As a twist, I've added an additional line to the end of the tables, which you will see at the end - the teams are still sorted the way the NHL wants them to be, but next to "actual points" is a new column labelled 3-1-0. That simply means, three points for a win, one for a tie, and nothing for a loss.
I love the idea behind the system, in that it would assess a premium on winning the game. I'd extend overtime to ten minutes, or even a full period (twenty minutes), to further increase the chances for a decision, and scrap the shootout, because it's inherently unfair to have teams cop extra points on a skills competition after the game is finished - especially one that is more luck than skill. Teams would definitely push for more wins, even at the cost of an occasional loss: 1-1 would be better than 0-0-2; heck, 3-5 would be better than 0-0-8. Notice how, below, the Sabres would be well ahead of the Bruins, on the strength of having four more wins? That's the idea - reward teams that win their games, knowing that ties are no longer an option in the playoffs.
The only downside is that, at the extremes, it could become almost as unfair as the system it replaces.
Assume two teams go to OT every game. One goes all out for every point and finishes 30-52 for 90 points. The other tries to stall for the sure point every time, only countering in the most obvious situations (blocks leading to breakaways, for example). They split their games with the all-out team, draw everything else, and finish 3-3-76 for 85 points.
A team that has 49 more losses than another would look very odd indeed above them in the standings, even given the 27 more wins. Not that either would make the playoffs anyway, but to take a less extreme example - say the same two teams with 20 OT games each, not an unheard-of total. They each go 40-22 in regulation, but the tie-up team takes its 20 draws, while the all-outers split their games 7-13. The 47-35 team will finish ahead of the 40-22-20 team by one point. That could be a problem.
One compromise is to muddle up the two systems - three for a win, nothing for a loss, but only for regulation and overtime. Once the game gets to a shootout, each team gets a point, with the successful team (it could hardly be called a "win") gets the third point. The standings would look odd: just as an example:
A. 35-30 (12- 5) 134
B. 38-34 ( 7- 3) 131
C. 34-28 ( 7-13) 129
D. 33-33 (10- 6) 125
E. 30-30 (11-11) 123
That's regulation record (shootout record) total points, where the total points equals 3*wins + 2*SO wins + SO losses. It looks odd, but people would get used to it if you broke it up in pairs like that; but I dislike it for a different reason. If you go through it and subtract shootout losses from the total points, you would make just one change: team C would finish behind team D, which would be more fair, because D's winning percentage (43/82, .524) is better than C's (41/82, .500). Whenever possible, we want the teams winning more often to be the playoff teams, because in the playoffs, it's win or lose, no pity points, and no pat on the back for hanging in there for 60 or 65 minutes.
The thing is, nobody - NOBODY - complained that the 2-1-0 system was unfair. They complained that there were too many ties, that the ends of games were boring. The league added the five-minute regular-season OT in response, but ties didn't go down "enough," so they cooked up solutions to a problem that really didn't exist, and made it worse. All the fixes debated above, and elsewhere in the hockey world, have varying merits, but the simplest fix would simply be to go back to the old, not-really-broken system... just make the OT a real hockey period, sudden death, and not the five-minute afterthought we currently have.
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