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Originally Posted by shadowlord
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Thanks for sharing.
The one thing that the article briefly alludes to is the effect that one player has on his teammates. Some statistics can infer these impacts, but again, event rates are so low for relevant situations.
I am not a huge fan of using counting stats or even Corsi to evaluate 5-6 games. I know that in the media, if you don't publish a story, the other guy will, so nobody is waiting around for enough data to demonstrate statistically rigorous results.
Just to demonstrate: Last year, Calgary had a total of 5005 even-strength shot events (2606 for, 2399 against). Overall, that's good for a 5-vs-5 Corsi of 52.1. Let's say Bill Peters wants to increase that Corsi by 5% (a HUGE Corsi increase) to 57.1. When will we be confident (mathematically speaking) that the Flames have increased their Corsi by 5%?
Well, that's a one sample test of proportions. It will need to be two-sided (Calgary could have plausibly also decreased Corsi by 5%). Let's assume that the 'power' of the test will be the commonly accepted 80% (meaning 20% chance that we will make a false negative conclusion; in other words, 20% chance that we did not observe an underlying 5% Corsi increase when there is indeed one). And let's say that the statistical significance ('alpha') will be set at the common threshold of 0.05 (which is only a 5% chance of a false positive conclusion; in other words, 5% of the time we did observe an underlying 5% Corsi increase when there actually was not an underlying improvement).
With those parameters, and a similar total shot rate / game as last year, we need to wait 12 games until we see a huge 5-vs-5 Corsi change of 5%!!! Interestingly, 2% is the SMALLEST Corsi change that we can reliably observe over an entire 82 game season, for an entire team.
Player events are (obviously) less frequent than total team events. Dougie had a very high event rate (even strength Corsi for/against) which is mostly driven by his high TOI. His total events over 82 games last season was 3147 shots (both for and against, while on ice, at even strength). The SMALLEST Corsi change that we can observe for him over 82 games, if event rates (shots / game) stay constant for him, is 2.5%.
Now let's apply this issue to the current article. Over 7 games, the SMALLEST even strength Corsi change that we could see for Dougie would be 7.7%. That is a HUGE Corsi change, and ignores all the other factors involved.
Looking at that explanation above, you are probably thinking 'well, lots of things change during that many games'. You're right; people get injured, momentum swings, coaches change approach. There are score effects too. We are not measuring a steady state, and this may not be an appropriate place to apply the 'normal distribution'. These issues exist in all sports, but to a lesser extent in some, such as baseball. But every time we account for these factors, we either need to A) stratify analysis and lose numbers (power), or B) create a regression model. Both introduce issues with interpretation, though I am sure that the professional stats guys who are hired by these teams qualify all of their analysis with logistic regression.
TL;DR:
Even though Corsi event rates are much more frequent than traditional stats (eg: goals, +/-, etc), it is dangerous to come to conclusions unless you have a solid understanding of statistics. Furthermore, we can't always apply basic statistical assumptions. That most often means that we need more data points.
Decisions in hockey need to be made faster than currently available statistics can become available. While the great 'Corsi' of an established player like Backlund can be stated with some certainty, the changes that occur during seasons or even between seasons cannot be robustly portrayed when there are only around 60 shots total per game.
This is why people with a good 'eye test' are still employed in this sport. And this is coming from somebody who works with statistics daily.