Vance was a member of the Wellington Colts XI that was undefeated in the 1946–47 season.

[1] He made his first-class debut for Wellington in 1947–48, and established his position as an opening batsman in 1950–51, when he scored 75 and 29 in a victory over Auckland.

Under Vance's captaincy in 1961–62 Wellington won their first four matches inside two days and went on to win the Plunket Shield.

[5] The R. A. Vance Stand at Basin Reserve in Wellington, built in 1979–80, is named in his honour.

[6] In the 1983 New Year Honours, Vance was appointed a Commander of the Order of the British Empire, for services to cricket and the community.