How does the Ruger 10/22 shoot out of the box with a good scope?

pretty good acually... shoots better after about a box of shells, and then your lookin and probly half inch groups and 20 -40 yards

What does a box of shells before it shoots well do?Is it sighting it in?Is it to clean out and scrap medal or oil?If it is to clean it out wont a good cleaning rod take care of that?

Think of it as a break in. get's everything settled in a bit. Also remember that your gun may not neccessarily like the ammo your wanting to use. May take some trial & erroe to find the ammo that your particualr gun prefers. As is from the factory it's not, nor intended to be a target grade gun.

Only gripe I have ever had with a 10/22 is the trigger sucks.....

Running a box of shells through your gun does a few things: 1st off-these are factory barrels, they're full of imperfections...running a few rounds through the barrel fills many of these imperfections with lead (usually with copper for jacketed rounds), which smoothes out the barrel... 2nd-it would exert high pressure on the barrel under high heat (temporarily) which will press the roughly/haphazardly arranged grain micro-structure of the steel of the bore faceinto a more streamlined and regular pattern...no, it's not going to perfectly allign the bore, and no, shooting a million shells won't create a perfect barrel, but these factors do increase accuracy.

Military marksman have believed in "fouling shots" for generations, filling the imperfections with fouling (carbon or copper) before calling your accuracy the "real" POI/POA relationship.