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Adjusted stats - how valuable?

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Old
10-31-2012, 03:27 PM
  #126
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Originally Posted by thom View Post
Jean Belliveau was playing in the Quebec senior league and making over 20 thousand a year.The Owners of the habs had to buy the league to get Jean to play for Montreal.Their are dozens of examples of players like jean.The vancouver team in the sixties might have made the playoffs in the nhl they were that good
If this was true, the quality of the NHL's total talent pool in those years was even lower than has been previously thought.

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Originally Posted by Master_Of_Districts View Post
Perhaps not, but it's worth noting that they'd be comparable in terms of percentile rank.

EDIT: For clarity, I'm not suggesting that percentile rank is perfect. The 90th percentile in 1966-67 is more impressive than the 90th percentile in 1967-68. But league size is still a relevant factor when assessing the impressiveness of the nth place scoring finish in one year versus the nth place scoring finish in another.
I believe the changes in total talent, due to population growth and players from US/overseas, is a much, much larger factor towards the top than is changes in opportunity due to expansion.

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10-31-2012, 03:35 PM
  #127
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Originally Posted by Czech Your Math View Post

I believe the changes in total talent, due to population growth and players from US/overseas, is a much, much larger factor towards the top than is changes in opportunity due to expansion.
Sure, I'd agree with that.

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10-31-2012, 03:38 PM
  #128
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Originally Posted by Rhiessan71 View Post
The first and by faaaar the biggest issue, is how they are used far too often by far too many.
This would be an issue with the people using them, not with the stats themselves, wouldn't it?

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Originally Posted by Rhiessan71 View Post
Sorry but how I said they do it is almost EXACTLY how they do do it.
Or, ALMOST exactly. When exactly is attainable.

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Originally Posted by TheDevilMadeMe View Post
Yeah, in a league that is larger than 6 teams, removing the player himself from the average makes so small a difference, it might as well not be there at all.
This is essentially true. Of course adjusted scoring is not only applied in such circumstances.

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Originally Posted by Rhiessan71 View Post
Not to mention that Gretzky is actually getting punished more than anyone else because the more he scores, the lower the average gets when his points are removed.
You've got this exactly backwards. The Nilan/Gretzky thing is a fluke result, likely resulting from the fact that results are rounded off. The higher-scoring a player is, the less he will be adjusted downward as a percentage. That's just how the math works in this case.

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Originally Posted by Rhiessan71 View Post
Please, for the love of god, show me how it helps Gretzky when his points are being multiplied by a lower number than Nilan's are?
Seriously!
It's a fluke. If you understand how the math works, it can't be anything other than a fluke. Dave Semenko is adjusted down to 77.8%, so it's clearly not a result of lower scoring players being adjusted less.

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Originally Posted by Rhiessan71 View Post
The pie %'s will change because you are attempting to pull everything towards the average and you know what, there actually is a term used to describe this phenomenon...it's called NORMALIZATION!
The claim that everything is pulled toward the average is incorrect. Players with zero goals will always have zero adjusted goals, and in a season all players are either adjusted up or all players are adjusted down. That is, some will be pulled toward the mean and some will be pushed away from it. This is not normalization.

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Originally Posted by Czech Your Math View Post
Also, as Iain has pointed out in response to Dalton's incessant use of power distributions and such, normalization has to do with the shape of the distribution. If a process (such as simple adjusted stats) affects all players roughly equally, then it won't change the shape of the distribution, it will only change the individual magnitudes for each player (but they will maintain the same proportional value to one another).
Like he said.

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10-31-2012, 03:42 PM
  #129
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Originally Posted by Dalton View Post
What you're not seeing perhaps is that whether I take players, teams or seasons there are outliers. At any point that one averages the 'bell curve' thinking occurs.
What does this mean?

All functions have averages for a particular set of values. NHL player stats, which follow a power-law curve, have averages but this says nothing about their distribution. How does having an average produce "bell curve thinking" (whatever the hell that means)?

