The grouping definition I use is the one that benchrest shooters use to score in the events I've attended. I am NOT saying this is a be all, end all rule, but it worked for that group as you work on your shooting technique or work to accurize your reloads (trying to figure out what kind of bullet, gunpowder, brass case, seating depth, OAL etc works best with a particular rifle).
So, how they measured it is: out of a group of five shots, take the longest distance between two, then SUBTRACT the caliber being used. Usual distance
For example, using .223 ammunition-, say you have 2 shots, from outside diameter to other outside diameter is 1". So- 1" - .223 equals
0.777" grouping. In benchrest, they do need to use that level of accuracy as their specialized rifles are very accurate and a match total aggregated score can be decided by a hundredth of an inch.
Using five shots also minimizes luck a little bit (compared to three shots) while keeping costs and barrel wear down (compared to say, 10) which are very real factors with (expensive!) real steel weapons.
So in the end, it's all relative. For airsoft where any hit counts, a 3-4" grouping at 100 feet is probably more than enough for in game accuracy. And for the record,
preciion and accuracy are similar- but NOT the same....
More info in case you are interested:
http://www.6mmbr.com/index.html
Clearly in airsoft we don't need that level of accuracy- but we can certainly use some of the same principles as we try to make our replicas more accurate.
The important part it would seem to me, is that whatever formula you use and methodology, the only way to know if you are making your replica more accurate is to try and minimize/equalize any factors that are beyond your total control (wind conditions, for example) and being as precise as possible in reproducing your firing of the replica:
-same distance
-same type of BB and if possible, hop up adjustment
-same rest/bipod/stance/shooting technique
-same optics/sights, zeroed consistently
-same EXACT point of aim (I'll explain more about the difference in point of aim and point of impact, as well as an easy trick to minimize waver when shooting at the bull later)
Try to ONLY tweak one factor at a time- be it BB weight, type of barrel or hop up bucking, etc. so you can get predictable results as you experiment.
Just an idea, hope it helps.
Full disclosure, I used to use a Remington 700 SPS in .223 and a Sabre Defence AR-15 in 5.56 for 100 yard benchrest competition. TOTALLY different from airsoft!
http://en.wikipedia.org/wiki/Benchrest_shooting