Simpson was mainly successful in the doubles competition on the ATP Tour . In the individual he did not succeed in a tournament victory, but he was twice in a row in the finals of his home tournament in Auckland , where he was defeated by Tim Wilkison in 1982 and John Alexander in 1983 . In the course of his career he was able to win five double titles, three of them with his compatriot Chris Lewis . He reached his highest ranking in the tennis world rankings in 1983 with position 47 in singles and 1985 with position 94 in doubles.
His best individual result in a Grand Slam tournament was reaching the round of 16 of the Wimbledon Championships in 1982. In the doubles competition, he stood alongside Billy Martin in the semi-finals of the Australian Open in 1980 , where they were defeated by the later champions Mark Edmondson and Kim Warwick . Towards the end of his career he was successful again in mixed ; with Belinda Cordwell he was in 1987 in the round of 16 of the Australian Open and the Wimbledon Championships.
Simpson played 25 singles and 15 doubles games for the New Zealand Davis Cup team between 1975 and 1986 . His balance is 16: 9 in singles and 6: 9 in doubles. The greatest success with the team was participation in the semi-finals of the world group in 1982, to which he had contributed by winning three individual games in the preliminary rounds against Spain and Italy . In the semifinals against France , he won the doubles game against Henri Leconte and Yannick Noah alongside Chris Lewis . In the 2: 3 defeat, however, he lost both individual games against Noah and Thierry Tulasne . He also represented New Zealand at the 1983 World Team Cup , where he defeated Yannick Noah in singles.