When I originally experimented with the Lehmann NY dough formulation using starters/preferments, I did all of the math and all of the adjustments to the values of quantities of ingredients by hand. Since I was experimenting, I didn't try for absolute precision.
These days, I use the preferment dough calculating tool at http://www.pizzamaking.com/preferment_calculator.html
. There are a few key inputs you need to use that tool. The first is how much starter/preferment you want to use. This can be stated in relation to either 1) the weight of the formula flour, 2) the weight of the formula water, or 3) the total dough weight. Different people use different ones of these methods, either out of personal preference or because they already have or can calculate the numbers for the selected method. I typically use a starter/preferment in relation to the weight of flour. A typical percent I use for a preferment application is 15-25%, depending on the strength and readiness of the starter/preferment that I will be using. The second key piece of information that you will need for the tool is the amount of water in the starter/preferment as a percent of the total weight of the starter/preferment. Usually, that number is determined by knowing how much flour and water (by weight) are used to regularly refresh a particular starter culture. As an example, Bill/SFNM refreshes his starter culture in such a way that it is 54% flour and 46% water by weight. Ed Wood, in the Appendix (pages 200, 201) of his book Classic Sourdoughs
gives representative flour/water quantities for "liquid" (48/52:flour/water) and "sponge" (65/35:flour/water) cultures. These work reasonably well. I believe the rest of the inputs required by the tool are fairly self-explanatory.
Unfortunately, the tool is not designed to work with strictly volume measurements. However, I have discovered that one doesn't have to be 100% correct with the starter composition. Most doughs will tolerate some variation without incident. You can also make minor adjustment to flour and water in the mixer bowl.
I have used the preferment dough calculating tool many times, under several different scenarios, and have yet to experience a failure that I could attribute to the tool. For more detail on the tool and how it works, you can click on the link "click here" at the page referenced above. If you have any questions about using the tool, maybe I can help answer them.