For this discussion, most folks are using a PAP location that is straight across from the gc.  While this makes it easier to visualize, most bowlers have a positive or negative vertical component to their PAP.  So let's use PAP components of 5" horizontal and 1" positive vertical.  First locate the PAP using whatever system you choose (the 4 1/2 x 4 you mentioned earlier works fine).  Now draw a 1" circle around the PAP, representing the vertical component.  ANY line that is tangent to that circle could be your midline.  (Most of them don't make any sense, but they still COULD be.)  Since the PAP vertical component is positive, you adjust the ball position so the tangent line you choose is BELOW the PAP (if the PAP had a negative vertical component, the tangent line would be above the PAP).  That's where another dimension is required.  If it's distance above the midline, choose your tangent line so the pin ends up there.  Hope this helps.  --  JohnP

As far as your example, all you'd have to tell the driller is that you want it drilled 4.5" x 4MB and 2.875" above midline. Make sure you've got an accurate PAP measurement, otherwise it's all for naught.

You COULD specify a left-to-right measurement from grip center, but it's being redundant. A right triangle is formed by 3 coordinates in the measurement: Pin, PAP, and the intersect of those 2 referenced to midline. The coordinates you're giving your driller are the distances measured between those points: Pin to PAP, Pin to midline (which the grip center is placed on in my example), and PAP to grip center (this one is the only one that's fixed). If there is a vertical component to the PAP measurement, then the bottom line is parallel to the midline (this only works on paper; on the ball it will appear bulged in the middle and thin on ends, because of the ball's spherical surface).

That left-to-right measurement is simply a function of the other measurements lining up. If you have the other coordinates, then you can calculate the pin's distance from grip center. Thusly, you don't really care about knowing that measurement, since it's actually determined by manipulating the others. Imagine a horizontal line with a dot floating over it. The dot has a line pointed down from it which is vertical and perpendicular to the flat line (that's your distance above midline) and a diagonal line to one end of our flat line (that's your P2P measurement). Keep your horizontal line still. Slide the dot along that diagonal line and you're altering the P2P distance (and consequently altering the distance from grip center). Slide the dot up or down the vertical line and you're altering the distance above midline (and because the ball is spherical, somewhat altering the distance from grip center).

As a side note, many drillers don't think about the distance above midline too much. They only reference the pin placement to the fingers, ie. above, below, or even with the fingers. This handicaps them in a way, by limiting their options for manipulating the ball's RG. However, it does make the layout process simpler.

Edited on 7/21/2007 12:35 PM

Edited on 7/21/2007 12:36 PM

That looks about right. Your driller will probably want to raise the pin to about 4" above midline, to get it an inch away from the finger holes. This is to keep from drilling into the bottom of the pin, which helps keep it from cracking.