"WCT_Editor"I think you may be overthinking this. The way I'm reading your question is that it has more to do with testing the precision of the barrel but not necessarily the accuracy of the air rifle. For precision, I think you'd need to install the barrel on a special machine that consistently reproduces each shot like what I've seen on some of the FX factory tour videos.
Keeping the same POA each shot helps with rifle zero, but I can't say that it helps with each shot. The reason is that there are too many variables each time that may affect where the pellet impacts which is why you're looking at an average from a group.
Items that affect each shot include, but are not limited to, the amount of air used for that shot, weight of that individual pellet, pellet head size, pellet defects, how the pellet is loaded (individually or magazine), and final position of the pellet once it has been seated. Now add in the potential issues with your optics and how they are mounted let alone what happens inside the optic when making windage and elevation changes and the issues with second focal plane optics versus first focal plan optics when adjusting magnification. Also add in environmental conditions such as humidity, wind, temperature and then human error with not being able to replicate each shot 100% with trigger squeeze and other forces acting on the air rifle as a whole and you can see some of the potential problems.
In other words, one or more of the above variables may change with each shot, every 5 shots or something else and cause a different result. If you're looking at your rifles accuracy, it may be better to look at what you plan to use it for and the distances you plan to shoot and then decide what results you'll be happy with. For instance, if you're looking at a wildlife control/hunting air rifle do you need 1" accuracy at 40 yards or 1" accuracy at 100 yards? Using myself as the example, I like to strive for chipmunk head shots out to 100 yards accuracy with the majority being in the 30 - 80 yards. This means I need a setup where I can consistently duplicate impacts within 1/2" one way or the other away from the POA thus giving me a 1" accuracy criteria at 100 yards. (My terminology may be confusing as I'm defining 1" by saying that a shot may be 1/2" high to a 1/2" low from the POA for a total acceptable distance of 1" from the top to bottom. So while some may view this as 1/2" accuracy based on where the pellet impacts from POA, I don't.) For air rifles that cannot do this, I know not to use them for 1" 100 yard shots and instead find out what the longest acceptable range is then limit their use to that or designate a different accuracy level such as 3" at 100 yard. This works good for me with wildlife control needs but if I was shooting bench rest at 100 yards I don't think 1" or larger accuracy would be acceptable. For this, I may require impacts within 1/4" of the POA thus giving me a 1/2" at 100 yard accuracy.
For both of these uses I want to shoot at the same POA for several shots until I'm satisfied with the zero; however, once I have my zero for practice I want to pick a unique spot for each shot as that is what I'm going to be doing during actual use. This way I can see individual shot discrepancies and try to figure out what went wrong (pulled shot, wind, low power, bad feed from magazine, etc.). You can't do this when you shoot a 1/2" hole at 50 yards and keep putting pellets into it as you don't know what that individual pellet did and if a tread is developing that you don't notice until you actually need the accuracy you though you had.