Tunney was the only member of the Hall of Fame to not be inducted at the annual Hall of Fame dinner, as he was seriously ill at the time of his election and was inducted in a special ceremony in St. Elizabeth's Hospital in Brighton, Mass. on January 20, 1968. He passed away two weeks later.
During his time at Holy Cross, Tunney was an outstanding pitcher at the beginning of the Jack Barry era. Tunney played on Barry's very first team in 1921. During his four years at Holy Cross, the Crusaders posted a 100-9-2 record. As a freshman, Tunney posted a 10-1 record and was a first team All-American. He had a 2-1 mark as a sophomore, missing most of the season with an injury. In 1923, Tunney was 6-0 as the Crusaders won the Eastern Intercollegiate Championship with a record of 28-2-1. In his senior year, Tunney helped Holy Cross to an undefeated (18-0) season and another Eastern crown by winning four games. He later signed with the New York Giants and played a few seasons in the minor leagues.