I originally got the idea to test quantities of ammo sorted by rim thickness from some discussion in a book I purchased years ago titled (if memory serves) "Customizing the Ruger 10/22", where they mentioned improved accuracy from rim thickness testing. To limit the other variables, such as head space, as much as possible, I did all the testing with the same rifle, a bull barreled Marlin target rifle that had always performed more than adequately for me. Once I advanced into the higher quality brands sold as match ammo as opposed to bulk pack ammo, I quickly determined that rim thickness was much more consistent, with a MUCH smaller range from thinnest to thickest, and skewed well toward or at the high end of what I was used to seeing previously in my sorting of bulk pack ammo. After shooting a few 5 shot groups with various of the the higher end stuff, I quit measuring them and just included them, straight out of the box, when testing any .22 to see what ammo(s) it preferred.
I have no way to scientifically explain why the sorted bulk ammo shoots better groups than unsorted bulk ammo, or why groupings at the thick end of the rim thickness range shoot better than those at the thin end, but I do have a best guess, based on discussion with center fire short range (100 and 200 yards) bench rest shooters, specifically my late cousin in law and the late Homer Culver, both bench rest Hall of Fame shooters. I had asked then about charge weight accuracy when throwing charges from a powder measure (I had noticed that short range bench rest shooters just threw the charge out of their measure into the case, no weighing and "trickling up"), and both said not to worry about it at 100/200 yards, just develop a rhythm for operating the powder measure that gave the most consistent charges I could throw and let it go at that, because at those ranges primer performance is more important than +/- a tenth of a grain or less of powder. After watching them and others test the same load with various different primers, I had to agree - even with weighed charges, primer choice could make or break a load with the level of precision they were looking for, and primer ignition consistency was king. So my best guess is that rim thickness effects ignition consistency, so that the best accuracy a batch of cartridges is capable of comes from grouping them by rim thickness when it varies a lot, as in bulk pack ammo, to improve ignition consistency, and that a thicker rim further improves ignition by maximizing ignition consistency still further - ammo that is all in the 0.040"-0.043" always shot great, you just got a whole lot more of it (often a complete box of 50) with high end ammo than with bulk pack ammo, where sometimes you didn't get enough to fire 2 five shot groups out of a 500 round brick. Anyhow, that's my best guess - sorting improves ignition consistency up to a point, and from 0.040"/0.041" on up, you've reached the optimum rim thickness with regard to ignition consistency.
Whether my best guess with regard to ignition consistency is right or wrong, it was a fun ride doing all that testing.
