I have fired scores of patterns (not thousands) at paper and my grease plate over the last 40 years or so. I have never found the need for statistical analysis of shotgun patterns. Not saying there isn't a need, just that I have not had one. My main purposes for patterning a shotgun are:
1) to determine if a doublegun's patterns are regulated, and to determine to what extent they shoot to point of aim
2) to determine what load they are regulated for
3) to determine the approximate percentage of the pattern of a certain load
Beyond that it is is "too much sugar for a dime", for me. Once regulation is determined, and the best load for the gun and purpose, I just need to shoot it, because at that point I have confidence in the gun and load. And, it's hard to overstate the importance of that, IMO.
