Boo.

http://hockeysimplified.blogspot.com/" onclick="window.open(this.href);return false;

It would be nice if you put some info in the post to inform people what they are going to see if they follow the link, so they can decide if they want to click it.

Thanks.

I most identified with your reference to the relative effects of luck and skill. My most practical application of statistics is in the poker room. In poker, in the short run, luck is a huge factor when evaluating the probability of success, especially on a hand-to-hand basis. In the long run, however, luck has almost no bearing on a player's rate of success because the uncontrollable variance of luck has been balanced.

As in your coin flip scenario, the volume of experiences (games, in the NHL) normalizes the expected outcomes. If you flip a coin 10 times, the likelihood of having it come up heads 50% of the time is relatively low. If you flip it 10,000,000 times it is virtually a certainty that it will be heads 50% of the time.

jist:

The less unexplained variability in a metric, the less the opportunity for regression to the mean.

MissouriMook wrote:I most identified with your reference to the relative effects of luck and skill. My most practical application of statistics is in the poker room. In poker, in the short run, luck is a huge factor when evaluating the probability of success, especially on a hand-to-hand basis. In the long run, however, luck has almost no bearing on a player's rate of success because the uncontrollable variance of luck has been balanced.

As in your coin flip scenario, the volume of experiences (games, in the NHL) normalizes the expected outcomes. If you flip a coin 10 times, the likelihood of having it come up heads 50% of the time is relatively low. If you flip it 10,000,000 times it is virtually a certainty that it will be heads 50% of the time.

Nice post.

It helps to explain why the Nashville Predator's slump starting at about game number 60 was probably not regression to the mean. And, it is always important to make explicit what mean is it that the regression to is expected.

In poker, the outcome of any hand is a combination of skill plus luck.

Over small sample sizes luck may appear to predominate.

But, with a large enough sample size the skill factor will be evident.

The more skill, the higher the R-squared of past performance with current performance.

The outcome of a hockey game is also a combination of skill plus luck (unexplained variability).

So, Nashville goes about 60 games this season, doing very well.

http://hockeysimplified.blogspot.com/20 ... ntral.html" onclick="window.open(this.href);return false;

Then they go flat for about 10 games.

What is our reasonable expectation of their future performance?

If there is no skill involved in winning hockey games then we would expect them to regress to the mean of simply winning by chance.

But, if there is no skill involved in winning hockey games then their performance over the first 60 games is almost impossible. As in the 10,000 coin flip example. Although in this case, 60. I'll spare you the math, but it's highly unlikely.

Well, if their skill hasn't changed (due to injuries, etc.), then our reasonable expectation would be regression to their mean performance for the first 60 games of the season.

As in poker, luck (random chance, unexplained variability) can predominate over a small sample size. But, as the sample size increases the skill factor will become clear. And, the higher the R-squared the faster it will become clear and the clearer it will be.

This sounds like a baseball thread. You guys must be baseball fans. Sabremetrics geeks....all of you.

WebSant wrote:What is our reasonable expectation of their future performance?

If there is no skill involved in winning hockey games then we would expect them to regress to the mean of simply winning by chance.

But, if there is no skill involved in winning hockey games then their performance over the first 60 games is almost impossible. As in the 10,000 coin flip example. Although in this case, 60. I'll spare you the math, but it's highly unlikely.

Well, if their skill hasn't changed (due to injuries, etc.), then our reasonable expectation would be regression to their mean performance for the first 60 games of the season.

I can't speak for everyone, but I think the concept of "regressing to the mean" even when using the phrase incorrectly, refers to their offense more than their defense, and incorporates more than just the games played this season. In your illustration of changes in skill due to injury, I expect them to be better defensively this year because of the health of Rinne. On offense, however, you had mostly the same cast of characters and the all of the new faces (except for Forsberg) were cast-offs. My expectation was that they had not improved enough talent-wise on the offensive side to translate into the increase in their scoring rate (2.63 gpg in 13-14 vs. 2.85 gpg in 14-15) from last year to this year.

Would a regression in their offensive production of 0.22 gpg (back to their scoring rate last year) be enough to cause them to fall in the standings? I don't know. But their defense improved from giving up 2.95 gpg last season to just 2.41 gpg this season despite the return of Rinne being the only major change, so maybe the effect of getting Rinne back was more than those of us who saw their improvement as unsustainable realized.