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Originally Posted by Dalton View Post
40 adjusted goals does not have the same value every season. It moves up and down according to the average number of goals scored per season without taking into account where that change comes from.
You mean like 40 actual goals, only somewhat less so?

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Originally Posted by Dalton View Post
A season with poor defence and average offence could be equal to a season with strong offence and average defence. Outliers are denied.
You need to stop taking posting lessons from C1958. You'll have to explain yourself better. What do you mean that "outliers are denied"?

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10-31-2012, 03:46 PM
  #130
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Originally Posted by Czech Your Math View Post
It would seem difficult to assess the value of adjusted stats without first trying to determine what flaws exist and their magnitude (and the reasons for those flaws). This would seem to pertain to whatever other system is being compared to adjusted stats to determine relative value as well. To me, it's all inter-related, but I am confident that in the vast majority of cases adjusted stats are much more accurate than raw stats. Since simple adjusted stats tell us the comparative value of each goal (but possibly not exactly how difficult it was to attain such value, etc.), that makes it much more useful than raw data IMO.



It would be difficult to find any system of attributing value to or comparing players that did not have some significant flaw(s). However, the mere fact that some are discussing potential flaws does not prove that such flaw(s) exist. Also, the mathematical basis of simple adjusted stats is very sound, because it tells us the approximate value of the goals/points based on the league scoring context. Again, that's different than telling us how difficult it was to attain that level of value, given the many changing conditions and factors in the league, but it's a rather important piece of information, much more than raw data usually is.



I (and others, such as Overpass) use % or percentile type tiers that are more fixed in proportion to the number of players in the league. I don't know what purpose using tiers based on arbitrary levels of production serves. E.g., Overpass has done some studies of scoring changes between tiers, and uses 1st liner, 2nd liner, etc. to group forwards into tiers, which sort of corresponds to the 25% tiers I used in my example. I've looked at the 1st N, 2nd N, etc. # of players (where N = # of teams). I've also looked at fixed numbers of players (e.g. #1-6, 7-12, etc.), which is the basis of comparing players to their peers (e.g. 2nd place or avg. of top 10). However, as previously stated, this method has its own (much larger IMO) pitfalls, since A) it has no basis of fixed value in proportion to the league scoring context, B) it is using a very small sample for comparison purposes, and C) it usually ignores the vast changes in the talent towards the top end of the spectrum of players.



The group of players in the NHL is already at the very far left of the spectrum of hockey players as a whole, but I understand your point. However, just because we are most often examining players at the very far left of the NHL spectrum does not automatically mean that adjusted data yields flawed results for those players. Yes, it's very possible that it can, but it's still a vast improvement on raw data, with a foundation in actual value based on quantified measurements. Any further adjustment should be thoroughly justified based on quantified and reasoned evidence as to the reasons and magnitude of distortions that occur from using the simple adjusted process.



Maybe adjusted stats are not as valuable as some claim them to be, due to potential inaccuracies when trying to equate the difficulty of attaining certain levels of adjusted production in different seasons. However, it is again important to remember that they are based on a foundation of value in proportion to the league scoring environment. I would also point out that whatever flaws or distortions simple adjusted data may have, it is likely no greater and probably less than that for most other systems: raw data, comparing players rankings amongst their peers or to a very small subset of their peers, using the results of awards/AS voting, quotes from writers/managers/coaches/players/fans, etc.



First, studying potential causes for distortion in isolation may result in each potential source to appear to have a larger effect than it actually does. Such distortions may often negate each other to a large degree. Second, no matter the size of the alleged "flaw", without knowing the reason for such a flaw, further adjustment may only cause further distortion. I previously gave the example of the influx of overseas players being composed of a disproportionately higher group of scoring forwards/d-men. When measuring scoring, this is like adding a bunch of high quality students to the classroom. It makes it look like it's suddenly substantially easier to get an A, when actually the student population became much higher quality on average (and particularly at the top). If one used a curve to further "adjust" those students' grades downward, it would unfairly penalize their achievements for the sake of making the distribution of grades look more "normal."



