The Kitchen Formula Calculator v3

Part 5   The Kitchen Formula Calculator v4 & The Logical Structure Of A Recipe

Baker’s Percentages & Cook’s Percentages

Baker’s Math is a special way of constructing bread formulae. For bread making the total weight of flour used in the formula is the key. Flour is the formula basis, and all other ingredients are expressed as percentages of flour. Flour is always 100%. If you compare the weight of flour to itself, it’s obviously 100%. If more than one flour is used, then each flour is expressed as a percentage of the total flour weight used, but together the different flours must always add up to 100%. For example, French T55 @ 55%, T80 at 30%, Light Rye @ 15%.

“Baker’s Percentage” simply means that the weight of an ingredient when compared to the total weight of all flours used in the formula is a ratio expressed as a percentage. It’s simple to understand. If total flour used in a formula weighs 100 grams, and water is 65g, then water has a baker’s percentage of 65%. The same goes for all other ingredients used in the formula. Despite it’s simplicity, there are ramifications that may seem odd at first glance, namely, if one adds up all the baker’s percentages in a bread formula, the result is always more than 100% because flour itself is 100%, plus water 65%, salt 2%, and yeast 1% means that this simple formula totals 168% Total Formula Baker’s Percentage. This is an important number for determining the actual weight of flour to be used if a formula is written using only baker’s percentages. This to be explained in a later installment of this series, but getting over the apparent oddity is not hard to do.

Here’s a useful way to visualize Baker's Math, and Baker’s Percentages. Imagine a bar graph that compares the power output of a variety of different motors to the power output of a typical Formula 1 race car engine, and then expresses each motor as a percentage of the Formula 1 engine. Each motor is a different color bar on the graph, and each bar is displayed as a height on the graph that corresponds to it’s power. On the left of the graph is a reference scale, which in this example might go from 0 up to 1000. The reference scale denotes horsepower, and at every 200 hp increment up the scale a horizontal line extends across the graph. The height of each bar reports the horsepower rating of each motor being compared. Let’s stipulate that the Formula 1 engine develops 800 hp, a cute little Mazda 2 rates 100 hp, a big bad Ford Ranger generates 270 hp, and a handy little Honda push mower squeezes out 5 hp. In this example, 800 hp is the reference point for the graph. Let’s call it the 100% (just as we do for flour in bread formulae) because it's the value that the others will be rated against, and if compared to itself it is always 100% as powerful as itself. The Mazda 2 engine by comparison is only 12.5% as powerful as the Formula 1, the Ford Ranger is 33.7% as powerful, and the Honda lawnmower is .6% as powerful. If one owned all these motors, they’d have 1175 total horsepower in their garage, which is equal to 146.8% of the Formula 1 motor alone. This is how Baker’s Percentages work. This is not something that lonely bakers created to amuse themselves. Baker’s Percentages have functional purposes. 

Curious math to grasp? This is the math of bar graphs, which is a different analytical approach from how a pie chart works. Pie charts report percentages of each slice of the pie compared to the whole. With pie charts, things always add up to 100%. Bar graphs are typically used to compare the values of several similar things, usually with a point of reference. The Unabaker has simply applied to all recipes other than for bread, the analytical logic of the pie chart, and bar graph logic to bread formulae. Baker’s Percentages is a well known concept, but in the big wide world of cooking things, the notion of “Cook’s Percentages” has been unexamined, and so, the benefits of thinking of a cook’s recipe in terms of it’s Cook’s Percentages unrealized.

Bar graph logic is the basis of Baker’s Percentages and Baker’s Math. It helps to dismiss the oddity of a thing being more than 100%. Bar graph logic has common applications. The logic of the bar graph is widely used for analyzing important stuff like the results of our investments. For example, suppose that we originally put 100 bucks into a stock, and its value grew over time to 123 bucks. The market value of the stock is now 123% of its original cost. We do not fret about this, nor puzzle over it. Our earnest hope is to have an ever increasing market value; the original cost being just a reference point. People think of the totality of something, and imagine a goblet which cannot be filled more than 100% without spilling over, but formulae used in bakeshops are not the same sorts of things as goblets. In any case, goblets have various attributes, not just utilitarian. Obviously, a goblet, or a vase, or a piece of crystal stemware cannot be filled more than all the way, but it might today be more valuable in many respects than when it was first manufactured, or 20 years from now perhaps even more so. Should you stumble upon the Holy Grail one day while cleaning out your deceased auntie’s attic, would you be wondering if you can fill it more than full? 

