Wow, that sounds horrible! All that hard effort over 82 games, and chances are the President's Trophy winner won't even win the Cup!
Think for a minute, however, and you realize that 6 out of 20 really isn't that bad - 30%, in fact. When you consider that the Stanley Cup Playoff is a 16-team tournament, saying that one team in particular has a 30% shot at winning makes them a pretty strong favorite.
I went back through the 1994-2006 playoffs to see how well teams of different seeds have done in the playoffs. Before 1994 you had two rounds of divisional playoffs before the conference final, so you really didn't have 1-8 seeding on each side as you do in today's NHL. Over that time, the President's Trophy winner has won, on average, 2.33 playoff series per season. Comparatively, the top seed in the opposite conference and both #2 seeds averaged only 1.08 series victories. Below is the complete table showing average series victories per seed:
|Seed||Avg. Series Wins|
There are some interesting fluctuations in there - for starters, the fact that the worst performing seed is the 5th spot (out of 24 #5 seeds over the last 12 seasons, they've been eliminated in the first round 20 times!). My guess there is that often the #4 seed is a better team than #3 or possibly #2, since division winners automatically get the higher slots, and thus the #5 is facing tougher opposition. The other particularly odd bit is how the #1 Opp. seed (top seed in the opposite conference from the President's Trophy winner) and the #2 seeds both fare worse than the #3 and #4 seeds. Your guess is as good as mine as to why that is the case. Regardless, the dominance of President's Trophy winners is clear.
Even just during the twelve years I'm looking at here, the President's Trophy winner won the Stanley Cup four times (33%), followed by #2 seeds with three (12.5%). That's not very close, considering there are two #2 seeds each year, and only one President's Trophy team. The #1 seed from the opposite conference has won once (2004's Tampa Bay Lightning), and two #3 seeds have won (Detroit in 1997 and 1998). New Jersey is the only team to win from the #4 and #5 seeds, in 2000 and 1995 respectively.
Perhaps a team that fights hard to the finish and wins the President's Trophy has the momentum and mindset to achieve great things in the postseason, and teams that let up may not find it so easy to "flip the switch" and start winning again. Regardless, it seems here that compiling the best regular season record might be worth something after all. Shocking, ain't it?