Kammala wannan jumla: Budaj an tsara shi ta Colorado Avalanche a cikin
2001 da aka zaba a matsayin na farko don Avalanche da kuma 63rd overall. Ya sanya lamba 31 don Avalanche bayan ya buga wa Hershey Bears na Ƙungiyar Hockey ta Amurka (AHL) da Toronto St. Michael's Majors na Ƙungiyar Hockey ta Ontario (OHL).