Babcock guided Detroit to a 54-21-7 record, the Red Wings' third consecutive 50-win season, and a league-high 115 points. They surpassed 100 points for the eighth straight season and won their seventh straight Central Division title by 24 points over second-place Nashville.
Boudreau, the coach at Washington, replaced the fired Glen Hanlon on Nov. 22. The Capitals were 6-14-1 when Boudreau was hired, went 37-17-7 and won the Southeast Division title with a 43-31-8 mark (94 points).
Carbonneau guided the Montreal Canadiens to the Eastern Conference's top regular-season record at 47-25-10 (104 points). Montreal hadn't won 45 games or reached 100 points in a season in 15 years, and also won its first division title in 17 years, 10 points better than Ottawa in the Northeast Division.
The winner will be announced June 12 at the NHL's awards ceremony.