A statistical breakdown of the first round of the NHL playoffs

I have used the Glicko-2 rating system to rank each NHL team's regular season results and assign ratings. Each regulation and overtime win was counted as 1 point. A draw or shootout result was 1/2 point, and a loss was 0 points. These ratings are shown in Figure 1.


Figure 1. Glicko-2 ratings for NHL teams at the end of the 2010-2011 season. (Click for a bigger version.)

Because the rating system works best when games are played in groups of 10 to 20, the games were divided into five epochs of roughly equal size (~250 total games each). The first three were before the All-Star break; the last two were after. More recent games are given a higher weight in this rating system, reflecting changes over the course of the season. The mean rating is 1502. The median is 1514.

Very recent injuries/comebacks aren't accounted for. Nor is home ice advantage. Nor is the fact that regular season overtime is 4 on 4.

The error bars shown are a single rating-deviation (RD); 95% confidence is within 2 RD. Based on the results of the regular season, most teams are statistically indistinguishable. Only at the very bottom end is there a significant difference between teams.

Canucks fans: it could very likely have just been a long lucky streak. Deal with it. Despite the President's Trophy, there are other teams just as good. That's what you get when you play Colorado and Edmonton all year. Dallas fans: it's unfortunate your team was in such a tough division. Their rating was higher than several teams that made the playoffs. Probably in any other division, you'd have made it, too.

The volatilities of these ratings are shown in Figure 2.

Figure 2. Volatility of ratings given in Figure 1.
These volatilities are a somewhat abstract concept, but basically they measure how much a team's rating would change if it won or lost the next game. As a consequence, they're a measure of how "streaky" a team was during the season (sort of, with lots of glossing over). Look at the Devils. They were awful in the first half, then went on a huge run, and then faltered at the end. During this time, they lost to some very bad teams and beat some very good teams. This gives a high volatility. If you're into long-term gambling, and you're in it for the money, don't bet on volatile teams. If you're into long-term gambling for the excitement, bet on volatile teams. The mean and median of these is 0.06. (The specific numbers don't mean much... the relative numbers are more important.)

Now that we have a set of ratings, we can compare teams. Glicko ratings are based on the Elo system, so the standard Elo comparison was used. In a game between team A and team B, if the rating of A is R_A it is expected that A will score E_A points.
E_A = Q_A/(Q_A + Q_B)
where
Q_A = 10^R_A/400.
A rating difference of 400 means that in a lot of head to head games, you will earn 10 times as many points as your opponent (where "points" are defined in the first paragraph, not the NHL standings). Equal ratings means you have equal chances of winning each game.

These odds are given in Figure 3 for each of the first round matchups.

Figure 3. Odds of winning a single game for each of the first round matchups. Percentages given are those of the home team (listed first on the x axis).

The chance of winning each series in k games is given in Figure 4.

Figure 4. Odds of winning the series in k games for each of the teams in the first round.

If a team has probability p of winning each game, then it has probability of winning the series in k games given by
p⁴ (1-p)^k-4 C(k-1, 4-1),
where C(a,b) is read "a choose b."

Curiously, Pittsburgh is a home team underdog (though they just won game 1).

I've yet to work out the odds of each team making it to the finals. Stay tuned for a future post!