At the FIL European Luge Championships, Rinn won 13 medals. This included seven golds (Men's singles: 1973, 1974, 1979; Men's doubles: 1973, 1975, 1978, 1980), six silvers (Men's singles: 1977, 1978; Men's doubles: 1974, 1977, 1979, 1982), and one bronze (Men's singles: 1975).