I wouldn't say adjusted stats should be taken at absolute face value and are the final answer, but they are still a heck of a lot better than most alternatives (raw data, peer rankings, award voting, etc.). I've actually studied and presented the results of a lot of relevant topics: scoring of a fixed group of high quality players over 60+ seasons... scoring of various % tiers over time... estimating the effective NHL talent pool over time. I also have read studies of others on various relevant topics. Actually, I was one of the first people that I know of to create and use adjusted stats (along with others like HockeyOutsider), long before HR.com existed. So to imply or state that I don't understand or know how to use adjusted stats is going a bit off the deep end, don't ya think?

It's hard for me to explain why adjusted stats are useful even when comparing players across the same range of seasons. Basically, as league scoring goes down, it becomes much more difficult to separate from the pack in raw point (not %) terms. So, if one player is 50% better than avg. and then becomes 20% above avg., and the other player is 20% player above avg. and becomes 50% above avg., changes in the league scoring context will distort that in raw point terms:

Year 1
--------
league avg. 50
player A 75 (50% above)
player B 60 (20% above)

Year 2
---------
league avg. 100
player A 120 (20% above)
player B 150 (50% above)

Each player was once 20% above and once 50% above league avg., yet their totals are: Player A 196, Player B 210. Because Player B was better at a time when the league avg. was much higher, he appears to be significantly better than Player B based on a sum of raw point totals over the same seasons, when that wasn't the case.
Honestly dude...most of this post is a lot of bla bla bla where you don't even answer to the points I made half the time.
Most of it is you skirting around admitting there is a big flaw (and there is a big flaw that you will see if you do the exercise I mentioned earlier) while at the same time saying we need to examine possible solutions.
And it's not whether or not further adjustments could make it worse.

Ok, now all that completely aside.
The single biggest thing I keep taking from your posts is that you keep saying that adjusted stats are a replacement for raw stats, that one should use one or the other but not both.
THEY ARE NOT AND YOU SHOULD NOT EXCLUDE EITHER OF THEM!

This whole thing is about what value to assign Adjusted Stats. They are not a replacement for anything! They are not an alternative! They are just another tool to be used to find a reasonable answer.
It sure as hell isn't about excluding anything.

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Old
10-31-2012, 04:22 PM
  #131
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Originally Posted by Iain Fyffe View Post
You need to stop taking posting lessons from C1958. You'll have to explain yourself better.
It's funny cuz it's true.

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Originally Posted by Rhiessan71 View Post
Honestly dude...most of this post is a lot of bla bla bla where you don't even answer to the points I made half the time.
I addressed your points as appropriately as possible. I don't think you have a valid retort, and so have resorted to accusations of "bla bla bla." It's not like you to give up a fight, but it's probably wise in this case.

I provided analogous, coherent examples, reasoned arguments and simple mathematical formulas in support of my assertions. You have already shown that you don't even understand the math involved in adjusted stats, yet accuse others (specifically me) of not understanding the very process that I was one of the first to create and/or adopt.

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Originally Posted by Rhiessan71 View Post
Most of it is you skirting around admitting there is a big flaw (and there is a big flaw that you will see if you do the exercise I mentioned earlier) while at the same time saying we need to examine possible solutions.
And it's not whether or not further adjustments could make it worse.
Is there a flaw? If you are using adjusted stats to compare the difficulty level of attaining equivalent levels of adjusted production in different seasons, then no, it's not absolutely perfect, so yes there's a flaw... but it's a much, much smaller flaw than there is in using raw data or the compilation of the opinions of a few sportswriters, etc.

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Originally Posted by Rhiessan71 View Post
Ok, now all that completely aside.
The single biggest thing I keep taking from your posts is that you keep saying that adjusted stats are a replacement for raw stats, that one should use one or the other but not both.
THEY ARE NOT AND YOU SHOULD NOT EXCLUDE EITHER OF THEM!

