Tommy,
Shameless plug but I finally sent the new ASGCA book, "Designs On a Better Golf Course - Practical Answers to Common Questions" off to the printer. it tries to answer those kinds of questions for committees and others. On the subject of pinnable areas, here is what I wrote (the book is a self edited compilation of my old columns in Golf Course Industry, which also focused on the practical aspects of design):
Superintendents need 14-21 separate pin locations (usually 8-10 feet in diameter) to move the flagstick around, allowing recently used locations to heal. That’s only 1600 SF of cup space, but we should add another 2-5 feet for collar, 10-12 feet as the minimum distance to place a flagstick from the edge, and if thinking ahead, several feet to account for inevitable green shrinkage over time. That equates to 3850-5025 S.F., but only if 100% of the area can be used for hole locations. Most greens have some internal contouring that prevents cup placement, requiring 20-25% more space. 4,600-6,280 S.F. is a more practical minimum green size.
The 14-21 days are influenced by both play levels and maintenance practices.
Busy public courses usually have lesser maintenance $$$, and low play private clubs are typically pretty aggressive in their cultural practices, and the range can be broader on the low end. A few privates may get away with as few as 5-6 pin positions. (Although if they are closed on Monday's, the same pin tends to show up for the once a week on Saturday player on a 6 pin rotation, so 5, or 7-9 is more practical. Or actually, most supers have a pin rotation system looking like a tic tac toe board, so 9 may be the ideal minimum. For public courses, each of the spaces on the board should have 2 or 3 cup locations within to get you to 18-27.
And, according to the USGA, these should be in the 2-3% range. Jerry Lemons (ASGCA) did a chart showing it can be more depending on green speed, and the USGA itself uses a field measure system that, if you run the math, sets pins at slopes of as much as 3.88%. Some architects contour greens as low as 1.5%, so a cuppable area is probably one that ranges from 1.5-3.75% (no need to absolutely push the limit, because a quarter inch grading mistake could put you over the edge.) I can tell you that measuring green slopes using the USGA system at a private club with stimp 13 greens, that the 3.88% is right where golfers complain about a pin position being unfair. And, that is why gca's spend a lot of time on greens, usually checking slope on 10 foot grids just to make sure.
Now, I know many will come back with a "That's too rigid a rule of thumb" and maybe even a few courses that make only a few pin positions work. Sure, but you can't really fool Mother Nature, and in my 37 years experience, every green without a suitable number of pin positions elicits similar questions from golfers and complaints from supers.
As always, just MHO.