Was curious about this so I went digging thru the stats...
In 1985, the President's Trophy came about for the team that finishes 1st overall in the league. And since this award was created, NO TEAM has ever won the Stanley Cup in their first year of winning the President's Trophy.
My theory, it's not a curse but just mental. You get thru the season basically winning all the time with a few road bumps along the way, but then as soon as you hit adversity ( and I mean playoff adversity, not the type you get in the regular season ), you start questioning yourself and why is it not working for us anymore. I think it takes losing in the playoffs after a great season to get you to realize that the regular season means nothing, and finishing first means nothing, and it's how you play in the playoffs that means everything.
Take Washington. They still had a chance to catch the Jets for 1st overall, yet ( other than Ovi for reasons we understand ) the Wash coach decided to shut it down. Rest some players and get ready for what matters.
The Jets on the other hand killed themselves to get 1st in the Division, conference, and league, for home ice advantage. And sure having that advantage is important, but if the Jets lose game #7, then you have to ask yourself, was that effort worth it, or could a different path had been a better approach.?
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On this series, I wonder if the standings had been reversed ( St.L 1st - Jets wildcard ), would we have had a different result? All the pressure of finishing 1st on St.L , no pressure on the Jets.