This whole thing is about what value to assign Adjusted Stats. They are not a replacement for anything! They are not an alternative! They are just another tool to be used to find a reasonable answer.
It sure as hell isn't about excluding anything.
It isn't exclusion. The raw data is simply an ingredient to make a much more satisfying end product. I'll bake cookies, but I won't exclude you from consuming a cup of flour, a cup of sugar, a raw egg, etc. You can lash out at those of us using indoor plumbing, and trudge out to the outhouse in two feet of snow. No one's excluding anything, but those of us who understand adjusted stats prefer not to go back to the dark ages, just because others are afraid of the boogey man.

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Old
10-31-2012, 04:36 PM
  #132
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Originally Posted by Czech Your Math View Post
I addressed your points as appropriately as possible. I don't think you have a valid retort, and so have resorted to accusations of "bla bla bla." It's not like you to give up a fight, but it's probably wise in this case.



I provided analogous, coherent examples, reasoned arguments and simple mathematical formulas in support of my assertions. You have already shown that you don't even understand the math involved in adjusted stats, yet accuse others (specifically me) of not understanding the very process that I was one of the first to create and/or adopt.



Is there a flaw? If you are using adjusted stats to compare the difficulty level of attaining equivalent levels of adjusted production in different seasons, then no, it's not absolutely perfect, so yes there's a flaw... but it's a much, much smaller flaw than there is in using raw data or the compilation of the opinions of a few sportswriters, etc.



It isn't exclusion. The raw data is simply an ingredient to make a much more satisfying end product. I'll bake cookies, but I won't exclude you from consuming a cup of flour, a cup of sugar, a raw egg, etc. You can lash out at those of us using indoor plumbing, and trudge out to the outhouse in two feet of snow. No one's excluding anything, but those of us who understand adjusted stats prefer not to go back to the dark ages, just because others are afraid of the boogey man.
As far as giving up the fight, I haven't and I do understand the math.
It does concern me though that you don't understand that a flaw of any sort gets magnified the further you go from the median in any formula giving results based on averages.

But don't you worry, I will soon provide an extensive analysis and breaking down of all of your premises provided throughout this thread.

As far as the issue of exclusion...I even bolded the part of your post where you said exactly that.
It's not about the boogey man and it's not about understanding adjusted stats.
It's about understanding that it's not adjusted stats vs every other way. That is it about adjusted stats + everything else.

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10-31-2012, 04:58 PM
  #133
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Originally Posted by Rhiessan71 View Post
Most of it is you skirting around admitting there is a big flaw (and there is a big flaw that you will see if you do the exercise I mentioned earlier)
I honestly couldn't quite grasp what you wanted me to try to calculate or look at. If you could explain it further/differently, and it's not too time-intensive, then perhaps I could try to do so.

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Originally Posted by Rhiessan71 View Post
As far as giving up the fight, I haven't and I do understand the math.
I was just joking, I know you aren't going to give up.

However, you evidently do not understand the math, or you wouldn't have even needed to attempt calculations about whether Gretzky's points were reduced more than some random player's. You would have known, just by knowing the actual process, that Gretzky would be favored more than any other player by HR.com's process of adjusting stats. No actual calculations would even be necessary, since it's a structural issue in the formula that someone with familiarity and understanding of the process/formual would know just by thinking about it for a moment.

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Originally Posted by Rhiessan71 View Post
It does concern me though that you don't understand that a flaw of any sort gets magnified the further you go from the median in any formula giving results based on averages.
First, I don't necessarily agree that there's a substantial flaw. As far as actual value (proportion of goals/game scored, since goals equate to wins), the formula/process is perfect in principle and in its relative simplicity for achieving the desired results. You, and others, allege that there are flaws when applying it to certain individuals and/or subsets, for the purpose of comparing their adjusted stats in terms of difficulty and/or the likelihood that they would translate equivalently to different seasons. This is a separate issue, although I recognize its important applications. You assume not only that there is a flaw (and it would be difficult for the data not to have any flaw in such an application), but that it is of a substantial magnitude. Also, most of those who propose to correct any such flaw, seem to do so by using a very similar methodology to that which may have created any such flaw in the first place: by using some measurement and applying it equally across the board, regardless of the underlying reason for the change in measurement. As I've stated and shown examples of, this may not improve the results, and could actually distort them.


