From a logical point of view, it's wooden stick => baseball bat => mace; and that way it would make perfect sense. A good mace is a devastating weapon. Much more so than any bat, due to better weight distribution and good impact material and shape of the head.
The steel club kinda looks like an improvised mace with all the pointy parts; but it should be slimmed down by a factor of 10 to actually look functional. (I'm no historian, so if one wants to argue that any reinforced bat is a mace, then go ahead; but I'm talking mostly of these types of things:
https://en.wikipedia.org/wiki/Mace_(bludgeon) )