Rubber composition and pneumatic tire

A rubber composition comprising a diene rubber and a filler;

• the diene rubber containing a styrene-butadiene copolymer and a natural rubber, wherein the content of the styrene-butadiene copolymer is not less than 40 mass % and less than 50 mass % of the total mass of the diene rubber;
• a radical generation index of the styrene-butadiene copolymer being not greater than 1.0 and being smaller than a value Y calculated from an equation:Y=−0.0186×(SV mass %+vinyl unit mol %)+1.5
• where the radical generation index is an index representation of a radical concentration using the radical concentration of a copolymer having a molar ratio of styrene units/1,2 vinyl units/1,4 trans units/1,4 cis units of 13/14/15/58 as a 1.0 reference value;
• and
• “SV mass %” in the equation is a mass % of a partial structure where a styrene single chain having one styrene unit and a vinyl single chain having one vinyl unit are directly linked relative to an amount of bonded styrene of the styrene-butadiene copolymer, and “vinyl unit mol %” in the equation is a mol % of vinyl units when a total of styrene units, 1,2 vinyl units, 1,4 trans units, and 1,4 cis units in the styrene-butadiene copolymer is defined as 100 mol %, and
• wherein the styrene single chain content having one styrene unit is not greater than 30 mass % of the amount of bonded styrene in the styrene-butadiene copolymer.