The optical rule-of-thumb is that the average (20/20) unaided human eye can resolve about an inch at 100 yards. That means it can see the difference between alternating 1/2" black and white lines. Beyond 100 yards the lines will appear gray.
With good optics the resolution correlates directly to magnification: a 4x scope will help us resolve 1/4" at 100 yards, a 10x scope 1/10", a 20x scope 1/20", etc. If we use an aiming point where the reticle can be pretty precisely applied, and there's no parallax in the scope at 100 yards, then a rifle will the ability to average .5" groups at 100 with a 20x scope should average .7" with a 4x scope, since .25" (4x scope resolution error) minus .05" (20x scope resolution error) is .2".
So yes, a higher-magnification scope SHOULD result in smaller groups at 100 yards, but the difference isn't nearly as much as many people believe. The difference in optical error between 10x and 20x scopes is only .05"--less than 1/16th inch at 100 yards.
If somebody's shooting groups at 100 yards with a 10x scope several times the size of groups shot with a 20x scope, then the error lies elsewhere than magnification--perhaps in parallax, but more probably in shooter error, including using an aiming point inappropriate to the reticle and magnification.
“Montana seems to me to be what a small boy would think Texas is like from hearing Texans.” John Steinbeck
