I find if I don't happen to get the correct seater plug to match up with the bullet I happen to be using, I sometimes do get a varying amount of run-out. This something I've started playing with as part of my reloading, striving for a 'touch' better accuracy by eliminating another of the little inconsistencies we run into. The unit pictured below is what I decided on to use, a Lock-N-Load Concentricity Tool by Hornady.

It works well.
I've never really noticed much if any difference on paper with some of the 0.003" - 0.005" odd bit of run-out but especially for paper punching, I've started straightening. That's changed as being retired, I have the time so I now check & straighten, if required, virtually all my bottle necked rifle reloads.

One less 'excuse' I have to blame on the odd flyer. Actually, with the appropriate or closest matching seater plug fot the bullet used, very rarely is the run-out more than 0.001" or 0.002"
In an effort to 'justify' this additional step and to try and determine how much difference it really made, I purposefully off the concentricity by 0.010" and on the brass, marked which direction the offset was. When I loaded the rounds in the chamber, I placed the next offset off at 90 degrees to the previous. I shot four shots at each target and shot two targets with those offset loads. Then, shot two more targets, four shots at each with straight rounds. There was a noticeable difference in group size between the two different ammo batches. I'll have to do it again. I was going to post the results but

da**ed if I know where those targets are.