There's often a lot of talk about the point where one is "mathematically out of the playoffs". Websites typically put an 'e-' in front of the team for whom it is impossible to make the playoffs. Often before you are officially eliminated the situation for you to make the playoffs would have to be really bizarre. That is to say in order for Philadelphia to make the playoffs at this point they'd need to win a lot of games and all the top teams would need to start losing. Sometimes the situation is so unlikely it's better just conclude it's impossible statistically speaking.
For example we currently have about 30 games left. A 50% team has a 43% chance of playing above 50% and 43% chance of playing worse (leaving 14% for 15 wins out of 30 games). Of course, what I care about here is that there's a 5% chance that a 50% team wins 20 or more games. In other words if a team needs to win 20/30 games to make the playoffs then they have a 5% chance of making the playoffs (if they're average). Of course most bad teams (those who don't make playoffs) are below 50%, but I'm assuming a team might play a little better to make the playoffs. This is done following the simple binomial distribution. As you get closer to the last game of the season there is a higher likelihood that you could win 100% the remaining games: (1/2)games left, and a similar relationship exists for winning 90% or 80% of remaining games.
Of course winning percentage doesn't make much sense in the new NHL. I use a system that assumes each team will get 8 additional points during the course of the season (10% of games) and so winning percentage equals:
w% = (W+OTL/2)/GP-0.05
Due to the fact that the binomial distribution is discrete you can't solve for an exact value so I did a regression on the last 30 games to show the sort of functional relationship between games remaining and statistically impossible winning percentage.
cut-off = 0.763 - 0.452 *ln(ln(ln(games left))) [or = 1 if games left < 7]
Although it looks complicated, the nested 'ln' functions are necessary to get the appropriate curvature.
Using this equation and a guess for the number of points to make playoffs (~93 points) you can estimate the required winning percentage
Required% = (93-2*W-OTL)/[2*(82-Games Played)]-0.05.
And if required% > cut-off then you have less than a 5% chance of making the playoffs.
Of course the opposite is true if required% < (1-cut-off) then the team is statistically making the playoffs.
Of course if the team is better than 50% for whatever reason (star player just got back from long term injury).
Most of the results are obvious, but in the Blue Jackets, Blackhawks and Kings are out and in the East just Philadelphia. Ducks, Predators and Red Wings are making the playoffs in the West and it appears that Buffalo has secured a spot out East. These statistics are presented on my website.