Here is an article that I did for Varmint Hunter a few years ago. It addresses some of the questions that have been raised here.
One other comment: If you're using a range type measurement (extreme spread or group size for example), you lose statistical power as the number of items in the group increases. The range of a group of 2 has 100% of the available information about variation. The range of a group of 5 has 90%. The range of a group of 10 has only 60%. Switching from 5 to 10 shots per group doubles your round count, but does not even nearly double your information yield.
That's a good article, and touches on a lot of stuff, but like most articles, it has some (IMHO) erroneous thoughts and doesn't really nail it down. No disrespect intended, I think that about all of them. Overall I like the article.
It really depends on what we want the rifle to do and what we will accept as proof to ourselves it will do that well enough to be personally satisfied.
My Bench gun is a 1/4 moa or better gun from a vise in a dead calm (Some would say smaller than that), but I can easily shoot groups bigger than that if I miss a pickup in the condition or even worse, a switch.
My .222 Mag heavy barrel varmint gun can shoot 1/4" groups, and has, but it isn't a 1/4" rifle, more like 1/2" in my mind, and again, I can shoot bigger groups with it in a heartbeat.
Some people blame everything on the gun, wind etc, no excuses, and then the other crowd claims all bad shots as fliers. Neither crowd is correct. In competition I always blamed everything on me and tried to focus better, while some people would blame scopes, barrels, actions, brass, anything but themselves, and then wondered why they didn't get better.
I have told this story before, but once the fellow next to me at Riverbend in a registered Benchrest match got mad and threw his brass in the trash. (We had bet a dollar a group and a dollar on the agg) I told him it wasn't the brass, got it out, loaded it, and beat him in the next group with his own brass. He got real mad then and screwed the barrel off. Looking back I should have just left well enough alone and encouraged him.