## R2 and Playing like Team Canada

Last week, Team Canada introduced a new style of play to international hockey, riding their revolution all the way to a gold medal. This style of play is being called "really really ridiculously good defense", and broadcasters, tweeters, and even NHL coaches are predicting teams will pick up on this drastically new way of winning games.

Defense is, of course, nothing new. But how important is defense? Can its importance be quantified? Can defense-first systems overcome offensive deficits reliably enough for long-term success or was Team Canada’s strangling of the world a two-week long anomaly? For these answers, we turn to R2 (said: r-squared). For the mercifully uninitiated, here’s a short primer on what R2 is and how it is used (those who are familiar feel free to skip ahead).

Hold on to your butts, we’re talking math. Let’s say you want to see how closely Corsi % relates to team success. You get some data points, build a graph, and you find that teams with better Corsi tend to have higher point totals. Great, you’ve found yourself some correlation. Next you grab your ruler and draw a trend line (line-of-best-fit). Now you’ve got a line you can use to predict how a team will do if they have a certain Corsi through a season. But how accurate is this line? In other words, how closely does Corsi relate to team standings? Here’s where R2 comes in. What R2 does is measure how far each of your data points is from your trend line. The closer the points are to the line, the better "fit" your model is. R2 can be anywhere from 0 to 1, with 1 being perfect correlation (good) and 0 being completely random (bad). What makes a "good" R2 value? Well it depends on what you’re looking at. In a "hard" science like chemistry or physics, anything below .9 will become suspicious. In contrast, any social scientist will get suspicious when R2 is above around .4. I think hockey lies somewhere in between; we still deal with human behavior, but the results are easily counted and repeatable (to an extent). Although the math behind this is more than we need to get into here, R2 calculations are fairly simple to do using a program like Excel. It’s because of this that I’m a little surprised, actually, that R2 is not reported more often in the hockey blogosphere. I think it is an effective tool to quickly test the "goodness-of-fit" for fancy stats and could be used to raise the profile of emerging stats in hockey. At any rate, I’ve applied R2 to test how well several stats correlate to team success.

The good people at Hockey Analysis have compiled stats (both fancy and not-fancy) for every year since the Second Bettman Lockout (never forget). As with any stat, the bigger the sample size, the better, and so this gives us a nice seven-year sample size to run this little test. As for team success, I’ve essentially considered this as if the league had played a seven-year long season, taking just the point totals from that time period and ranking them (i.e. first overall, second, etc.). I did the same thing for all the stats form Hockey Analysis so we have both the net totals and the rankings form each team to work with. Now we’ve got all we need to test these stats and see how well they correlate to team success.

Here’s a summary of what I found comparing the stat totals to point totals at 5v5 in close situations (remember: high numbers mean better correlation):

 Stat R2 Goals For 0.311 Goals Against 0.683 Goal % 0.756 Corsi For 0.236 Corsi Against 0.446 Corsi % 0.567 Fenwick For 0.303 Fenwick Against 0.398 Fenwick % 0.556 Save % 0.262 Shooting % 0.003

And here’s what I can say about that:

· Corsi and Fenwick % are fairly good indicators of success, ranking among the highest R2 values I got.

· Shooting % is basically useless for explaining team success (we knew this already).

· Save %, while better than shooting %, is not the best way to explain team success.

· I also ran this test comparing all combinations of team rankings and raw totals, and found there was no significant difference between methods (i.e. comparing point totals to Corsi For totals was no different than overall standing to Corsi ranking).

· I again ran all this with all 5v5 situations with no significant difference.

· Every defensive category correlated much closer with success than its offensive counterpart.

It’s this last point that I find most interesting. I’m not exaggerating when I say that every single defensive stat that Hockey Analysis has tracked over the last seven years has correlated much closer with success than the offensive partner. Look at the Goals For (R2=0.311) and Goals Against (R2=0.683), for example. At the most basic level, this says that defense is twice as important as offense to a team's success. Of course this might seem a like a little too much of a generalization but what it indicates is that (over the last seven years) a team’s ability to prevent goals has lead to success much more reliably than their ability to score goals.

What does this mean for the Leafs? Seeing as the whole "team defense" concept ran its dick into the metaphorical fire hydrant a long while ago, this analysis has done nothing but add to the outlier mythology that this season is building. The Leafs rank dead last in Fenwick, Corsi, and shots against (5v5) so far this year. That said, the Leafs have been getting elite-level offense and goaltending the last couple years, so maybe they can serve as evidence that defensive shortfalls can be sustainably overcome by surpluses in other areas. We’ll see how this plays out, but R2 has not added much confidence to the Leafs’ season. As we get more years in the fancy stats era, this hypothesis can be better developed and we can move from correlation to causation. R2 is not perfect, it can’t tell us explicitly about causation and it would be foolish to say that any team that improves its defense will be guaranteed to improve its standing in the league. What it does say is that good defense indicates success much more reliably than good offense, and this should be useful when thinking critically about a team's advanced stats. My hope is that we start to look at defensive metrics with a little more weight than offensive ones. Either way, R2 is still useful tool to add to our fancy stats Batman utility belt.

Hockey media’s barometer tells us that a shift is coming towards defense thanks to the world-class performance Canada rode to the top of the hockey world. There is no shift coming: its already here.

Find the raw data used here

Take a look at my Excel file here

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