Has little to do with headspace, unless it is excessive. The spring could be weak, but not likely. The problem is lack of firing pin fall, resulting in loss of inertia. If Federal primers are the only ones that work, you still have an ignition problem. Federal primers have a softer cup than most others, requiring less impact to fire. One phenomenon that occurs a lot is a "cold fire". When a primer is struck with minimal amount of impact, it will not exspell all the available energy, resulting in a loss of velocity, change in the pressure curve and change in harmonics. When struck with the optimum inertia, the primer will exspell all the energy it contains with a consistent fire.
I said the problem was lack of firing pin fall, this is because in that time era, Savage rifles had the worst timing problem that ever plagued them. They tried to correct the problem by
"filing" ramps on the leading edges of the bolt lugs to reduce the effort to close the bolt. It made the bolt easier to close, but only made the timing more retarded, leading to a under cocking striker. When the bolt is lifted 90 degrees, it is at full cock. Once the bolt is closed, the striker would start to de-cock until the cocking piece pin catches on the sear, resulting in a loss of travel, sometimes up to .090". That puts you in the "cold fire" or no- fire zone, or even the "sitting on the fence" between the cold fire and the optimum fire zone.
To achieve optimum fire, you need a minimum of .200" fall, measured to the bolt face. Firing pin protrusion only needs to be .035". Most are set at .055" or thereabouts from the factory, however the firing pin will only penetrate the primer no more than .025", so the extra protrusion is actually robbing you of travel.
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