We've been talking at the range about movement of the group center as the shooter moves from location to location on the target. If the gun is zeroed at, say, the top left bullseye on a 2' square paper, and the shooter moves around the paper from  bullseye to bullseye, they see/he sees the group center move. Or so they say. I don't see this, but I shoot with a muzzle clamp/anti-cant device a lot of the time. My bench rest is a Hoppe's with a bag double-sided-taped to it. The bagholder gizmo is free to turn on the screw, the round nut is loosened and the screw turned to raise and lower the rest, then the round nut is tightened. I don't know if somebody taught me to do this or what. 
I kind of thought the two guys who asked/talked most about the moving centers were new or inexperienced or something, but they both-and others who mentioned the problem-shoot some small jacketed bullet groups. 
Today I noticed that one of the rests didn't have a movable top, the top didn't swivel. A gray palstic but substantial rest. I looked at the other, didn't get into it, but  that one wasn't free to swivel but  would swivel. 
Is it the swiveling top that keeps my groups in the same relative position, or am I nuts? Or both?
Do you have your top bag holder thing free to swivel?
Do your group centers move as you move the point of aim around the paper?
joe brennan