1986 Second Baumann in the German Championship in 1987, he won the team silver at the European Championships. For the 1988 Olympics in Seoul he qualified with Shamrock after his other horse had goofed alabaster. In Seoul Baumann finished second in the individual standings with 68.80 points for sixth place. The German team came into Seoul with Claus Erhorn, Matthias Baumann, Ralf honor Brink and Thies Kaspareit to. While honor Brink was disqualified Erhorn, Baumann and Kaspareit won the gold medal in the team competition.
1990 Baumann was in the World Cup third party with the team. 1990 Shamrock and 1991 and 1992 respectively on alabaster Baumann won three times in a row, the German championship. He was the first rider at the German Championships managed the hat-trick. At the 1992 Olympics in Barcelona Baumann finished with 157.40 points on alabaster rank 34 and thus supplied the void result for the team score. After Herbert Blocker, Ralf honor Brink and Cord Mysegaes reached the third place in the team standings, also Baumann was honored as the fourth team rider with the bronze medal. Four years later, Baumann was nominated as a replacement rider for the 1996 Olympic Games in Atlanta, came there but not used.
Matthias Baumann studied veterinary medicine at the Ludwig- Maximilians- University of Munich; In 1991 he received his doctorate. Since 1994 he leads a training and rehabilitation center for sport horses in Reichertsheim.