The SOG Myth, Or: Why You Shouldn't Use Statistics to Talk About Hockey

WARNING:  Consumption of the statistics contained in the FanPost may lead to head asplosion.  Read at your own risk!

Welcome back for my second stats-based FanPost -- this time we're looking at the SOG (shots on goal) statistic, and other game-by-game statistics that may shed some light on, essentially, what wins hockey games.  After reading gmh's excellent and comprehensive summary of SOG for the regular season, the question came up --  how is it that the Blackhawks lose games in which they outshoot the opponent by 30+ shots?

Damn you, Hiller!

To answer this question I turned to NHL event summaries like this one, summed the numbers up for each game, and did my own home-baked stats work on them.  What follows is pretty heavy, so if you intend to sit through it, please put away all sharp objects immeeeeeeeeediately and pour yourself your beverage of choice.

(I apologize in advance for making this sound like you need a degree in statistics -- ask questions and I'll try to clarify and simplify)

Shots on Goal (SOG)

To figure out how important each shots (no, not that kind) are to winning a game, I compared shot differential (CHI SOG ‒ OPP SOG) against goal differential (CHI goals ‒ OPP goals).  This is our yardstick -- the more the 'Hawks outscore their opponent, the better they've done.

To get a relationship between the two, I ran a regression to get an equation (by fitting the red line to the data) and an R-squared value to determine how tight that relationship was:

(For all you young stats geeks out there:  Linear regression is good for continuous sets of values.  Since you can't win or lose by half a goal, what you get from the equation might not make sense.  I won't get into the details here, but the shading you see under the graph tells you the probability getting that goal differential given the corresponding shot differential.  If you really want to know how this is done, click here.)

The R-squared value to tells us how well the shot differential explains the goal differential; since it's practically zero, I can say that, for the 'Hawks at least, outshooting the opponent doesn't have much to do with scoring more.

There are some hockey explanations for this.  While protecting a lead, a teams may be more focused on protecting the puck than taking shots.  Or when behind, they'll be trying to put as many shots on goal as possible (which may not go in).  But, this is a stats post.  Y'all can discuss in the comments section.  Let's do more stats!

What Wins Hockey Games?

Okay, so if running up the shot total isn't the key to winning, what is?  Well, this is a question that's been asked before, believe it or not.  Our frenemies over at On The Forecheck had did a nice post way back in 2006 about it, and concluded that teams that have a lot of takeaways also win a lot.

Good, because the NHL event summary data includes that, along with the usual stuff like blocked shots, hits, and face-off percentage.  It also had interesting stats like shift lengths, which, after reading this article on Behind the Net, got me thinking.

One stat you can use to compare numbers is correlation, like the OtF guy (Dirk) did.  So, I just ran all of these stats together to get a correlation matrix:

(I've actually already calculated the correlation between SOG differential and goal differential -- it's R, so it's the square root of R-squared in the graph above.)

To interpret the table:

• Positive correlation describes how well two numbers move together.
• Negative correlation describes how well two numbers move in opposite directions.
• Zero correlation means the two numbers' movements don't affect each other.
• The last row contains correlations between Goal Differential and everything else.

I also used a couple of non-standard stats:

• Shots Directed Towards Net (SDN) Differential is similar to SOG except that it includes blocked and missed shots; it's like a Corsi rating for the whole team.
• On-Net % Differential is the difference between the percentage of shots that are on net for each team.
  

As we have already seen, SOG differential has little correlation with goal differential.  But we can get some interesting observations here:

• As you'd expect, the two types of shot differential are closely correlated.
• Likewise, more shots tend to lead to lower shooting percentages.
• One interesting relationship is that more SDN tends to happen with fewer PIM; but it would make sense you would be able to shoot more if you're taking fewer penalties.
• The negative correlation between SDN differential and goal differential, then, is interesting -- shooting more (not necessarily on net) looks like a bad thing.  Perhaps it's a sign of 3rd period desperation when trailing?
• Longer shift lengths don't lead to more goals -- but, as BTN pointed out, they do lead to more (but less accurate) shots.  Our players aren't immune to getting tired.
  
• Stats highly correlated with goal differential are indicators of success, so we ought to spend our time looking at those.

To get a clearer picture, I re-ran my regressions on two of the stats most correlated with goal differential: Takeaways ‒ Giveaways and On-Net % Differential.  I excluded shooting percentage because 1) it's pretty obvious and 2) it's calculated using goals scored, which means that in stats geek world at least, it's cheating.

Takeaways and Giveaways (TK & GV)

It's not the best relationship, but for every extra takeaway over the number of giveaways, the 'Hawks tend to score 0.143 more goals than their opponent:

It might be more informative to compare against this stat for other teams in the league, but it does demonstrate the importance of puck possession.  And I agree with Dirk's conclusion (on OtF) that these are important stats.  So, hanging onto the puck is better than shooting haphazardly... which brings us to our next stat.

On-Net Percentage (On-Net%)

One criticism of the 'Hawks in the games where they've out-shot the opponent but lost, has been that they were making low quality shots.  If you think of blocked and missed shots as an indication of how badly they're shooting, this stat makes sense -- and at 40% correlation, it seems to be one of the best indicators of success:

If you remember the SDN (shots directed toward net) discussion above, high SDN differential tends to result when a team is pressing while behind -- ending up with high quantity but low quality chances.  In such situations it will have a low On-Net% differential, which, is not good.

Before you jump to conclusions -- just because this statistic is correlated with goal differential doesn't mean the 'Hawks should just work on shot accuracy in all their practices from now on.  If the relationship comes from teams playing aggressively when behind, it's basically just showing that they aren't coming from behind to win.

Conclusions

A quick note before I finish this drivel with a mindless laundry list -- even if you didn't read the "for experts geeks" italicized text, you might've noticed that the shaded strip along the +3 goal differential is darker than the stuff around it.

This is because, for no reason whatsoever, the 'Hawks have won an abnormally large number of games by 3 goals:

This is probably just a fluke, but maybe somebody has an idea how this could've happened.  But anyway, to end the misery (look at Toews!) you must be going through by reading this (do you really have nothing better to do with your life?), here are some overall observations:

• Protecting the puck and shooting the puck accurately are keys to success.
• Running up SOG isn't.
• Shorter shift lengths help in these areas, but not really overall.
  
• These numbers all compare the 'Hawks against their opponents; it would be interesting to see these for other teams (and also way too much work).
• Also way too much work, but a legitimate discussion point is how these numbers would break down if we split them (home/away, Huet/Niemi, East/West, etc.).
  
• None of the statistical relationships are all that strong (don't get me wrong, 40% is a pretty strong correlation for something like this, but it still only explains 16% of what's going on).  There are a lot of intangibles that go into how a game will turn out.
• In the end, I spent way too much time doing this, only to come up with some vague conclusions about what works.  Clearly, while they can be descriptive, statistics are a waste of time for talking hockey.  But I'm going to keep doing it anyway.

Thanks for reading.  Since I'm all out of cookies, and since you were such a trouper for making it through all this, have a puck instead:

(courtesy of Luscious Layers Bakery... ooooh, I want one too!)

Feel free to ask lots of questions (so I can edit this and make it clearer/simpler) or talk about this stuff.  There's a lot I didn't cover or described poorly, and somebody with more hockey IQ can probably add a lot more insight.

(I was hoping to finish this before the playoffs started, or at least on an off-day, but hope you enjoyed this as a welcome distraction from whatever... or as a form of self-torture.  Oh, and apologies to gmh for blowing off the whole collaboration idea on this one... we'll do one next time!)