The present invention reveals a tire having a tread that is comprised of (1) 30 phr to 80 phr of a non-random styrene-butadiene rubber comprised of polymer chains that are derived from styrene and 1,3-butadiene, wherein from about 10 weight percent to about 50 weight percent of the repeat units in the styrene-butadiene rubber are derived from styrene, wherein from about 60 weight percent to about 90 weight percent of the repeat units in the styrene-butadiene rubber are derived from 1,3-butadiene, wherein from about 30 weight percent to about 50 weight percent of the styrene repeat units are in sequences containing 5 to 20 styrene repeat units, wherein the bound styrene content found in the first half of the polymer chains differs from the bound styrene content found in the second half of the polymer chains by at least 5 weight percent, wherein the styrene-butadiene rubber has a 1,2-vinyl content which is within the range of about 8 percent to about 20 percent, wherein the styrene-butadiene rubber has a number average molecular weight which is within the range of 200,000 to 475,000, and wherein the styrene-butadiene rubber has a glass transition temperature which is within the range of −82° C. to −50° C. and (2) 20 phr to 70 phr of polybutadiene. The tire tread formulation can optionally contain silica and lignin.