I know this could be more than a little late, but that has never stopped me
Savages are out of the box great shooters. They are one of the things in life that surprise me when it comes to the rule of "you get what you pay for." I have a few Savages, two packages with cheap scopes and one I set up on my own, and everyone of them has shot great since day one.
I would start with fundamental shooting: Shooter and gun in exactly the same location on the bench and sandbags for every shot, hand position exactly the same for every shot, and procedure exactly the same for every shot. I would then forget the three shot group and do a five shot group - I have seen what I thought was a flier on shot two or three, and then the next five shots all printed with the "flier."
Next I would move to the optics, as mentioned earlier, starting with rail, through rings, and ending with the scope itself.
Next would be the muzzle crown for damage.
Finally would be the chamber and bolt - This is a factory issue.
Did I mention starting with a good clean barrel with no fouling or corrosion? Eight year old gun that goes south after six years leads to believe something happened to my above, but maintenance can be the obvious and overlooked item.
Hope it is all working out!
By the way, a gun that prints great on shots one and two will drop that deer, and a five inch group will drop a deer. Not a reason to ignore, but we get worried about one hole groups at a hundred yards when we are shooting at an 8" target at 25 - 50 yards.