Roger Hverven began his sporting career as a junior with Vålerenga IF, playing both football and ice hockey, and becoming the Oslo champion in the latter in 1959. Still as a junior, Hverven then joined Oppsal IF, where he switched to playing handball, winning the Norwegian Junior Championship in 1961, before winning a senior title with the team in 1964. The team then enjoyed its best record in the championship, winning five league titles, in addition to competing at several editions of the European Cup. From 1964 to 1973 Hverven played in 52 matches for the Norwegian handball team, scoring 56 goals. During this time he was part of the squad that competed at the München Olympics, playing in four matches and scoring seven goals. After his playing career Hverven worked as a coach at Oppsal IF.
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