The NHL does overtime right -- sort of. I don't like the shootout but the 5-minute OT period of 3-on-3 hockey is very exciting and encourages the teams to play all-out to score.
The problem with the NHL OT system is it actually encourages teams to relax the last few minutes of regulation to “preserve” a point, the last 5 minutes of tied regulation are boring. And having value of the games vary on how long they take stinks. If they must vary the points by length it should go the reverse:
3 points for a regulation win
2 points for an OT win
1 point for a shootout win
0 points for losers no matter when they lose
That would encourage teams to play all out and score all the time, not just a burst of energy in OT for the second point.