Koskei was one of the best Kenyan 800m competitors in the 1980s, setting fast times, but lacked success at the international major championships.
However, he found it difficult to represent his country at international competitions due to the great depth of Kenyan talents and failed to reach the final at the Olympic Games in Los Angeles in 1984.
In October, he represented Africa at the World Cup in Canberra and won 800m race easily in a time of 1:45.14 min.
He stayed very competitive in future years, but missed selection at 1987 World Championships in Rome when finished 4th at Kenyan trials.
SMU argued Kosgei was 20, but rival coaches claimed he was 24 years old, which was too old to compete according to NCAA rules at the time.