A 3 7/8" black spot makes for a very difficult 50yard target for sure. Years ago, I did very well on a 4" bull, but benched, with open sights. That was my normal
target for testing loads. It was also used with apertures for 100meter shooting with my buffalo rifle as it gave perfectly symmetrical sizing of the sight's 'rings'
and thus very good groups were possible, under 1".
To some extent, the smaller the aiming point, the smaller the group, but it has to be visible. Today, that would be a very difficult open sight offhand 50yd. target.