one member selected from the group consisting of r 1 r 2 r 3 and r 4 is a low molecular weight polydiene arm having a number average molecular weight of less than about 40 000 with the proviso that at least one member selected from the group consisting of r 1 r 2 r 3 and r 4 is a high molecular weight polydiene arm having a number average molecular weight of greater than about 80 000 and with the proviso that the ratio of the weight average molecular weight to the number average molecular weight of the asymmetrical tin coupled rubbery polymer is within the range of about 2 to about 2 5 it should be noted that r 1 r 2 r 3 and r 4 can be alkyl groups because it is possible for the tin halide coupling agent to react directly with alkyl lithium compounds which are used as the polymerization initiator the ratio of silicon containing stars to tin containing stars will be within the range of about 20 80 to about 80 20 in cases where the rubber is coupled with both a silicon and a tin coupling agent in most cases four polydiene arms will be covalently bonded to the tin atom or the silicon atom in the asymmetrical tin coupled rubbery polymer in such cases r 1 r 2 r 3 and r 4 will all be polydiene arms the asymmetrical tin coupled rubbery polymer will often contain a polydiene arm of intermediate molecular weight as well as the low molecular weight arm and the high.