The present invention is directed to golf balls having at least one layer formed from a rubber composition comprising a base rubber and from 10 parts to 120 parts of an oily substance, by weight per 100 parts of the base rubber. The base rubber is a polybutadiene having a Mooney viscosity of 40 or greater. The rubber composition may be present in any one or more of a core layer, a cover layer, or an intermediate layer.