Cika wannan jumla: An zaba 220th gaba ɗaya ta Buffalo Sabres a cikin
1993 NHL Entry Draft, Moore ya taka leda a Sabres, Edmonton Oilers da Washington Capitals, yana wasa wasanni 39 na kakar wasa, ya zira kwallaye 2 da kuma taimakawa 4 don maki 6 kuma ya tattara mintuna 18. A shekara ta 1996, ya lashe gasar Calder tare da Rochester Amurkawa.