Totaling more than 100% is fundamental to future value projections. Such stuff is familiar to all. What’s the projected value of your home ten years from now? How much can I get for my brand new car in five years. If I buy that crazy expensive bottle of Pappy McDoo 22-year-old Bourbon, what’s the return on my investment likely to be in five years? Future value projections are fundamental selling points, and the core selling point for every investment prospectus ever written. After we’re hooked by that rosy prospect, we earnestly hope things don’t continue to add up to just 100% for very long, now do we? This is how Baker’s Math works as well. Nothing ever adds up to 100%. It starts there, just as the value of your home at the point of purchase is 100% of what you paid for it. If a bread formula only amounted to 100% total formula baker’s percentage, then we’d have to enjoy eating flour alone. In bake shops, as we add ingredients to a formula, it increases in value, which in this case means, its Total Formula Baker's Percentage increases, and of course, the cost to produce it as well. Could I write a bread formula as a future value projection, something worth investing in? Yes, of course! It would be part of what we call a business plan. Can you imagine what sort of index we’d use to do so, or its core selling points? Even if you cannot, here’s some math that baker’s (and potential investors in baker's new bakery bizplan) also understand. A baguette formula (flour, water, salt & yeast) costs $20.00 to produce, and yields 18 kilograms of Total Dough Weight, which is then cut into 60 each 300 gram portions of dough, and shaped into baguette loaves. After baking they can sell for four bucks a piece. The future value of this dough is therefore $240.00, and it’s a not such a distant future, it’s later today! Not a bad investment, right? Assuming that we make the dough and the baguette properly, and each baguette finds a buyer, then we calculate the future value of the investment made to produce the dough as 1,200%. Bread formulae, and their Baker’s Percentages might very easily be written in bar graph format, but I think it would not be so convenient for busy baker’s. 

By contrast, The Kitchen Formula Calculator uses what I call “Cook's Percentages”. Cook’s Percentages are similar to Baker’s Percentages, but with important differences. Wanting to develop a mathematical structure for kitchen recipe writing, I developed the idea of analyzing non-flour based recipes in terms of each ingredient’s ratio to the whole, and I called these “Cook’s Percentages”. This was not a difficult piece of work. I used food product labeling as a model to construct the Cook's Percentage format. Looking at a can of baked beans, in many countries the producer is obliged to list ingredients by the percentages of the total each represents. Thus beans might be 50%, tomatoes 20%, tomato paste 5%, brown sugar 12%, onions 8%, various spices 3%, salt 2%. If a bread formula is more akin to a bar graph, then a food product label is like a pie chart, and so are all recipes, but unlike the bar graph, pie charts always add up to 100%. For example, we might want to visualize our various monthly expenses over a period of time as slices of the pie, the whole thing adding up to 100% of our monthly expenses for that period. Unlike bar graphs, pie charts are useful for breaking down the percentages that each of the various elements represent compared to the whole because it gives us data that is useful for stuff like managing our money, and creating budgets for projected future expenses. The same goes for Cook’s Percentages in a recipe. Each ingredient is a certain percentage of the whole thing, and the whole thing always adds up to 100%. Baker’s Percentages never add up to 100% because that’s where they start. Flour alone is 100%. Cook’s Percentages always add up to 100%, not more, not a shred less. Even though baker's use Baker's Percentages to write bread formulae, all bread formulae can be written just as easily using Cook's Percentages, but unless a recipe has a flour centric ingredients list, it cannot be expressed using Baker's Percentages. Here's an example.

Pain Ordinaire, typical French Bread is expressed in Baker's Percentages as: 

Flour 100%   Water 65%   Salt 2%   Yeast 1%.  This formula has a Total Formula Baker's Percentage of 168%. Using the 168 figure, I can derive the weight of flour in a formula once a Total Dough Weight is specified by the baker. I do so by dividing the Total Dough Weight by 168. For example, if baker desires to produce 2000 grams of dough, then the weight of flour will be 1190.47 grams. Since all other formula ingredients are expressed as percentages of the weight of flour use, then the weights of all other ingredients can be calculated:  water = 1190.47 x .65    salt = 1190.47 x .02    yeast = 1190.47 x .01. 

The same formula for Pain Ordinaire can be expressed using Cook's Percentages. If you do the calculations above, the values derived for each ingredient weight can then be compared to the total weight of dough, which we stipulated as 2000 grams. We will find that Flour is 59.5% of 2000, Water is 38.7%, Salt is 1.2%, and Yeast is .6%. You will see that 59.5% of 2000 grams = 1190, 38.7% of 2000 = 774, 1.2% of 2000 = 24, and .6% of 2000 = 12. These are in fact the rounded values for ingredients using 1190 in stead of 1190.47...as a baker would likely do in his shop.

Cook's Percentages can be used to write any type of formula or recipe. I sometimes use The Kitchen Formula Calculator (which is based upon Cook's Percentages) for simple breads such as tortilla, chapati, and paratha, Baker's Percentages are traditionally only useful if making bread, although I could use baker's percentages and The Unabaker's Master Formula Calculator to write recipes for such stuff as batters, or any other preparation as long as the recipe for it requires flour as a crucial ingredient.

Baker's Percentages and Baker's Math is the logic of bar graphs. Cook's Percentages and Cook's Math, that of pie charts.