As an English major it is difficult not to look at a piece an analyze it for overarching metaphors and allegories which create theme. This is especially true under the theory of deconstruction, which always places the reader and the reader's interpretation over the actual text itself. While I agree that Tolkien's work on Middle-earth as a whole is not allegorical, I cannot help but look for smaller allegories within it.
In high school we are taught that authors never make decisions arbitrarily. Numbers, locations, names all carry meaning, whether explicit or implicit. When something seems random, we are to assume that it is intentional.
One thing that seems random within Tolkien's subcreation is how the rings of power were distributed among the different races of Middle-earth.
Three Rings for the Elven-kings under the sky,Seven for the Dwarf-lords in their halls of stone,Nine for Mortal Men doomed to die,One for the Dark Lord on his dark throneIn the Land of Mordor where the Shadows lie.One Ring to rule them all, One Ring to find them,One Ring to bring them all and in the darkness bind themIn the Land of Mordor where the Shadows lie."