The "Math" says that "All else being Equal" the range at which various loads will put the same number of pellets on target is proportional to the Sq Root of number of pellets.
The catch of course is that "All other things" are not always equal.

The bottom line though is "IF" a lighter charge gives an equal effective range it has to do so by giving a tighter pattern, thus less margin for aiming error.

The "Inconsistency" of thinking along these lines though has never failed to amaze me. So many think the small charges from a small bore as a .410 or 28 will "Kill as Far" as a 12 but you have to point closer, while at the same time they think that 10 or 8 gauge guns have simply "Fantastic" killing ranges which a mere 12ga cannot come close to, due to their large "Holes" down the bbl.


Miller/TN
I Didn't Say Everything I Said, Yogi Berra