

Quantity	Ingredient	Wet	Dry
3 1/2 cups	all-purpose flour	-	3.5
1 teaspoon	baking powder	-	-
1 teaspoon	baking soda	-	-
3/4 teaspoon	salt	-	-
16 tablespoons	butter	0.5	-
2 cups	sugar	-	-
3	large eggs	0.5	-
2 teaspoons	vanilla extract	-	-
2 cups	old-fashion rolled oats	-	1

Table 3. Sample mystery recipe

(1)

(2)

In equation (1), a, b, c, and d represent quantities for wet ingredients x₁ (butter) and x₂ (eggs) and dry ingredients x₃ (flour) and x₄ (oats) respectively. Equation (2) provides an accompanying practical calculation for equation (1).

Note the following relations:
3 teaspoons = 1 tablespoon
16 tablespoons = 1 cup

The resulting moistness value, butter content, and egg content are: 0.22, 11.1%, 0.67E; (0.5/4.5) and (3/4.5) gave us the butter and egg content respectively (see next section for an explanation of moistness, butter content, and egg content). These are our characterization numbers. You can save time and just use this web application to get the same numbers. From using Table 4 and our characterization numbers, we see this is some sort of a cookie.

[Note from the editor, Michael Chu: Michael Ohene's Table 4 was too detailed to present in HTML here, so click on this image to load a PDF showing the complete table.]

Table 4. Periodicity of Baked Goods in the USA

Explanation of the chart (Table 4)
Moistness - wet ingredient to dry ingredient percentage^{1 2}.A higher moistness value corresponds to a more fluid/less stiff batter.
Butter content - butter/oil/shortening to dry ingredient ratio. On the chart the butter content values are divided into "low", "medium", "high", and "very high" to make the chart more intuitive.
Egg content - number of eggs to dry ingredient ratio.

Table 4 was formed by plotting hundreds of recipes. Anything falling within a grid is what that grid is labeled (e.g. scone). Some grids are empty because it would not make sense for them to exist. For example, a very moist bread (0.60) with a low butter content would be airy and tasteless.

Results and interesting facts
Unlike most other baked goods cakes have an extra criterion, when buttermilk is replaced by a constant value of 1.75, a cake must equal a value between 1 - 1.25. This requirement is due to the acid content in buttermilk.

Also notice that having one or more eggs per a cup of dry ingredients results in a cakey baked good. Therefore if you are experimenting with chocolate chip recipes and use a cup of flour, you must discard some of the egg you plan to use.

A moistness value of 0.35 - 0.47 usually results in a yeast dough. A moistness value above 0.50 cannot be kneaded.

The baked goods (brownies, cookies, cakes, etc.) that kids like are on the outer edges of Table 4.

Can you find a recipe that defies the logic (is outside the groupings) of this chart? Sometimes, but it most likely received bad reviews.

Final notes: Mixing instructions, directions on how to combine ingredients, are usually shared for similar types of baked goods. For example, you always use cold water for pie crust recipes.

Leavening (baking soda and baking powder): used to make a dough or batter rise when baked. Table 5 below shows common leavening ratios. What is a leavening ratio? Comparing teaspoons of leavening to cups of dry ingredients is a good rule of thumb. For example, in Table 3 the leavening ratio was 0.44 for our cookie. Also, if you use an acid (e.g. buttermilk, vinegar), baking soda must be included.

Baked Good	Leavening Ratio
shortbread cookie	0 - 0.15
cookie	0.15 - 0.5
pound cake	0 - 0.8
muffin	0.8 - 1.66
cake	0.8 - 1.66
biscuit	1 - 2.5

Table 5. Leavening ratios

Have fun!

Footnotes
¹When a glaze is used - usually for pound cakes - the moistness value increases by 0.05. For example a moistness value of 0.66 will become 0.71 if a glaze is used.^{^
2}This assumes standard/normal baking temperature and pressure/altitude.^{^}

Update (July 31, 2010): Added a link to Michael Ohene's web-based recipe characterization numbers calculator.


Michael Ohene is an electrical engineer by profession with an interest in the modeling and classification of artistic disciplines including: baking, knot tying, and floral design. At the heart of his research at www.whatsthesequency.com he demonstrates the ability to transform random logic into more accessible visual logic.

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