If I used your formula for a .50 caliber bore and subtracted twice the thickness of a .015 thick patch I would end up with a .470 diameter ball for the answer.
If I used a .45 caliber bore and subtracted twice the thickness of a .015 thick patch I would end up with a .420 diameter ball.
Seems to me that combination wouldn't do a thing to seal off the rifling grooves.
IMO, using a standard ball size that is .010 smaller than the bore is a good place to start.
That equals a .440 ball for a .45 or a .490 ball for a .50 cal barrel.
Using that simple "bore size - .010" to figure the ball size then leaves figuring out the patch thickness as the next thing to do.
In order to seal off the rifling grooves, the patch must be thicker than the groove is deep.
A thickness of about .002 minimum thicker is about the minimum that can seal off the thousands of pounds of gas pressure that happens when the main powder charge ignites.
Using this .002 value for rifling grooves that are .010 deep (like the Lyman GPR) says a .012 thick patch would be the minimum that could be expected to work well.
A little problem comes up now.
If I use a .440 diameter ball in my .45 and if I use a .012 thick patch adding the .440 ball size plus two thicknesses of the .012 thick patch, (there's patch material on both sides of the ball) I get a ball/patch diameter of .464.
The .450 diameter bore plus .010 rifling groove on one side + .010 rifling groove on the other side adds up to .470 groove diameter. The .464 patch/ball diameter is .006 smaller in size than the grooves.
If I use a .015 thick patch the .440 + 2X the .015 thick patch/ball diameter becomes .470. That's just enough to cause the patch to touch the rifling grooves.
If I use a .018 thick patch plus the .440 diameter ball the combination adds up to .476. That will seal off the rifling grooves nicely.
The only problem is cramming a .476 diameter patch/ball conbination into a .450 diameter bore takes a bit of work.
Fortunately, the patch material will crush down quite easily and a pure lead ball will deform if the loading pressures get too high.
This patch crushing and ball deforming is why getting the patch/ball started into the muzzle takes a bit of force. After it is started into the bore it becomes quite easy to ram it down the rest of the way to the powder charge (unless the bore is fouled).
At least that's my take on the subject. :hatsoff: