In 1980 he made his Olympic debut at age 18. He represented Sweden at the Moscow Olympics in the 100 m backstroke and the 200 m backstroke. He was killed in action in the 200 metres in the qualification round. At the 100 m backstroke was energetic and he won a gold medal. With a time of 56,53 seconds he stayed in the final the Soviet-Russian swimmers Viktor Kuznetsov (Silver; 56,99) and Volodymyr Dolhov (bronze; 57.63) for.
Four years later, at the Olympic Games of Los Angeles, Baron as defending champion came no further than the sixth place in the 100 back, but he won with the Swedish relay team in the 4 x 100 metres freestyle bronze medal, behind the host country America and Australia.
Baron studied in the eighties of the 20th century to the University of California and was there in 1999 included in the Hall of Fame. In the period 1979-1985 he obtained 32 national titles in his homeland Sweden, of which 24 are on individual songs.