I went to see the movie, Open Waters. Let me just say that it is best not to stray from a spot, unless someone you know is at the spot. Now that I'm totally depressed from the movie, let me see if I can answer your questions.
In general, I've worked in entire industries that relied on rule of thumbs (ROTs), and I've generated my share of them. When I see things like 1%, I see signs of a rule of thumb, which is meant to get customers within an acceptable level, while reducing error by its consistency and simplification. My calculation, on the other hand, considers only the actual numbers from the manufacturer and was used to verify the accuracy of the 1% number.
The calculation can have a degree of inaccuracy, depending on these factors that come to mind:
1) The number of decimal positions. I used 4 which has negligible impact on the final number.
2) The variation given by the manufacturer. In the case of Keith and Giusto's, for example, they provide their specifications within a given range. Giusto's Baker's flour is 11% - 11.5% in their specs; I decided to choose 11.5%.
3) Unless you work with the manufacturer specs, the numbers extracted from the labels can be inconsistent, with wide variations. All Purpose standards call for 9% - 12%; bread flour calls for 12 - 13%; and high gluten up to 15%. Yet, Giusto's 11.5% "bread" flour does not fall within standard labeling convention (it's even less than KA's All Purpose). In addition, the numbers on the labels can be way off because of the rounding you mentioned. Giusto's label says "3 g protein for 30g serving." This is 10%, which is way off from their 11.7% in their specs.
4) Do you add the Vital Gluten to 2 cups; or do you extract the number of Vital Gluten tsp from the Baker's flour to create a total of 2 cups? In either case, you will be a bit off, since the calculation is based on 2 cups, not 2 cups +/- the amount of vital gluten (in this case, about 1 TBL).
Q #1: does the 4.05 gram figure represent the number of grams of protein for a 1/4-cup portion of an existing Giusto flour with 13.5% protein (a Giusto spec figure), and did you weigh a 1/4-cup portion of the vital wheat gluten to get the 21 gram figure?
Response: Since manufacturer specifications were available, I was able to avoid the use of labels, and produce the actual protein levels per 1/4 cup (30 g serving). I am able to reverse engineer the formula you normally use to determine % proteins, since I am working with manufacturer specs for % protein that have not been rounded.
Bakers flour is 11.5% Protein: .115 * 30g (1/4 cup total serving) = 3.45g.
vital wheat gluten is 70%: .7 * 30g = 21g
Hi-Gluten Preference is an arbitrary number. I picked 13.5% protein because that is what their protein level is that I am looking to purchase, and I want to be able to compare the differencs between how I achieve these numbers, and however Giusto's achieve their high gluten level. The protein level was achieved by: .135 * 30g = 4.05g
Question #2: is there any way to tell which of the two approaches you used is the more accurate one?
Response: Rule of Thumbs normally pick a sweet spot and the accuracy goes down as you deviate from the sweet spot. The calculation does not rely on a statistical reference, and is as accurate as the multiplication and division used within the equation. In both cases, they rely on numbers not from the manufacturer, which is far better if provided by the manufacturer, rather than the label.
Question #3: Your analysis seems to suggest that one can effectively convert all-purpose flour to high-gluten flour by adding about 3 teaspoons of vital wheat gluten to each 2 cups of all-purpose flour. I realize that the precise amount will depend on the percent of protein in the all-purpose flour and the particular vital wheat gluten used--which may vary from brand to brand--but I would think that about 3 teaspoons of vital wheat gluten for each 2 cups of all-purpose flour would pretty much do the trick for almost any brand of all-purpose flour. Does that seem about right?
Response: Well, 11.7% is at the high end of the All Purpose flour, and as long as you use King Arthur, you're within this number. But, if you use other All Purpose or Unbleached White Flours, the 11.7% can easily be 1% over in protein. As you move into the Bread flours, you will be off by 1% the other way and you only need to add 1.1 tsp of vital to these flours (e.g., KA Bread & Gold Medal Specialty Bread are examples of 12.7%).
I did the calculation for Bob's Red Mill Vital Gluten, since it is readily available at different stores in small bags, including Whole Foods (I even saw it at Safway or Albertsons). It has very little impact, since it is 23g (just over 75% protein according to specs) instead of Giusto's 21g vital gluten. For Giusto's Baker's Bread or KA All Purpose, you need to add 2 1/2 tsp (2.5) of Bob's Red Mill Vital Gluten.
Hence: To reach a high gluten level of 13.5%,
* Add just under 1 TBL (3 tsp) of Giusto's 70% Vital Gluten or 2 1/2 tsp of Bob's Red Mill Vital Gluten to KA's All Purpose flour or Giusto's Baker's flour.
* Add just over 1 tsp of Giusto's Vital Gluten or exactly 1 tsp of Bob's Red Mill to either KA's Bread or Gold Medal Specialty Bread flour (5 lb yellow bag available just about anywhere).
The 13.5% was used with Giusto's high gluten in mind. Other High Gluten flours are around 14.1% protein. Since Vital Glutens, such as Bob's Red Mill, is from the endosperm, it is similar to unbleached wheat flour that usually discards the outside bran, which is found in whole wheat.