Matson's weight-throwing ability was recognized when he was in the eighth grade by the high school coach of Pampa, Texas, who went on to train him. Matson set state high school records in both the shot put and discus. After his freshman year at Texas A&M University (College Station), he won the silver medal in the shot put at the 1964 Summer Olympic Games in Tokyo. He bettered his 1965 record in 1967 with a put of 21.78 m (71.46 ft) and won the James E. Sullivan Award that year as the country's outstanding amateur athlete. At the 1968 Summer Olympics in Mexico City he won the gold medal with a put of 20.54 m (67.39 ft). He also won United States Track and Field Association shot-put titles (1969–71). Matson retired from competition in 1972 after he failed to make the U.S. Olympic team. He later served as an executive of alumni relations at Texas A&M University.