A golf ball includes an inner core layer formed from a thermoset rubber composition. The inner core layer has a first outer surface Shore D hardness and an outer diameter of about 1.0 to 1.6 inches. A thermoplastic outer core layer is formed around the inner core layer, has a second outer surface Shore D hardness, and is formed from an acid copolymer of ethylene and an α,β-unsaturated carboxylic acid, optionally including a softening monomer, such as alkyl acrylates and methacrylates; a plasticizer; and a cation source present in an amount sufficient to neutralize about 70 to 100% of the acid groups present in the material. The golf ball an inner and outer cover layers. The second outer surface Shore D hardness is greater than the first outer surface Shore D hardness.