Is Corsi really as predictive as we think?

A Maple Leafs goalie always needs to be ready for an opposing shot. - Claus Andersen

Let's look at the link between shot differential and shooting percentage.

Most analysts rely heavily on shot differential, or Corsi, to make predictions for teams. When they do that, they're largely ignoring shooting percentages -- a decision they make based on evidence that shooting percentages have a lot of random variance, and that shot differential is actually a better predictor than the number of goals scored or wins compiled.

But Phil Birnbaum had an interesting post Tuesday challenging that idea, proposing that shooting a lot might be correlated with taking lower-quality shots.

He pointed to some pretty well-established score effects, or changes teams make depending on the score of a game, wherein teams adopt a defensive shell with a lead, taking fewer shots but for a higher percentage. He additionally noted that on some plays a player might pass on a low-percentage shot for the chance at a higher-percentage one, and wondered if there weren't strategies and/or random fluctuations that could result in both a low shot total and a high shooting percentage.

All of which is mostly conjecture that's been made before. The key piece of supporting evidence he provides is this:

I looked again at the last six years of the NHL, 180 team-seasons. The correlation between shooting percentage and Corsi was -0.22. When I took only the 36 most extreme shooting percentages, the correlation was -0.37.

In other words, he's saying that over the last six years, teams with a bad shot differential also had a modest tendency to have a good shooting percentage.

If true, that would mean that teams with bad shot differentials do a little bit better than you'd expect. It wouldn't change our observation that shot differential is a strong predictor of future results, but it would make it a little easier to believe that system might play a role worth considering.

Score effects

But there's a catch. Phil's study didn't account for the score, and as he noted, the score influences shooting percentages.

That means it's possible that Phil's link between shot total and shooting percentage derives entirely from score effects. It's possible that the causal chain is as follows:

Correl_medium

In that case, there would be no causal link between the poor shot differential and high shooting percentage, so we need to account for the score if we want to make claims about players choosing to pass rather than shoot.

The easiest way to do that is to focus on situations where the score is tied. If there really is an underlying link between shot totals and shooting percentages, we should see it in the score-tied data. So let's take a look:

Corsi_vs_sh_percent_medium

The link here is much weaker than what Phil saw -- weak enough that there's better than a one-in-four chance of seeing a link that strong just by random chance in a data set this size. That's bad news for proponents of system effects.

The defensive shell

So if there isn't much correlation during the score-tied minutes, where do we see it?

Situation Correlation between shot differential and shooting percentage
Trail -0.06 (could easily be random)
Tied -0.08 (could easily be random)
Lead -0.19 (significant)
Overall -0.22 (significant)
Overall, score-adjusted -0.16 (significant)

The correlation is negative in each case, but in trailing and tied situations it is so small that we might as well call it zero -- it explains less than 1 percent of the differences between teams, and could easily just be random chance (for example, we see a stronger correlation between the number of letters in a player's last name and his height).

When teams trail or are tied, they all play essentially the same way. What difference exists is almost entirely in how teams play with a lead; it appears that some play more conservatively than others, which I find very interesting.

People have often wondered about the value of playing a defensive shell (here's a recent example) but the question is difficult to answer since the trailing team's strategy changes too. The observation here gives us the ability to compare the performance of teams that play most or least defensively with a lead -- since both cases will involve an opponent playing the same desperate style, this will give us a direct window into the value of the defensive shell.

Summary

Phil's point that it's possible for a team to deliberately adopt a low-shot high-percentage strategy in all situations is obviously true. But the only place where there is any real evidence for teams doing that is when they are protecting a lead, and even there the differences aren't terribly large.

So if we're going to make a case for a team doing better than shot differential would suggest, we should focus specifically on their performance with a lead, and expect that impact to be minor.

Of course, it's possible that they've hit on a radical new strategy for tied and trailing situations. But since we've never seen that before, with each subsequent team that has a high shooting percentage in those situations, the safer bet is that they've simply run hot and will slide back to the pack.

Eventually, a team will surprise us, but we'll probably win a lot of bets between now and when that happens.

More from SB Nation NHL:

Chris Pronger "is never going to play again," Flyers confirm

Kaleta suspended 10 games

How to forecast NHL goaltending performance

Here's why the Rangers should (and shouldn't) be worried

X
Log In Sign Up

forgot?
Log In Sign Up

Please choose a new SB Nation username and password

As part of the new SB Nation launch, prior users will need to choose a permanent username, along with a new password.

Your username will be used to login to SB Nation going forward.

I already have a Vox Media account!

Verify Vox Media account

Please login to your Vox Media account. This account will be linked to your previously existing Eater account.

Please choose a new SB Nation username and password

As part of the new SB Nation launch, prior MT authors will need to choose a new username and password.

Your username will be used to login to SB Nation going forward.

Forgot password?

We'll email you a reset link.

If you signed up using a 3rd party account like Facebook or Twitter, please login with it instead.

Forgot password?

Try another email?

Almost done,

By becoming a registered user, you are also agreeing to our Terms and confirming that you have read our Privacy Policy.

Join SBNation.com

You must be a member of SBNation.com to participate.

We have our own Community Guidelines at SBNation.com. You should read them.

Join SBNation.com

You must be a member of SBNation.com to participate.

We have our own Community Guidelines at SBNation.com. You should read them.

Spinner.vc97ec6e

Authenticating

Great!

Choose an available username to complete sign up.

In order to provide our users with a better overall experience, we ask for more information from Facebook when using it to login so that we can learn more about our audience and provide you with the best possible experience. We do not store specific user data and the sharing of it is not required to login with Facebook.