NHL March Mathness

Usually this time of the year is fun for the math geeks among us because we get to play with playoff odds. The most adept start talking about permutations about now, while we'd expect an article from the mainstream to come out explaining how the results of the last three games determine a whole season of work.

Talk of odds was on the rise for a few minutes in February, but has thoroughly subsided with consecutive losses. The Habs could make the playoffs in theory, but only in about 0.03% of scenarios, most of which ask them to win 15 games in a row.

So odds aren't making the rounds much these days. That doesn't mean there isn't some math to talk about.


Toronto Maple Leafs
First, we have the Leafs. When the Canadiens were in the running with a nearly 20% chance at the playoffs, the Leafs stood at 70% or higher on most days. But since they fell from 8 games above 0.500 to none, the Leafs have shed a lot of playoff hope.

This may be of little interest to many, but to Habs fans who conceded a season 30 games too soon, watching falling Leaves is about as good as things can get.

Their chances of making the playoffs according to simulation at Sports Club Stats stands at 8.3%. The most likely scenario now placing them with a mediocre 83 points and no chance at games in April or top two picks. So exactly in that zone we would dread to be in as Montreal fans, and one which is so familiar (and possibly responsible) for a playoffless Toronto franchise.


Edmonton Oilers

Second, we have the Edmonton Oilers. I am not alone in citing them as the chief rivals to Montreal's bid to win a top two pick. Tonight, the Habs meet the young bucks in what I am calling the Grigorenko Cup -- a battle to the ends of the clock for most goals against and most credible losing display.

The math with Edmonton is simple. They stand at this time 2 points behind the Canadiens with a game in hand (admittedly games in hands for teams like these two mean 0 points more often than not). A regulation loss in the Grogorenko Cup would give the Canadiens the coveted lower hand in this race to Russian redemption.

Obviously the Oilers would stand equal on points and would have one more game to negotiate without slipping up to grab a point. That's just the start.

The tie-break is also important here.

Currently the Habs have one less regulation or OT win (ROW) than the Oilers, and consequently would win the first tie break. By manoeuvring Edmonton into a win this evening, the advantage would be doubled and make a tie in points a win (remember loss is win now) to the Canadiens.

The next tie break is head-to-head record. In a symmetrical season series such as this one, the tie break is simple -- who got the most points. With an early season loss to the Oilers, the Habs already have the edge in this tie break and could reinforce it with another loss. Winning this tie break would make a tie in the previous tie break a winning scenario too, giving that much more wiggle room for the futile home team.

In the worst case scenario, the Canadiens will win in regulation producing a gulf in points of 4, an equal number of ROWs and a deadlock in the 3rd tie break. This wouldn't be great, not only because of the points, but also because the Habs currently lose the fourth tie break of goal differential, where they haven't been quite bad enough.

An OTL wouldn't be ideal, but is workable.


Draft lottery 2012

I'm sure there are some of you out there who have the same misguided notions about the draft lottery that I used to have. I thought long ago that the lottery was like a raffle where the bottom 5 teams had so many tickets and each was drawn until the order was established.

This is not so. There is only one drawing in the draft lottery and after that team is drawn they merely move up 4 places in the order and the rest shift down accordingly. All 14 non-playoff teams have a chance to be drawn (with diminishing odds, of course). If the 17th place team is drawn, what happens is that they move up to 10th in the draft and 18th to 21st become 11th to 14th picks. All the teams from 22nd to 30th continue as if nothing ever happened retaining the first nine picks.

So the odds for being drawn are not exactly the odds for getting the pick you want.

These are the odds for being drawn:

25.0% - 30th
18.8% - 29th
14.2% - 28th
10.7% - 27th
8.1% - 26th
6.2% - 25th
4.7% - 24th
3.6% - 23rd
2.7% - 22nd
2.1% - 21st
1.5% - 20th
1.1% - 19th
0.8% - 18th
0.5% - 17th


Columbus as it happens will come last. So they have a 100% chance of a top two pick. Because they don't have to win the lottery to pick first, their odds of winning that pick are 25% + the sum of all the odds for teams 17 to 25, which amounts to 48.2%. That would be a lovely position to be in (though I'm not sure the hundreds of fans in Columbus would agree), but it's just not in the cards for the Habs.

Instead we look at positions lower in the order.

Were the Habs to come 29th (beat the Oilers), their odds would look like this:

1st pick: 18.8% (need to win lottery)
2nd pick: 42.0% (CBJ or team lower than 6th wins)
3rd pick: 39.2% (a team from 3rd to 6th wins lottery)

A whopping 60.8% chance of a top two pick.


If the Habs maintain their current position without "passing" Edmonton, the odds are as follows:

1st pick: 14.2%
2nd pick: 0.0%
3rd pick: 56.1%
4th pick: 29.7%

A paltry 14.2% chance of a top two pick.


Since top two is really where it's at, teams from 25th to 28th still have a hope, but only through winning the lottery (you can see those odds above). The benefits of finishing lower come in the position that is retained if a team higher (30th) or lower than wins.

Where the Habs may be lucky is in the fact that it is the Oilers and not another rival in the catbird seat. Looking up and down the Oilers, one finds dynamic scorer after dynamic scorer, but nary a goalie or defenceman around. The team needs a young defender like the Habs need two full scoring lines (a lot), and though they might be happier to retain the losing position, a trade down the road might not be out of the question.


2013 Draft lottery

I don't mean to disturb some sleeping monster, but to those unaware, the NHL and their players association currently have no CBA for next season. The last time this happened, there was no season. And though it's hard to imagine the league taking another PR hit of that magnitude, several factors suggest it's not out of the realm of possibility:

1) The US barely noticed a season without hockey last time
2) Canada came back in stronger numbers to support (though another strike may be a step too far)
3) The NHLPA don't like where they are and have brought in a harder line lawyer to lead their negotiation
4) The NHL owners don't like where they are and wish to reduce the proportion of revenues allotted to players

There are some sticking points there and based on judgments of things most important to owners (PR vs. more revenue in the pocket) and players (share of revenue vs. year of short career), there could be a standoff.

Let's assume for the sake of argument that there is no season. What happens in that scenario is a draft in 2013 without a season's standings to inform it. Last time this happened, Montreal walked away with a high pick by beating the odds somewhat and Pittsburgh nabbed their corner piece.

There's no formula set in stone for a draft of this kind, and perhaps it will be part of negotiation. But last time, it was based on a few things: results of the previous three seasons of play (specifically playoff participation) with some sort of penalty for getting a first overall pick (though it didn't hurt Pittsburgh or Columbus, only Washington). The system is flawed and was clearly dreamt up by someone more likely part of the Penguins than the Capitals organization.

But let's imagine the season is lost and a system that is more equitable to teams that are actually bad at that moment in time (as the real draft is). The Canadiens would stand in good stead.