Stockton quit Washington University (St. Louis) to cover the 1917 Jack Johnson-Jess Willard boxing match for the St. Louis Post-Dispatch and remained with that paper until he retired in 1958, serving as sports editor from 1946. Respected for his integrity, he was president of the BBWAA in 1931. Stockton wrote many profiles for The Saturday Evening Post; his book, The Gashouse Gang and a Couple of Other Guys, was published in 1945. In 1921 he was part of the first remote radio coverage of a golf tournament, the U.S. Amateur in St. Louis, and he broadcast an evening sports program on radio for 15 years. After his retirement, he became president of the Florida State League. He received the J.G. Taylor Spink Award from the Hall of Fame in 1972.