What Are Good Concentricity Values for New Brass?

My new toy arrived - a Forster Coax Case & Cartridge Inspector - and I just did some playing around with it. My main goal was to learn how to use it. Anyway, I did some runout measurements on loaded rounds.
The first set were six, loaded 30-06 rounds. These are brand new, unfired Winchester brass. I had run them through a Lee FL die to round the mouths prior to loading. Average concentricity was .002-.003, though two of the rounds were at or slightly over .001. Since I've only started with this; what are expected values with new brass?

I also checked a few, loaded 7mm-08 and .243 rounds. These are also Winchester brass and they've been reloaded 3-5 times. The main difference is these were all sized with a Lee Collet Die. Runout on all of these were .001 or slightly over.

Since I also have some Redding FL Type S Bushing Dies; I'll be doing a future project to compare runout values on collet sized rounds to bushing sized rounds to conventional FL sized rounds.

Those are a great tool to learn with.I was able to determine that I had a bad die years ago by having a concentricity gauge.It was a redding and they sent me a new one asap.
I like to check new brass both before and after sizing,,not all the time mind you but every once in awhile to check my die setup and technique.I use forster coax presses and they are
nice for making ammo with low runout.
As for you question..001-003 as always been acceptable to me for my hunting guns.If you seperate the brass at the range and check em later for runout it can be enlightening.I mean keep track of any flyer brass.I shoot almost no paper so I don't get that chance.

Welcome to the never ending school of precision reloading! :p

Fireform the brass, then start the worry process!

There is a LOT more to it than just having straight cases.

Less run out is always better in theory. Run out is something that is a constant fight to control. You must also have a chamber that can take advantage of a properly concentric round or you're wasting time even doing it.

If the chamber isn't concentric the bullets will never get a straight start into the rifling. Measure a few rounds that have been fired and that will tell you something about the chamber. The chamber also must be in perfect alignment with the bore, or you're wasting time again. A bore scope will tell you this.

Many people do not use the ejector pin in the bolt head of a Savage rifle for targets because of the concentric issue. We pluck the brass from the bolt head after shooting. The pin will force the brass out of alignment in the chamber.

The brass must also be sized properly and the dies need to match the chamber as closely as possible. There are different methods of mounting the dies in the press that can help or hinder run out.

Bullet seating has a LOT to do with run out also. A die that supports at least the neck (Hornady dies) of the brass is always better. Supporting the entire case works well too such as with the Wilson dies.