He reached the semifinals of Wimbledon in 1974, the quarterfinals of the U.S. Open in 1976 and 1977 and the semifinals in the 1978 French Open. Stockton played on the U.S. Davis Cup Team five times (1973, 1975, 1976, 1977, 1979), including the U.S. Davis Cup Championship Team in 1979.
Stockton reached notable tournament stages, including semifinals at Wimbledon in 1974 and the French Open in 1978, quarterfinals at the U.S. Open in both 1976 and 1977, and participated on the U.S. Davis Cup Team five times between 1973 and 1979.