Thursday, November 07, 2013

Corsi, shot quality, and the Toronto Maple Leafs, part IV

My argument, the last three posts, is that shooting percentage and number of shots taken are negatively related, so when the 2012-13 Leafs have a low Corsi, but a high shooting percentage, that might be an indication of evidence that they took higher quality shots.

Many hockey analysts think that's not true.  One of the reasons they give is that shooting percentage seems to be completely random.  This year's shooting percentage is no indication of what the team's shooting percentage will be next year.  If shooting percentage isn't a skill, how can it mean anything?

I tried to explain, in my first post, how SH% can be important even if it's random.  That was the analogy with the foreign currency.  Let me try a different story that might make things clearer.  

(To be clear, this story is NOT new evidence ... it's just another way of explaining my argument.  It still requires the assumption that SH% and Corsi are negatively correlated. The evidence for that, from the data, was in the previous post.)


Suppose, in a certain country, everyone pays a different rate of income tax.  And the percentage is random.  Every year, each employee goes into a government office, spins a big wheel, and where it lands, that's his tax rate. 

Some people claim that certain employees are so good at spinning that they're able to regularly get themselves a low tax rate.  Researchers test this theory.  They compile census data, and they run regressions, and they conclude that it's not true -- your tax rate this year is not predictive of your tax rate next year.  "Spinning a low percentage doesn't appear to be a skill," they conclude.  "It's just random."

But after-tax income ... that's a different story.  The researchers find that when you take home a lot of money this year, you take home a lot of money next year.  The correlation is quite high.  It's not perfect, of course, because you might get promoted, or lose your job.  And, more importantly, there's randomness.  You might spin a low tax rate this year, and a high tax rate next year, just by luck.  

One year, Carlton Leaf takes home only $43,800 after taxes. That's way below the average for employees in his league.  In fact, 28 out of 29 comparable co-workers took home more money than he did.

The researchers say, "Look, Leaf didn't bring home a lot of money this year ... and the correlation predicts that he won't take home a lot of money next year, either.  Obviously, Leaf isn't very good at what he does."

Leaf's wife doesn't like that. "Wait a second!" she says.  "If you notice, my beloved Carlton's tax rate was especially high this year, much higher than normal, and that's why he brought home less money.  So he's a better employee than you'd otherwise think.  You need to take the tax rate into account!  I think he's going to be employee of the year soon, but ... at least, you have to admit that even if he's not a superstar, he's at least better than the $43,800 makes him look."

The statisticians reply, "The problem is, that tax rate is random.  It doesn't predict anything.  It might be hard to accept because you're a Leaf fan, but, unfortunately, that's how it is.  The low $43,800 is meaningful.  The high 10.8 percent tax rate is not.  You can't use tax rate to measure Leaf's true ability to bring home income, because, after all, you can't give credit for something that's just luck."


Um, that may sound a bit too sarcastic, which is not what I intended.  I'm caricaturing the argument, in order to make the point clearer.  I'm trying to explain better why, even if SH% is random, you might have to still take it into account when you evaluate Corsi.  

The argument boils down to: you have to take SH% into account when evaluating Corsi for the same reason you have to take tax rate into account when evaluating take-home income.


OK, here's an even better analogy that I thought of later. Instead of SH%, consider injury days lost.  It's likely injuries are pretty much random -- if you have lots of injuries this year, you'll probably revert back to the normal amount next year.  

But: if a team has a low Corsi, but high injuries, the high injury rate DOES affect your estimate for next year.  "Injuries are random so we shouldn't consider them in evaluating the team's talent" doesn't fly.


As I said, I'm not trying to be snarky.  The hockey sabermetricians who disagree with me don't dispute my main argument.  They just disagree that there's a real negative correlation between SH% and Corsi.  They know much more about hockey than I do, so there's a good chance that they may be right.

If so, my argument falls apart.

(There are seven parts. Part III was previousThis is Part IV.  Part V is next.)

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At Friday, November 08, 2013 11:51:00 AM, Anonymous Alex said...

That's a good analogy. But I think it needs to end with Leaf's wife saying "well, I guess we'll see what his income looks like next year!" because there's a good chance his random tax will be lower and so his income will 'look' higher. The researchers should expect his income to stay low. And I assume someone knows how this turns out for the NHL, but that person isn't me.


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