Thursday, April 7, 2011

Loose Ends - Part III B: The Power Play

This is basically an extension of my previous post, which looked at whether team talent differences in terms of shooting percentage are larger on the powerplay or at even strength.

The purpose of this post is to explore a related issue, that being the relationship between even strength shooting percentage and powerplay shooting percentage. In particular, the extent to which even strength shooting talent and powerplay shooting talent are distinct skills.

In the six seasons from 2003-04 to 2009-10, the average seasonal correlation between the two variables at the team level was 0.296.* While that may seem small, it must be remembered that lucks accounts for a majority of the team to team variation for both metrics. That is to say, each team's single season performance with respect to each metric provides a relatively poor estimate of it's true talent.

As discussed in a previous post, the 'true' correlation between two variables can be approximated so long as three pieces of information are known:

1. The reliability co-efficient of the first variable in respect of a given sample size.
2. The reliability co-efficient of the second variable in respect of the same sample size.
3. The correlation between the two variables observed in respect of the same sample size.

I elected to use 40 games as my sample. In calculating the reliability co-efficients, I determined the correlation between one randomly selected 40 game sample and another 40 game sample, each independent of the other. I then calculated the correlation between those two variables with respect to one of the 40 game samples. Finally, I averaged all three correlations over 1000 simulations and repeated the entire exercise for every season from 2003-04 to 2009-10. Here are the results:

As indicated, the average split-half correlation between even strength and powerplay percentage over the six year sample was 0.167. The average split-half reliability of powerplay shooting percentage was 0.078, and the average split-half reliability of even strength shooting percentage was 0.205.

Having ascertained all three necessary pieces of information, those values can then be inputted into the below formula in order to approximate the true correlation between the two variables.

r xy adjusted = r xy observed/ SQRT( reliability x * reliability y)
r xy adjusted = 0.167 / SQRT ( 0.078 * 0.205)
r xy adjusted = 1.32*
*

This result implies that both powerplay shooting percentage and even strength shooting percentage are actually measuring the same underlying skill.

Is this result surprising? I would argue that it is not. We can reasonably assume that team differences in even strength shooting talent are concentrated at the top half of the roster. In other words, I don't think that the bottom six forwards and bottom pairing defencemen for any given team have materially more shooting talent relative to the lower end players on any other team. As powerplay time tends to be overwhelmingly awarded to players that also receive the most even strength ice time, we should therefore expect a close relationship between even strength and powerplay shooting percentage, once sample size limitations are accounted for. That's precisely what we find.

*even strength goals were removed from the data for all figures referenced in this post.

** Nothing should turn on the fact that the correlation is larger than 1. If the average observed correlation was only slightly smaller, and the average reliability values only slightly larger, the adjusted correlation would very nearly equal 1. For example, if 2009-10 is excluded from the data, the average correlation changes to 0.145, and the two reliability values become 0.122 and 0.21. If these latter values are substituted into the equation, a more reasonable adjusted correlation of 0.91 is obtained.

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1 comment:

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Skills at the end it summarized everything related to even shots and powershots.