Nicknamed "Evil Dick" by his team-mates, Sincock was called "one of the most interesting bowlers I have ever played against" by Garry Sobers, who claimed that Sincock turned the ball more than any other bowler he had faced and had an unreadable googly. However, Sobers noted that Sincock was too inconsistent, bowling an over of long hops and full tosses for every unplayable delivery. His last Test was against England in the Third Test at Sydney in 1965-66, Sincock was hit for 0/98, but made a fighting 29 and 27 as Australia suffered their worst home defeat in over 50 years. The selectors promptly dropped five players including Sincock and the stand-in captain, Brian Booth, neither of whom played for Australia again.
Sincock dropped out of first-class cricket after the 1965-66 season, moving to Sydney where he played for club side Northern District. He later said, "I definitely didn't want to be a professional sportsman ... Once I'd got a guy out I couldn't really see the point in getting him out again next week." He became a successful business executive.