He made his Major League debut for the Kansas City Athletics on April 19, 1966. This marked the first time that a starting pitcher made "his big league debut in his team's home opener in the state in which he was born".[3] This feat was repeated 51 years later by Kyle Freeland of the Colorado Rockies.[3] In 1970, Dobson earned a career-high 16 wins and threw five shutouts, tying with Jim Palmer and Gaylord Perry for the major league lead. Despite a 15–5 record in 1971, Dobson experienced significant pain in his pitching elbow due to growing calcium deposits. Surgery that off-season kept him out of the majors throughout 1972. Although he returned to the majors for brief stints in 1973 and 1974, his career was effectively ended by the elbow injury.
Dobson died on November 30, 2021, at the age of 77.[4]