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His undoubted cricketing highlight was selection in the first Scotland squad for the Benson & Hedges Cup, in 1980.
He made his debut for the team in a List A match against Somerset in the 1985 Benson & Hedges Cup, playing a further match for the team in the same competition against Glamorgan.
During this season, Norris helped Sheffield win a Grand Slam of all available trophies when they won the Benson & Hedges Cup, the Challenge Cup, the league championship and the playoffs.