After a standout junior career with the Medicine Hat Tigers, Murdoch was selected 6th overall in the 1976 NHL Amateur Draft by the New York Rangers and joined the team that year as a 20-year-old. He scored 56 points in 59 games his rookie season, including a Rangers rookie record of 32 goals, and finished as runner-up for the Calder Trophy for best rookie.[1][2] On October 12, 1976, Murdoch tied Howie Meeker's record for most goals in one game by a rookie with 5,[2] against the Minnesota North Stars.[3] A torn Achilles tendon ended his season in February.
On August 12, 1977, Murdoch was caught by customs agents at Toronto's Pearson Airport with 4.5 grams of cocaine stashed in his socks.[4] He was suspended by the league for the entire 1978–79 season (later reduced to 40 games) and later admitted to having a drinking and drug problem.[5][6]
In the 2009 book 100 Ranger Greats, the authors ranked Murdoch at No. 99 all-time of the 901 New York Rangers who had played during the team's first 82 seasons.[1]