A low compression, resilient golf ball having a center and a cover, wherein at least a portion of the ball is formed from the conversion reaction of an amount of polybutadiene, a free radical source, and a cis-to-trans catalyst including at least one inorganic sulfide at a sufficient temperature to form a polybutadiene reaction product which includes an amount of trans-polybutadiene greater than the amount of trans-polybutadiene present before the conversion reaction and a cis-to-trans catalyst including at least one inorganic sulfide. The reaction product preferably has a first dynamic stiffness measured at -50.degree. C. that is less than about 130 percent of a second dynamic stiffness measured at 0.degree. C. A multi-layer golf ball having a center, at least one intermediate layer disposed concentrically about the center, and a cover, wherein at least a portion of at least one of the center, intermediate layer, or both, are made from the reaction product. Also included are methods of forming such golf balls.