As a college player, Oates was a standout forward for the RPI Engineers. He set single-season school records for assists and points and was named an Eastern College Athletic Conference (ECAC) all-star and National Collegiate Athletic Association (NCAA) All-American in both 1984 and 1985. Oates was named a tournament all-star in helping RPI win the 1985 national championship, and in 1990–91, the NHL included him in its Second All-Star Team; he played in five All-Star Games. He holds the record for most points all-time of any NHL player who also played NCAA Hockey. Oates was inducted into the Hockey Hall of Fame on November 12, 2012.