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Rivalries are usually born in the playoffs, and even though it only takes one series to spark a dislike between two teams, multiple postseason meetings are how the best rivalries take shape.
Even though the Montreal Canadiens and Boston Bruins have played in some memorable regular-season games filled with fights, physical play, lots of scoring and a high level of intensity, the main reason why these historic franchises have the best rivalry in the league is because they have met in the playoffs an NHL-record 33 times.
Competing in a playoff series against the same opponent multiple times, which results in one team ending the other's dream of winning the Stanley Cup, is the most effective way to form rivalries. Losses from the playoffs hurt much more than defeats in the regular season, especially when one team has won the majority of the postseason series (Montreal has an all-time 24-9 series record versus Boston).
Falling short of winning the best trophy in sports is tough for every player and team, but when that failure results from a loss to a bitter rival, it's a memory you will never forget.
Multiple playoff series also help teams that don't often meet during the regular season form rivalries. The Vancouver Canucks and Chicago Blackhawks only play three or four times each year because they are in separate divisions, but because these franchises have played in the postseason three times in the past four years, their rivalry is alive and strong again.
One of the most recent examples of teams creating a rivalry after a single playoff matchup was the 2011 Stanley Cup Final between the Canucks and Bruins, which was one of the most entertaining and physical series in a long time. But these two teams play in separate conferences and play each other just once or twice in the regular season, so it's tough to form a rivalry because meeting in the Stanley Cup Final on a regular basis is highly unlikely.