Don, the problem with "projecting patterns" is that said projection has to depend on choke. Indeed, I agree that if you know how a gun patterns at 20 yards, you can work backward. And forward. BUT ONLY RELATIVE TO THAT PARTICULAR GUN WITH THAT PARTICULAR CHOKE. (And in fact, only with that particular LOAD.)
So you have two very important variables to consider: choke and load. Thus, projecting distribution of hits is valid ONLY FOR ONE SPECIFIC GUN, AND THE SPECIFIC LOAD BEING USED IN THAT SPECIFIC GUN.
Pretty hard to generalize, given those very important variables.
Larry, this would be the usual logic. However, Dr. Jones did not find this to work. He found more variability within the 10 patterns per gun-load than between various gun -loads provided that the constriction of the choke was the same. Soft shot in one load vs hard shot in the other may show a difference. That's about it until someone comes up with more data that will stand up to analysis.
DDA