"Hardened"? I don't understand, do you mean pure lead round ball that was dropped into water and so is a tad harder than air-cooled lead round ball, or do you mean a lead alloy like some with tin, or modern lead bullets recast into round ball, or wheel weights, or even linotype?
I agree with Hanshi, the caveate over lead alloys has been because as he mentioned, when they cool the alloy lead doesn't quite shrink as much... so if you have a pet load of X diameter pure-lead ball and Y thickness of patch..., you may find that the alloy ball with diameter Z just won't load.
Otherwise, even a .45 ball is pretty big, and an alloy ball will expand less when using a harder alloy, so developes less friction because it doesn't mushroom, especially when passing through bone. Some folks are really particular about mushrooming, especially with .40-.50 caliber ball, but I haven't seen any advantage. I prefer to use a load that will go through-and-through a broadside deer, as my opinion is two .45 sized holes would be better than a .45 hole going in and a mushroomed ball staying inside. :wink: Of course, a bigger hole on the way out would be even better, but on Eastern Whitetail, I'm not sure that's a requirement.
Since you are on the left-coast, you are going for mule deer, n'est-ce pas? So you might want something at least .50 if not larger. That's what I was taught, but I have no personal experience on the larger deer. I think .54 and larger round ball, alloy or pure, would be pretty academic concerning deer.
LD