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Originally Posted by Rhiessan71 View Post
But don't you worry, I will soon provide an extensive analysis and breaking down of all of your premises provided throughout this thread.
Whew, I was really worried that there wouldn't be a long-winded, biased post that would be as much confusing as illuminating, and I might not get sent off on some wild goose chase, or not allowed to explain some relatively simple concept for the third or fourth time. Thanks for allaying any such concerns!

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Originally Posted by Rhiessan71 View Post
As far as the issue of exclusion...I even bolded the part of your post where you said exactly that.
It's not about the boogey man and it's not about understanding adjusted stats.
It's about understanding that it's not adjusted stats vs every other way. That is it about adjusted stats + everything else.
I agree that adjusted stats are far from the only way to assess or evaluate players' production and value, although I do believe they are often the best way, and certainly the fairest, most objective way. When we were talking of exclusion, it was my impression that you meant that when I (and many others) use adjusted stats, we basically exclude raw stats in the process. If so, then yes, I basically exclude the raw ingredient once the superior, finished product is available.


Last edited by Czech Your Math: 10-31-2012 at 05:03 PM.
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Old
10-31-2012, 05:21 PM
  #134
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Originally Posted by Dalton View Post
If the graph is not acurate for whatever then perhaps that should have been the initial response to my complaint about it. I guess its useless in this debate.

You take every NHL season ever and adjust all the stats to 82gp and 6gpg (skaters). What is that? What have you done to the seasons?

I alter every result in a set of test scores so everyone gets 60%. Someone asks to audit the tests. Now I have to go in and alter the mark for each question. What happens to the 0's and 100%'s achieved for individual questions? If the original result was 40% on a particular test, do I just add 50% to each individual question?

I can show you that graph.
---------------------------- 60%
____________________ 40%

It doesn't matter how I shape it, the two graphs would be parallel in some geometry. But now I'm giving value to 0's. I'm creating value where none existed before.

If I use some multiplier so as not alter the 0's and perhaps the 100's then I've completely changed the relationship between the grades on individual questions. My graphed results for a single test would look like two uniquely formed pieces of string with the ends tied together. Perhaps even a circle. There may be some visible correlation since the new curve comes from the values of the first curve but the shape would clearly be distorted.

Both these methods fail to maintain either the integrity or relationship of the grades recieved for each question on each individual test.

Now suppose that to prevent cheating I have more than one test. They have different questions and even different numbers of questions. Some of the questions are not changed however except perhaps the wording.

I need different formulae if I want to keep the 0's. In that case people who got identical results on questions that every test had might now have different results.

If I don't care about 0's then many would have different results on questions that they originally had identical results.

Making all the tests have the same final result only leads to errors on the individual test questions.

Call it whatever you want but making all the seasons exactly equal with respect to gp, gpg, players per team can only lead to errors.

The only reason to even do this is a misplaced notion of bell curving. The belief that there exists an average. The refusal to accept extreme outliers as a possible real outcome. The 'bell curve' is a way of thinking that permeates evaluation and prediction of productivity.

You need to read that study or read it differently. Ignore the data and read what the authors purpose was and how the results support it.

If you are averaging and making all the seasons have the same values, if you are forcing the outliers to conform to average then you are bell curving whether you see the physical thing or not.
Iím sorry, but all I see here is irrelevant drivel.

