## Comparative Studies: Winning in the NHL Playoffs

I figured I would give everyone a break from the NFL for a little bit by moving to the NHL.  This post is basically following what I did previously with the NBA.  So I’m taking the regular season goal differentials for teams that make the NHL playoffs, comparing differentials for a match-up, and then predicting which team will win the series using the difference in differentials (which I’ll just call differential) and home ice advantage in a logistic regression.  If you don’t feel like clicking back to the NBA post, here’s the skinny: bigger differentials lead to a better chance of winning your series, which you should expect.  The more you typically win by compared to how much your opponent typically wins by, the better you are than they are.  Also, home court gives you a better chance of winning.  In the data I have the effect is fairly small, but it’s a trend in the model and the ROC shows that using home court leads to better prediction accuracy.  You can be a point worse than your opponent, but if you have home court you’ll have a 50/50 chance at winning the series.  How about in the NHL?

First, I’ll note that ESPN doesn’t list average goal differential like it does for the NBA (e.g., last year the Cavs won by 6.5 points on average), but total goal differential.  So the Washington Capitals, the best team in hockey by goal differential last year, outscored their opponents by 85 over the course of the season.  So I’ll be using that number of 85 instead of average margin of victory, which would be 85/82 = 1.04 for the Caps (the worst team in hockey last year were the Oilers at -70 or -.85 goals per game).  In the NBA last year, the average total points per game was about 201 as best as I can tell.  So when the Magic won by an average of 7.5 points per game, that’s only 3.7% of all the points scored.  In the NHL, the total goals per game was about 5.7, so when the Caps win by 1.04, that’s 18% of the total goals scored.  Thus a good NHL team seems to account for a lot more of the points scored than a good NBA team.  But, NHL games are counted by single goals, and so there might be a lot more noise in final results.  When a playoff series can end in as little as four games, that becomes important.

Second, in the past five years (which is my data set), there have been a lot of upsets.  At least a 6 seed, if not worse, has always made it out of the first round, and do you remember 2006?  The whole bottom half of the Western Conference made it through, and the Oilers made it to the Stanley Cup as an 8 seed.  The NHL Playoffs: Where Crazy Happens.  Consider this foreshadowing of the most blatant kind.

So let’s get to the data.  In my NBA post I had three graphs.  Here are the same graphs for the NHL.  First, win probability by goal differential.

Next, the same graph but with one line for home ice advantage and one for without.  The higher line is for the team without home ice.

And finally, the ROC for the models with and without home ice included.  The dashed line is for the model that includes home ice.

So a few things to note.  In the model with home ice, home ice advantage is not significant (p = .7), and the coefficient is negative (hence, the line being lower in the second plot).  Also, in the ROC plot the two models go back and forth; in the NBA they were similar, but the only one to have an advantage was the model that included home court.  If you get the area under the curve as a measure of total accuracy, the home ice model is very slightly more accurate.  So, we can come to one of two conclusions: either home ice doesn’t matter in the NHL playoffs, or it does and being at home hurts your chances of winning the series.  Third, the probability of winning curve looks much more linear (although the logistic function is the proper fit) than it does for the NBA.  This basically means that the worse teams in the NHL have a better chance of winning than they would in the NBA, and good teams have a worse chance (since the curves are symmetric).  For example, the top seed in the NBA is pretty much a lock to advance out of the first round – the model says over 95%.  If you are around the best hockey team of the past 5 years, with a 100 goal differential, they would only be 87% to get out of the first round against an average 8 seed with a 0 differential.  So the intuition about noisy playoff results plays out in the data.

So, to sum up: even though good NHL teams might be proportionately better than good NBA teams, they have worse prospects in the playoffs.  It’s just my feeling, but this is probably because goals are discrete entities and so a single game can be decided by a fluke play or random chance more easily than an NBA game where scoring is much more continuous.  Since the playoffs are relatively short, there is plenty of room for upsets, whereas we can get a better sense of who the good teams are over the course of the 82 game regular season because those bounces even out; this is true in the NBA as well, but more true in the NHL.  The bounces and random chance are so strong that home ice either doesn’t exist, or it may be reversed (although I think this is implausible).  Which means that come next June, if the Red Wings are in the playoffs I’ll be simultaneously sweating each game even more while I tell myself that the playoffs are dumb luck and that I should be happy the regular season went well.