Moran began his playing career with the Quebec Hockey Club in the
Canadian Amateur Hockey League (CAHL). Over four seasons, Moran appeared in 30 games, winning 19 of them. For the 1905–06 season, the Quebec Hockey Club joined the
Eastern Canada Amateur Hockey Association (ECAHA). Over the next four years, Moran appeared in 38 games, but won only 11 of them, while his lowest
goals-against average in a season during that span was 6.79. In the Stanley Cup challenge against the Moncton Victorias of the
Maritime Professional Hockey League (MPHL), Quebec won the first game 9–3, and the second game 8–0. Moran finished with a 1.50 goals-against average, while
Jack McDonald and
Joe Malone combined for 14 out of the 17 Quebec goals as Quebec won the
Stanley Cup. Quebec repeated as champions, winning the three-game series 2–0. In the first game, Quebec won 14–3, as Malone scored nine goals, while in the second one, Quebec emerged with a slimmer margin of victory, winning 6–2. Moran finished his career with the Bulldogs, retiring after the NHA's last season. He played four more seasons, during which he played 69 games, winning 34 of them. Over his career, Moran's teams often had losing records, or they had a winning percentage barely over 50%. Some hockey legends often recall that he was the best goaltender of them all. He was elected to the Hall of Fame in 1958, with the help of Senator
Chubby Power, once a teammate. He is still the earliest goaltender in HHOF, starting his senior hockey venture in 1901. ==Playing style==