## Mulling over defence vs offence in advanced statistics

Sometimes my brain leads me into some strange places. Other times, it asks incredibly mundane questions, such as is it better to score goals or prevent goals? To win games, you obviously need to do both, which is why the question sounds dumb. But it’s a fundamental part of team philosophy. The cliché is that “defence wins championships” and even if defence and offence are nearly equal in determining success, that “nearly” can make all the difference.

In this case, that dumb question led me to spend a whole bunch of time poring over numbers, creating graphs, and pondering how defence is handled by the current advanced statistics we have available. I probably should have left well enough alone.

Now, I am not much of a statistician. I stopped studying math after 1st-year calculus, but I understand the broad strokes. For this, I just wanted to do some quick and dirty statistical analysis. I just wanted to figure out whether goals for or goals against correlates more strongly with winning.

So I took the last 5 NHL seasons and all 30 teams and took a look at their goals for and against. I stuck with 5-on-5 and took out empty net goals to keep things relatively even for all the teams. I then charted those totals against each team’s wins each season. Here is the result:

When I saw these two graphs, I have to admit to being surprised. It’s not just that allowing fewer goals correlated with winning more strongly than scoring goals, it’s the degree to which it is the case. It appears that preventing goals correlates far more strongly with winning. Now, I may be mistaken, and someone more knowledgeable in the area of statistics may come in and explain that the correlation I’m seeing here isn’t statistically significant, but it looks fairly significant to me.

19 teams reached 50 or more wins in the last 5 seasons. 8 of those teams scored fewer than 160 goals at 5-on-5. Only one team, the 2011 Pittsburgh Penguins, allowed more than 160 goals at 5-on-5. In general, a far surer path to victory is paved with solid defence, while teams can do far more than get by with a mediocre offence. The 2006 Dallas Stars got to 50 wins with just 122 goals at 5-on-5. Even the 2009 Washington Capitals, who had the most 5-on-5 goals for in the last 5 seasons with 213, only allowed 136.

Now, this isn’t anything ground-breaking, but it got me thinking about how defence is usually treated in advanced statistics.

The big two most referenced advance statistics, Corsi and Fenwick, are built around the idea of puck possession. They’re founded on the basic principle that getting more shots on the opposition net is better than allowing more shots on your own net, which seems pretty sounds.

In some ways, proponents of puck possession would advocate that the best defence is a good offence. A defensive tactic like blocking shots is downplayed in importance, as blocking a shot means something has already gone wrong: the opponent is shooting the puck. Cam Charron once paraphrased General Patton regarding shot blocks: “No bastard ever won a game by blocking shots. He won it by making the other poor dumb bastard block his shots.”

As long as the puck is in the offensive zone, no trouble will come to the defensive side of the ice.

This is all well and good, but it feels like something is missing. It strikes me that the advanced statistics we currently have available do not have a particularly good grasp on goal prevention. The general tactic seems to be to wrap it up with puck possession as part of a package and use Corsi or Fenwick as a catch-all for both offense and defence. But if preventing goals does have a stronger correlation with winning than scoring goals, it seems like that should be taken into account.

Defencemen seem to get short shrift, to the point that Vic Ferrari, creator of the essential timeonice.com, was quoted as saying, “It becomes obvious very quickly that forwards are driving the outchancing-at-evens bus … defensemen are just riding it.” Poor defencemen.

But if the focus is on outchancing the opposition and possessing the puck, this is likely true. But the role of the defenceman is, mostly, to ensure that the results of the opponents’ chances and possession are foiled rather than creating chances and puck possession for their own team. How do we take measure how well a defenceman performs in that role if something like Corsi doesn’t capture it accurately?

One of the other problems is that there aren’t many advanced statistics that take goaltending into account. While even-strength save percentage, the various “quality start” metrics, and GVT are useful for evaluating goaltenders, there doesn’t seem to be anything that integrates a teams quality of goaltending with overall team performance. Advanced statistics also don’t seem to have much of a handle on shutdown defencemen, beyond pointing back to Corsi and Fenwick.

This isn’t meant to be a criticism of advanced statistics; I’m just honestly curious how these problems can be solved or, if a solution already exists, I want to know about it. It just seems that, right now, the advanced statistics community is focussed so much on what pushes possession forward that it might miss what prevents the opposition from doing the same. It might seem like they are one and the same, but preventing goals appears to be more important than scoring them when it comes to winning.

