Magnification

More magnification = better aiming precision = smaller groups

However it also means a smaller field of view and poorer brightness. These factors are more of a consideration for hunting than they are for target shooting, and are pretty well wiped away by having a variable power scope that you can dial back when needed.

Personally I prefer high magnification for hunting situations too. Reason being, a literal head shot isn't good enough with small caliber air rifles. It has to be a brain shot, and the brain of a gray squirrel is a teeny, tiny target at the 30 - 60 yards I'm typically shooting.

One more thing, many people prefer low-ish magnification for offhand shooting. At high magnification, it can be frustrating waving back and forth trying to hold steady on the target. It's just easier to coordinate the necessary muscle control to get it on target "good enough" when your sight picture is zoomed out a bit.
 
For paper punching I would recommend getting as high as you can just as long as you get a clear sight picture. I have scopes that are 6-24 but notice 20x is very clear. Anymore the scope is not as clear.

For hunting, I like 10x for most situations but I have used 4x for following fast moving objects like tracking a running coyote. Once the coyote stops you have seconds or less to make your shot and 4x does just fine. Even 10x seems to close for some situations and I'm actually looking at several fixed 6x scopes to try out for coyote hunting.
 
I've done so much research on scopes lately I have analysis paralysis. The number of brands and options leaves a person dizzy. I also struggle with finding an optimum scope magnification as it relates to airguns, and have come to some conclusions during my quest. The first question to ask is, what do you intend to use the scope for? If you're mostly bench/target shooting, then higher mag seems to be favored. Allows you to really "zone in" on punching the bullseye, and you don't need a large FOV for target shooting. I think 5-25 and 6-24 are popular but I don't shoot bench so not sure what people are using. If you want to use your airgun for close range (less than 50 yards) pest control then a 2.5-10 or 3-12 should work fine. If your pesting out to 100 yards, then a 3-15, 4-16, or 3-18 should work well. For me, the 3-18 covers a nice range for most pesting applications. These are my opinions of course based on experiences.

Why 15-18x power for pesting? Take a quarter out your pocket and set it 100 yards away. This is your kill zone on most small critters. Now look at the quarter on 9x power, then look at it on 18x power. You will quickly see why some airgun enthusiasts prefer the higher power scopes. Similarly, you won't want to use 18x mag on a target only 10-15 yards away. For close range you'll need to dial back down to 3-4x mag for those shots. 

Hope this helps.


 
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I’ll tell ya what I’ve learned. Last spring & summer we were knee deep in ground squirrels at a max range at about 60 yards. This year they’re out farther, must have really gutted them. Since this year the close ones are like 100 yards to 150+. Strelok has really helped getting those longer shots that anything inside 100 yards is relatively easy. Beyond that, I’ve learned that for me and the small size of the squirrels, I prefer my 30x Bushnell over my 20x sightron. My point being, last year I would have thought a smaller mag scope would have sufficed for my shooting needs. Now I’m more convinced that the scope is an equally important part of the equation. 
 
High Power scopes can be turned down. that gives you somewhre to go, and not be stuck at some point. Also lets you calibrate it easier and still have some mag left over. My AEON 10-40 is locked around 36.5x. at that power its calibrated to 1" per "dot".....

My issue for hi power scopes and off hand _isnt_ "shakiness", its acquistion. FOV is quite narrow, and just finding the target off hand is the challenge.....



Count me in the "more power the better" camp....