He was an active member of the team that won the 1970 Davis Cup, winning both his singles matches in the final against West Germany, and was voted the most valuable player.

[5] In September 1971, Richey quit the Davis Cup team before the final against Romania citing his disagreement with the USLTA over the choice of surface and the lack of consultation with players.

[7] Richey was the winner of the first Grand Prix tennis circuit, organized in 1970, finishing ahead of Arthur Ashe and Ken Rosewall.

1 ranking was decided by the outcome of the semifinal match at the Pacific Coast Championships against his direct competitor, Stan Smith, and ultimately came down to just a single point when both players had a match-point at 4–4 in the sudden death tiebreak of the final set.

His last Grand Slam semifinal appearance came two years later at the 1972 US Open where he defeated Rod Laver in the fourth round but was beaten in the semis in straight sets by compatriot Arthur Ashe.