In 1924 Richardson and his compatriot partner Jack Condon competed in the men's doubles event at the 1924 Summer Olympics in Paris and reached the semifinal, defeating the American team of R. Norris Williams and Watson Washburn in the quarterfinal. In the semifinal they were defeated in four sets by the French team of Jacques Brugnon and Henri Cochet and in the bronze medal match lost in straight sets to René Lacoste and Jean Borotra. In the singles event he lost in the third round to Cochet.