Despite his lack of success in the majors, Bragan was highly respected as a minor league manager, winning championships in 1948-49 at Fort Worth of the Double-A Texas League during a successful five-year run, and with the 1953 Hollywood Stars of the Open-Classification Pacific Coast League.
Bragan was a protégé of Branch Rickey, the Hall of Fame front office executive, who hired him as an unproven young manager at Fort Worth when both were with Brooklyn and then brought Bragan to Hollywood and the Pittsburgh organization, where Rickey was general manager from 1951-55.