Disclosed herein is a game ball and method for making the same. The game ball has an ionomeric cover which includes a combination of ionomeric crosslinks and covalent crosslinks. The game ball cover is superior in at least one of cut resistance and scuff resistance to a conventional cover that does not have covalent crosslinks but is otherwise substantially identical in composition. Crosslinks within the composition are achieved by irradiation. The game ball cover of the invention is particularly useful for improving the durability of golf balls to be struck with sharp-grooved clubs.