1. Some good points here, but I would imagine a big portion of the difference between goals for and goals against can be accounted for through the nature of scoring goals versus allowing goals. Teams can pile up goals for in a blowout, but they can never lower the number of goals against. I think the results would prove more valuable if you looked at goals for and goals against when the game is tied or within 1 goal.

2. When I play rec-league defense, I use a simple formula. I don’t count ‘goals for’ since all I care about is that we have 1 more at the end of the game. I do count the ones that go into our own net. Zero or 1 goal against (GA) means I did good. Two GA means I need to do better next time. Three GA means it’s someone else’s fault and I was fantastic, no, really, it was all the goalie’s fault, and my forwards didn’t pinch. Four GA never happens, I stopped counting at 3 GA.

It seems to work pretty well. :)

3. You have a good start here and you are asking some good questions, but as for your math IMO you have a couple more steps to complete. You want to quantify the correlations you are seeing. You are probably using Excel right? So if the data are in, let’s say A1 through A100 and B1 through B100, type ‘=PEARSON(A1:A100,B1:B100)’ and then in another cell, ‘=A123^2′ where A123 is the cell in which you did the Pearson correlation test.

Correlations aren’t “significant” or “non-significant,” it’s just a matter of degree. Generally, +/- 0.3 is a weak correlation, +/- 0.5 is medium, and more than that is strong, but those are just guidelines, there is still some subjectivity in interpreting them. It sure looks like GA is more correlated to wins, but to quantify it would really go a long way. Then, the square of the correlation tells us the amount of variance that is accounted for by the correlation.

If you decide to run this test I’d be curious to know what you come up with! Today’s Pearson Correlation 101 has been brought to you by @Hashtag_Hockey and hashtaghockey.com

4. I agree with derek. Goals 2-5 are meaningless in a 5-0 game. In this example, it only took one goal to win. The other four just activate bonus clauses!

• It’s not just that those goals are meaningless, it’s that those goals are available to a team, where there is no equivalent for goals against. A good offensive team can keep scoring goals in a game, but a good defensive team can do no better than a shutout. Comparing the two is essentially comparing apples and oranges.

• Along with that, goals 2-5 aren’t meaningless in a 5-0 win; or at least, you can make a case for goals four and five being meaningless, but before that, you are talking about very important goals. A 2-0 lead means that you can’t be tied back up by one guy suddenly going into hero mode, or worse, by a fluke or a soft goal. You can sit back more and concentrate on keeping everything to the outside, not giving up dangerous chances on odd-man rushes and stuff. No one-goal lead is really safe until the clock runs out. Going up by two changes the dynamics of the rest of the game, and often you then get that third, backbreaking goal precisely because the other team has to start pressing and taking risks to create offense and get back into the game.

This is why a lot of advanced statistics generally concentrate on tied or one-goal situations. Corsi and Fenwick can be especially misleading when one team has a comfortable lead and is sitting back, while the other takes long or poor-quality shots in the hopes of getting a cheapo to get back into the game.

• nightfly, goals 2-5 are meaningless in this analysis because it only took goal one to get the win and the 2 pts. In reality, of course they are important but they still only get you one win which is what is important in this analysis.

5. To add to my comment, given that the flipside of what i said is also true: once it is 1-0 the other four goals against don’t make you lose any more than you have already, perhaps add to your analysis some consideration for blowout wins and losses by each team, that is, calculate the variance of goal differential for each team for their losses and their wins. Two teams may have the same avg. goals against/for, but one team may have only tight games or blowouts while the other is more consistent.

6. Also, did you include shootout wins and losses? A team particularly good at shootouts will have more wins but will not necessarily be better at 5-on-5 either offensively or defensively.

• I think a couple of people have proven that, statistically, no team is good at the shoot out. They have not been able to sustain a strong performance so shouldn’t have too much impact.

• What I meant to say, was that there is too much element of luck involved.

• Good to hear. I would hate a team to get ahead in a skill that is no part of real hockey.

7. Great article, and one of many reasons us Wild fans don’t give too much of a flip over the puck possession stat-heads. Corsi and what not don’t hold up across teams and situations but GAA is a pretty universal measure of a team’s defense. It’s barely any better than trying to compare plus-minus. It’s a relative measure rather than an independent measure.

8. When I played Lax, we were taught that your best quality scoring chances come from within a 15 foot scoring “arc” around the cage.
Is there a chart that would show where opponents are shooting from?
One could use it to see how d men force low quality shots, and clear the puck on scoring chances.