The book Sporting Shotgun Performance by Dr. A. C. Jones is the only work I find combining theoretical work with accurate experimentation. O&T's work just doesn't cut it. Read Dr. Jones if you haven't done so yet. I don't believe Jones left room for any "magic." One of the biggest 'BUGBEARS" for pre-Jones is lack of statistical analysis. Dr. J discovered that there is so much variation in patterns as to require a ten shot sample. Secondly, meaningful statistical analysis (by hand methods) is real time consuming - - - so time consuming that nobody did it. Note that Dr. J automated his analysis from photo capture of each pattern, computer analysis of each pattern and analysis of each ten shot data set. Read the book.

If you run into something you don't understand, ask and you will get an explanation.