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10-27-2012, 02:26 PM
Iain Fyffe
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Originally Posted by Dalton View Post
I can't prove anything to someone who has made up their mind. Read the study. NHL goal scoring data and penalties were used to prove the author's thesis. They proved it. Prove them wrong. You are just ignoring everything I say anyway.
The irony is just dripping off of this paragraph.

The authors' thesis was that NHL production takes on a power-law curve, which is absolutely true, and is demonstrated in the graph I posted.

But you have moved your thesis beyond this, claiming that adjusted scoring assumes a normal distribution, and is therefore flawed. My graph shows that both actual raw scoring and adjusted scoring both take the shape of a power-law curve.

Therefore, your claims that adjusted scoring is flawed because it assumes a normal distribution are defeated. You have failed to demonstrate that adjusted scoring assumes a bell curve. If you can't demonstrate that (which you can't, because it doesn't) then your assertion is invalid, and you'd be well-served to stop making it.

Originally Posted by Dalton View Post
Your bumpy curve does not conform to the power curve of the raw data.
What's wrong with it being bumpy? The raw data is bumpy. These are not fitted lines.

Originally Posted by Dalton View Post
It is not a simple translation of the raw data.
Yes it bloody well is. Every player's goal-scoring total is multiplied by a coefficient within a very narrow range of coefficients. That's all there is to it, nothing more.

Prove me wrong.

Originally Posted by Dalton View Post
It is a different curve. The end points don't even conform.
Why would they conform? The adjusted stats are, on the whole, slightly higher than the raw stats due to the relatively low scoring environment that season. That's the whole point of the adjustment.

Originally Posted by Dalton View Post
Stop arguing with me and try out the methods the author suggested. I'm just a messenger.
I'm not arguing with their point, which is that NHL production follows a power-law curve. This is demonstrably true and uncontroversial.

I'm arguing with your point, which is that adjusted scoring is flawed because it does not follow a power-law curve. It does follow such a curve, and therefore your objection is invalid.

Originally Posted by Dalton View Post
I have answered these questions.

This is normalization:

"Adjusted Statistics

In order to account for different schedule lengths, roster sizes, and scoring environments, some statistics have been adjusted. All statistics have been adjusted to an 82-game schedule with a maximum roster size of 18 skaters and league averages of 6 goals per game and 1.67 assists per goal."

A bell curve. Everyone's stats are adjusted to suit a 60% average so to speak.
No, no, no. You really don't get what normalization means. If the data were normalized, the big bottom tail (the very low scorers) would be pulled away from zero torward the mean. It isn't. Even if you're looking at all players from all time, all you'll see is the curve shifting a bit to the left or to the right. The bottom tail will stay right where it is, maintaining the shape of a power-law curve.

Originally Posted by Dalton View Post
You apply this to a power curve and get a blip in the middle of the data where players results are increased at a greater rate then those on either side of the median.
The blip exists in the raw data, and that's the only reason it exists in the adjusted data. Why aren't you jumping on the raw data for being flawed, because you see a bell curve in it when it should be a power-law curve (which it is).

Originally Posted by barneyg View Post
Why the hell do you think the bolded creates a bell curve? Please explain. You keep arguing two points at once. One of those is completely wrong, the other is likely right:

a) the adjustment leads to a bell curve (completely wrong)
b) the adjustment shouldn't be uniform (likely right).
Precisely. The first is flatly wrong, the second is likely right, and indeed HR's adjusted scoring doesn't quite use a uniform adjustment. The individual player's numbers are removed from the equation when doing the adjustment, meaning (for example) that a high-scoring player is adjusted downward less than other players are in a high-scoring-environment season. This seems to be what Dalton is arguing for in general, so his objections to adjusted scoring are baffling.

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