The present invention is directed to rubbery block polymers containing a polylactone, such as polycaprolactone, methods of making the same, and to rubber compounds containing those block polymers. The rubbery block polymer is an anionically polymerized block polymer defined by A-B, wherein A includes at least one type of polymerized conjugated diene monomer, a polymerized vinyl aromatic monomer, or a mixture thereof and wherein B is a polylactone, such as polycaprolactone, which is hydroxy terminated. The rubbery block polymer may be compounded so to provide, for example, a tire tread with desirable properties for use in an automobile tire. Such rubber compound, for example, can include the rubbery block polymer, an organosilane coupling agent, such as a bis(trialkoxysilyl) alkane, bis(trialkoxysilylalkyl) polysulfide, or mixtures thereof, and silica filler in specified amounts.