A while back I had a discussion where a poster took exception to my statement that a hunter could ethically take a 300 yard shot on a moose with a 4 MOA rifle, provided he could shoot up to the rifle. A true 4 MOA rifle will always place it's bullet within 6" of the point of aim on a target at 300 yards, but a good hunting rifle might always place the first cold bore shot within a half inch of the point of aim, regardless of where it might place the 20th.
If a good hunting rifle always places its first cold bore shot within half an inch of (somewhere), then it is shooting a 1" group at 300 yards, and it is therefore a 1/3-MOA rifle.
If it places subsequent, non-cold-bore shots in a larger group, but it still reliably places the first cold-bore shot within 1/2" of a particular point, then it is a 1/3-MOA rifle with an asterisk beside it (i.e. is has a warm barrel wandering zero problem).
The hunter is not concerned that his 20th round fired in quick succession might be 6" away from his first, because if he hasn't solved the problem with his first couple of shots, he probably won't solve it. Yet he has a 4 minute rifle not a 1 minute rifle.
With hunting rifles, in particular with factory-built hunting rifles, there are very real problems that we might have to be aware of, and learn how to work around (e.g. point of impact shifting as a barrel warms up). These problems in theory could be fixed by a gunsmith, or they can be "worked around" by the experimenter during testing (e.g. shooting each shot with a cool barrel).
But the important definition of a group, is where you expect your shots to land. There are a variety of legitimate definitions too, each with their own uses - for example, where all your shots land, where most of your shots land, where many of your shots land, where "the-average" (defined in whatever way you wish) shot lands.
It's also OK if you define each shot that "counts" in a special way (so long as you do it ahead of time, before you've fired the shot and seen where it has landed!). You can consider only "the first cold bore shot of the day", or "a shot fired from a fully cooled barrel". That doesn't change the stats any, though it can make your testing *much* more labourious(!).
A hunting rifle with a wandering zero that shoots honest 4-MOA groups when the barrel is allowed to get too warm may well shoot quite a bit better if every shot is fired from a cold (or cool) barrel. But except for the truly extraordinary "lucky" factory rifles that really do come along once in a blue moon, a realistic accuracy figure might be 1.0-1.5 MOA group size (for groups with ten or more shots in them).
So if you had a hunting rifle that delivered a true 1.5 MOA grouping with its cold-barreled shots, you would expect every cold bore shot to go into a 4.5" diameter group at 300 yards, or phrased another way, each individual shot to be no more than 2.25" from the group's centre (and BTW you won't know where the group's centre is, until you have finished firing all the shots in your group).
"Anywhere within 2.25 inches" means literally that. Shots number 1,2,3 and 5 might be within half an inch of each other but near the left edge of the group, and shot number 4 might be nearly at the right edge of the group. This might look like "a half inch group with a flyer that opened it up to 4 inches", but it isn't; it is just one of the many ways that groups can form. Especially when statistics decides to be perverse and pick on you.
The computer program represents the results accrued from a huge sample size, while the real world results are from a relatively small sample.
A minor nit (which doesn't detract from the actual point you are making). Ballistics programs compute trajectories of a single, idealized bullet. To the extent that the right parameters are used, they give pretty darn good results. (it is true that the data that are used to derive the information that goes into ballistics programs come from real world measurements of many actual fired shots - but all of these data are blended together and combined to form an idealized internal "model" of how a bullet interacts with the air).
