May 21, 2014

## Correlations between hockey variables

Lots of people ask the basic question: are the Corsi and Fenwick statistics any good? The logic behind them — that teams that control the puck more are more successful– is sound, but often unexamined. One way to judge their usefulness is to check how they relate to other variables, like goals for/against, or how they correlate to winningness relative to another statistic like save percentage.

Pairwise correlations compare two variables at a time. The diagonal (with the histograms) shows the distribution of a particular variable as well as its name. The left diagonal has a scatterplot of the two variables above it and to its right; the right diagonal prints the correlation coefficient for the same variables, with the font size increasing for larger correlations. An obvious example is the comparison between the Fenwick% and Corsi%: the correlation coefficient is 0.97, and the scatterplot forms a nearly perfect line — telling us that the Corsi% and Fenwick% are very, very closely related.

Looking at the rightmost column tells you how each of the variables relates to the percentage of possible points a team could earn. The Corsi% has a coefficient of 0.51, and the Fenwick 0.54. Save percentage is also at 0.51, meaning that a high save percentage correlates to winningness about as strongly as puck possession does. The top row relates to outhitting your opponent. I’ve discussed that a bit in my first post, so it suffices to say that if it’s a useful metric at all, it tends to be negatively related to winning.

The two remaining variables are Goals Against Per Game (GAPG) and Goals For Per Game (GFPG). The obvious conclusions are evident: GAPG is very negatively correlated with earning more points (-0.74), whereas GFPG is very positively correlated (0.62). The less obvious conclusions are there too, telling us that puck possession is positively correlated with GFPG (0.32 and 0.31 for Fenwick% and Corsi%, respectively) and negatively correlated with GAPG (-0.50 and -0.49 for Fenwick% and -0.5 for Corsi%, respectively). All of this demonstrates that puck possession stats look to be good predictors of success.

**Controlling for save percentage**

In my first post I uploaded graphs that showed a strong link between puck possession and success in the regular season and playoffs. The issue with that, though, is that some teams had very good possession numbers, yet didn’t qualify for the playoffs, while others achieved the opposite. The 2010-2011 Bruins had an even-strength Corsi of 50.73% — fairly average — and yet they won the Stanley Cup. Last year’s Toronto Maple Leafs, however, managed to have possession numbers among the worst in the last five years, but still qualified for the playoffs. One explanation that gets thrown around is save percentage — and it turns out it’s a decent one.

This graph plots the percentage of possible points that teams earned in a regular season against the Corsi%. The graphs are split into six groups based on a team’s save percentage. The teams with the lowest save percentages (roughly below .910) are in the bottom left, and the teams with the highest at the top right (roughly above 0.928). The main things to notice here:

- The teams with the lowest save percentages necessarily need a good Corsi to qualify for the playoffs. As the save percentages get lower , teams with lower Corsi percentages have a harder time making the playoffs — you can see this by the positions of the black dots (non qualifying teams) in the bottom row.
- Stanley Cup champions have had middling goaltending in the regular season (Chicago, 2009-2010), but they need damn good possession stats
- Teams with consistently elite goaltending (Boston, 2010-2011) can win the Stanley Cup with a fairly average Corsi

What’s the moral of the story then? Good puck possession and a solid goalie are keys to winning (duh). If a team is weak in one of the two areas, though, then they must counterbalance with strength in the other, especially if the weakness is possession.^{1} A team with terrible possession stats might sneak into the playoffs, but don’t expect them to go anywhere without their goalie stealing the Cup.

^{1}If your Fenwick % is floating around 0.45, you should probably work on that instead of hunting down Dominik Hasek for his blood.