I can shoot some 3" groups at 20 yards
That has a much different meaning than "I do shoot 3" groups"
I would be much more concerned with your worst groups at 20 than your best. Most decent shooters "can shoot 3" groups" and those are the ones they talk about. But what about the groups inbetween, or before you get into a groove???
A consistant 95% of the time, 5 arrow 3" goup is excellent and above most bowhunters ability. Well above any criteria for taking out a deer.
But if you shoot a few 3" ers than a few 6"ers, be honest with all arrows you shoot and work on getting those that miss by "more" than the others to tighten up.
Remember a 60 arrow 3" group is the magic 300 score on five spot - do a few in a row and it will get you into the playoffs of ANY national tournament