We might term this 4” at 100 yards practical field accuracy and is a combination of rifle accuracy and what we may term shooter accuracy.
If you are getting a 4 moa group then it isn't a simple as 1.5" from the gun therefore its 2.5" from the shooter that's not how random errors work.
This level of field accuracy (4” at 100 yards) is actually pretty good in typical field conditions.
No it's not. Better shooters than me would say you should be aiming (sic) for 2 moa in the field
So ignoring conditions like wind, you can keep your shots within a 12” circle at 300 yards with this rifle. The question arises as to whether you should seek more rifle accuracy, say a true 1 MOA rifle.
Obviously the dominant error is the shooter rather than the rifle so you would be trying to reduce the non-dominant error. You should try to improve shooting skills . Marginal improvements in rifle precision will be lost.
It turns out that given your shooter accuracy and under field conditions, this new 1 MOA rifle will now put your shots into a 3.84” circle at 100 yards (instead of the earlier 4” with your 1.5 MOA rifle)
That's not how it works. Using your terminology then the variation of the shooter error has to be combined with the variation in the rifle precision errors. These are probability driven effects so cannot be analysed by simple addition or subtraction. In practice some of your shots will be closer to the poa but the overall group will not actually change very much. You would need to run a monte carlo analysis a bit like the WEZ analysis tool does in the Applied Ballistics solver to get a true reflection in the reduction in group size. But as I said above, pick the biggest error first ie the Shooter.
Accuracy is a chain and if you reduce one error you do not necessarily get a better result as the improvement is overwhelmed by the dominant errors. In this case a marginal imporvement in the inherent rifle accuracy will be overwhelmed by the shooter error.
and will put your shots into a 11.52” circle at 300 yards (instead of the earlier 12” with your 1.5 MOA rifle). So you gain less than ½” smaller impact zone at 300 yards with the more accurate rifle. And just for fun, let’s consider a super-accurate ½ MOA rifle. What advantage do you have at 300 yards under typical field conditions? Well, it turns out that your earlier 12” circle at 300 yards with your 1.5 MOA rifle has been reduced to a 11.22” circle, so a net gain of about a ¾” smaller impact zone at 300 yards.
No, a crap shooter will still shoot a 4" group even with a 0.25 moa rifle. The rifles error will be dwarfed.
So the question is: will you benefit in a meaningful way with a 1 MOA or ½ MOA, rifle for deer hunting under typical field conditions? Seems to me that the answer is pretty clear. What do you think?
Learn to shoot is the answer.
It's the same point with reloading. People get lost down that rabbit hole trying to produce ever "better" ammo but the reduction in errors in the ammo are dwarfed by other errors in the system.
A similar analysis of the typical medium calibres for improved ballistics on the WEZ calculator will show that the improvement of hit probability from the shiny new cartridge isn't worth it unless you are shooting very small targets and can shoot small enough to reap the benefits. ie waste of time for stalking.
The WEZ calculator has saved me a fortune !