Baumann has played for many rugby clubs in the USA and overseas. In the USA, he has played for; Steamboat Springs RFC, University of Wyoming, Aspen RFC, Tempe, Life University, Los Angeles RFC, Glendale, New York Athletic Club, and Santa Monica Rugby. Playing mostly year round he also played club seasons overseas for: East Kilbride RFC "Scotland" University of the Sunshine Coast " Australia, Yokohama Country & Athletic Club "Japan" and Randwick Rugby Club" Australia.
Baumann made his full international debut with the Eagles against Tonga in a Pacific Nations Cup match in June 2015, and played in three of the U.S.'s four pool matches at that year's Rugby World Cup in England.
Following a title-winning season with PRO Rugby's inaugural Denver Stampede franchise, he signed a contract with Wellington Rugby Football Union, helping the Lions to a Championship berth in the Mitre 10 Cup competition.