The problem with using a circle to pattern your shotgun is that you could get dense patterns in some places of the circle that would never touch the vitals of a bird. Part of having a good pattern is not only a high pellet count, but also having an even distribution of pellets that will cover an area the size of a turkeys brain and vertebrae (to handle different head positions, moves, turns, ect.) The only way to check for an even distribution of pellets, is to check the pattern at several different locations. Using the vitals allows you to do this, because you are taking samples from small areas throughout the total pattern.

When most hunters pattern their gun using the vitals, they take an average of several targets and list their pattern with a range (e.g. 8-10 pellets in the vitals). Since a shotgun never patterns exactly the same every shot, it is importatant to figure out the range of results it will produce at a given distance.