Burch won the Hart Trophy as the NHL's most valuable player in 1924–25. In that same season, he joined his teammates in precipitating the first player's strike in NHL history and which led to the dissolution of the Hamilton franchise. Transferring to the newly formed New York franchise, Burch served as the team's captain, scored the first goal in Americans' history in 1925 and won the Lady Byng Trophy in 1926–27 as the NHL's most gentlemanly player. He was inducted into the Hockey Hall of Fame in 1974.