Golf balls having a core including a material formed from polybutadiene, a crosslinking agent, and a free-radical initiator, and a cover having a plurality of dimples disposed about the core, wherein the material includes at least about 80 percent trans-isomer polybutadiene and no more than about 10 percent vinyl-configuration polybutadiene and wherein the material has an absolute molecular weight of at least about 100,000. In another embodiment, the vinyl-configuration polybutadiene is present in no more than about 15 percent and the absolute molecular weight is at least about 200,000. Methods of preparing such golf balls are also recited.