Although Baumann came second in the 3,000 m at the European Indoor Championships in 1987, few considered him a medal chance at the 1988 Summer Olympics. The 5,000 m final at Seoul was won by John Ngugi from Kenya who broke away from the field early in the race. However, Baumann used his superior 1,500 m speed to outsprint the rest of the field in the final lap to win the silver medal. Baumann missed most of the 1990 season due to tendon trouble, but he returned in 1991 to finish fourth in the 5,000 m at the World Championships in Tokyo. At the end of the season, Baumann unexpectedly beat the Kenyan 5,000 m world champion Yobes Ondieki over 3,000 m in Cologne.