The starting point for any analysis along the lines you are considering begins with this simple expression:
DW = Pi (3.14) x R x R x TF,
Where DW is the desired finished dough weight, Pi is the Greek letter equal to 3.14, R is the radius of the pizza to be made using the weight of dough DW, and TF is the thickness factor. If you have any two of the variables in the expression, you can solve for the third variable. It’s a bit difficult to explain but the thickness factor TF is somewhat of a fiction. The part of the expression represented by 3.14 x R x R gives you the surface area of a circle with a radius R. Multiplying that surface area by the thickness factor TF arguably gives you a volume. But knowing the volume of a pizza dough isn’t particularly useful. The thickness factor TF is better viewed in the context of a particular pizza crust thickness, from thin to thick. Undoubtedly through experimentation, early pizza makers made doughs of different thicknesses and came up with a set of thickness factors TF that corresponded to the different thicknesses and could be used, along with the desired pizza sizes (diameters), to calculate the dough weights corresponding to those sizes.
In this vein, the value of 0.10 was assigned to a thin-crust pizza thickness, the value of 0.11 was assigned to an average (medium) pizza crust thickness, and a value of 0.12-0.13 was assigned to a thick-crust pizza. These values are not fixed in stone. If you make a thin-crust pizza having, say, the thickness factor 0.10 and find that the crust is too thin for your taste, you can increase the thickness factor to 0.105 and use that value the next time to determine the amount of dough to make the same size (diameter) pizza (but with the slightly thicker crust).
Baker’s percents come into play once the dough weight DW in the above expression is determined. Sometimes a dough formulation will come with baker’s percents, as (gratefully) was the case with the basic Lehmann NY style pizza dough recipe. Knowing the value for DW and using the baker’s percents, one can calculate the amount, by weight, of every ingredient in the recipe. The baker’s percents are valuable because they enable one to scale the recipe up or down pretty much at will. At other times, recipes are specified entirely in volume measurements, such as cups, tablespoons, etc. To make effective use of the above expression, one must first convert the volume measurements to weight measurements since baker’s percents only work with weights. Doing volume to weight conversions is not always easy to do (volume measurements are prone to substantial variation) and it can take several iterations of a recipe, and substantial use of a digital scale to weigh volumes of ingredients, to get results that are good enough to give confidence in the baker’s percents you calculate. I have done these types of conversions several times so I know it can be done. It’s just a lot more work.
Turning to your first question, the relationship between dough weight and pizza size is not linear in the sense I think you have in mind. To give you an example, assume that a piece of dough weighing 20 ounces can make a thin-style 16-inch pizza with a thickness factor of 0.10. Taking half of that amount of dough, 10 ounces (DW), and assuming the same thickness factor 0.10 (TF), solving for R in the above expression gives you a value for R of 5.6 inches (R is equal to the square root of 10/(3.14 x 0.10). Doubling that value gives you a pizza size (diameter) of 11.28, or a bit over 11 inches. Not 8 inches. To carry the analysis a bit further, if you decided you wanted to make a 12-inch pizza (R = 6) with the 0.10 thickness factor, the amount of dough you would need (DW) would be equal to 3.14 x 6 x 6 x 0.10, or 11.3 ounces. So, if you wanted, you could carve out 11.3 ounces from the original 20-ounce dough ball to make that 12-inch pizza. The remaining dough, 8.7 ounces, would be sufficient to make a roughly 10-inch pizza. So, as you can see, the above expression for DW is a versatile one and guarantees that the thicknesses of different sized pizzas will be constant for any given value for TF. I sometimes joke that I can scale down the Lehmann dough recipe to make canapes.
The thickness factor does come into play with deep-dish crusts, in a manner similar to that described above but quite a bit more complex. That is because a deep-dish pan has a side that also is covered with dough, along, of course, with the bottom of the pan. So the calculation of DW for a particular crust thickness has to be done in two steps with the results being added together. The first step is to calculate the amount of dough needed to cover the bottom of the pan (3.14 x R x R x TF). The second step is to calculate the amount of dough needed to cover the side of the pan (3.14 x D x PD x TF), where D is the diameter of the pan and PD is the depth of the pan. When I do the second calculation, I usually subtract a fraction of an inch from the number PD because the bottom crust uses up part of the side of the pan.
I don’t have good answers for your last two questions. I usually don’t have to worry about the actual dough thickness (whether in fractions of an inch or in centimeters) because I know that if I correctly calculated the dough weight for a particular size of pizza and made the dough properly I should get the desired thickness automatically so long as I shape and stretch the dough out to that size. The only doughs I have made that require rolling out are for thin-crust pizzas. It would be nice to have a sheeter to do this, but I have learned to live without one.
If you wish to read more on the above subject, you might take a look at Reply # 29 at page 2 of the Lehmann thread, at http://www.pizzamaking.com/forum/index.php/topic,576.20.html
. That post is a tutorial on the use of the expression DW and baker’s percents, and how to handle the small quantity lightweight ingredients like salt, yeast and sugar that can’t be weighed on most digital scales. If you’d like, I can also track down some of the baker’s percents work I did on the deep-dish case.