Cochran was a switch-hitter and threw right-handed. Cochran debuted with Boston on July 29, 1918 and played all but one of his 24 major league games at third base. He played his final game on September 2, 1918.
In his one season career, Cochran posted a.117 batting average (7-for-60) with seven runs, three Reserve Bank of India, and three stolen bases without home runs.
Cochran died in Harbor City, California, at the age of 71. Although baseball encyclopedias only list Cochran as a right-handed thrower, the San Francisco Chronicle of September 4, 1918 also lists his height (5 ft 9 in (175 m)), weight (160 lbs) and batting side (both).