## A few of the reasons why Corsi regresses

In an ideal world, we would have a perfect metric that has near perfect repeatability and near perfect predictive power for future success. However, we don't live in a perfect world, and so for now, we are stuck with measures like Corsi and Fenwick that have better repeatability than most measures and predict future success pretty well (see below chart).

Anyways, even though Corsi and Fenwick are good measures, they aren't perfect. For example, when looking at the correlation for forwards who played in either both the 2007-2008/ 2008-2009 seasons or 2010-2011/ 2011-2012 seasons, Corsi Rel from one season to the next regresses about 39% towards the mean and Corsi regresses about 40% towards the mean for forwards (200+ EV minutes or more) (n = 702).

So what causes Corsi to regress. Why isn't it a perfect measure?

Well, we don't need data to come to a few hypotheses. A few ideas that come to mind are:

1) Players face different levels of competition year to year

2) Players are deployed differently by their coaches year to year

3) Players play with different teammates year to year

4) Players battle through injuries or rough stretches of play more in certain years than others

There are others certainly. Let's examine a few of these ideas and see why Corsi regresses.

So let's look at competition, deployment, and teammates.

It's intuitive that players won't face the exact same competition year after year. One good measure of competition is Rel Corsi QoC (Relative Corsi quality of competition).

For deployment, our best measure is Zone start%, which is basically the ratio of offensive zone starts to defensive zone starts.

For strength of teammates, we will use Behindthenet.ca 's Rel Corsi QoT.

So using the data from two pairs of seasons (2007-2008 and 2008-2009) (2010-2011, 2011-2012), we can repeat our correlation analysis and see how Rel Corsi QoC, Rel Corsi QoT, and zone start% changes from year to year.

 Rel Corsi QoC Zone start % Rel Corsi QoT r value 0.451165158 0.539110378 0.580473944

The r-value is the correlation coefficient. As you can see, for all three statistics there is quite a bit of change from one year to the next.

We know that the competition a player faces, his zone start percentage, and the teammates he plays with all affect his performance, as measured by Corsi in this post.

So if those three above contextual stats change from year to year, it makes sense that we should see changes in Corsi as well. In fact, we can make the argument that the year to year correlation for Corsi would be stronger if not the changing circumstances that a player faces.

This item was written by a member of this community and is not necessarily endorsed by <em>Broad Street Hockey</em>.

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