The primary benefit of barrel breakin is easier cleaning. Improved accuracy is secondary and very hard to determine. Most people tend to describe the breakin process and not the goal which is a polished bore that cleans very quickly.

I was taught to clean the bore completely before each shot until the cleaning almost suddenly begins to go much quicker. Such things as fire lapping and J-B bore cleaner should speed the process. The point is that the microscopic burrs in the bore left from the rifling process must be removed to stop copper collection at these tiny burrs. If the bullet does not remove a burr, it will leave a tiny bit of copper and thus protect the burr from the next bullet fired and collect more copper. A thorough removal of all fouling, especially copper, before the next shot leaves those burrs exposed and therefore subject to the lapping effect of the next bullet.

The number of shots needed to breakin a given barrel are strictly dependent on the barrel' s smoothness to start with. Factory barrels are generally quite rough and take quite a bit of breakin shooting. A couple of Shilen barrels I' ve used broke in with under ten shots. IMO, barrel breakin is probably not worth the trouble with a factory hunting rifle as barrel cleaning is generally a once a year issue and the breakin shots will be excessive. A varmint or bench rest rifle however is surely worth the trouble of a proper breakin as it is often cleaned a few times in an afternoon of shooting. I hope this helps.