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Originally Posted by Rhiessan71 View Post
Not to mention that Gretzky is actually getting punished more than anyone else because the more he scores, the lower the average gets when his points are removed.
While Nilan, who is below the average, when his points are removed, the average actually goes up and he benefits from it.

That's hilarious
CYM showed you this is absolutely incorrect.

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Originally Posted by Czech Your Math View Post
As I tried to show previously, Gretzky's points would not be multiplied by a lower number (the calculated league avg. gpg that season), but multiplied by a constant (6.00 gpg is the most frequently used standard) and divided by the lower number (league avg. gpg). Dividing by a lower number yields a higher result, hence why I said that such a calculation would help the higher scoring player, such as Gretzky.
.
This kind of got glossed over by Rhiessan taking this entire post and replying to it as one block instead of addressing this individually. But you are obviously correct.

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Originally Posted by Iain Fyffe View Post
You need to stop taking posting lessons from C1958. You'll have to explain yourself better. What do you mean that "outliers are denied"?

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10-31-2012, 06:01 PM
  #135
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CYM showed you this is absolutely incorrect.

This kind of got glossed over by Rhiessan taking this entire post and replying to it as one block instead of addressing this individually. But you are obviously correct.
I was led to believe that the calculated league avg. gpg was calculated with the exclusion of the player's points or goals that is being adjusted.
In the example of Gretzky from 85/86, his 215 or 52 gaols is excluded from the calculation to figure out the the calculated league avg. gpg.

Is that incorrect?

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10-31-2012, 06:21 PM
  #136
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Originally Posted by Rhiessan71 View Post
I was led to believe that the calculated league avg. gpg was calculated with the exclusion of the player's points or goals that is being adjusted.
In the example of Gretzky from 85/86, his 215 or 52 gaols is excluded from the calculation to figure out the the calculated league avg. gpg.

Is that incorrect?
That's correct, but again, you don't seem to understand the actual formula (the simplified version of which I've already presented in this thread):

Adj. Points = Actual Points * Constant (which is 6.0) / League Avg.

If a player scores 90 points when league avg. is 7.5 gpg, then:

Adj. Points = 90 * 6.0 / 7.5 = 72

If the league avg. is lower, it increases the adjusted points (one can see that if league avg. was 6.0, adj. points would be the same as actual points or 90).

What is mystifying to me (and probably others) is that you are arguing about the subtle nuances and much more complex applications of a process/formula which you don't seem to understand in fundamental principle and in its most basic form.

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10-31-2012, 10:20 PM
  #137
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Quote:
Originally Posted by Rhiessan71 View Post
I was led to believe that the calculated league avg. gpg was calculated with the exclusion of the player's points or goals that is being adjusted.
In the example of Gretzky from 85/86, his 215 or 52 gaols is excluded from the calculation to figure out the the calculated league avg. gpg.

Is that incorrect?
No that's correct. This means that his stats are divided by a smaller number, since more is taken away from the denominator. And understanding of basic arithmetic tells us that dividing by a smaller number produces a higher result. It isn't complicated.

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11-01-2012, 01:38 AM
  #138
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The big problem with adjusted stats as HR does them is as has been noted; the fact that scoring differences are not linear.

In the 80s, depth players increased far more than top players. But top players were far more responsible for a team's success than nowadays.

A great example? The 85-86 Oilers vs. The 85-86 Maple Leafs.

Take off the top four scoring forwards and the top defenseman. Which team has the better roster, skater-wise, at that point? Toronto does. Interesting, isn't it?

Now let's look at last season and perform the same task. The Oilers were 1st overall, so we'll use the Canucks. The Leafs were 19th of 21, which translates to about 27th of 30; that's the Islanders.

Taking away the top four scoring forwards and top scoring defenseman, the remaining roster for each team features the following 20+ point players plus goaltender tandem:

Vancouver
F Chris Higgins
F Jannik Hansen
F David Booth
F Mason Raymond
D Dan Hamhuis
D Kevin Bieksa
D Sami Salo

Islanders
F Kyle Okposo
F Michael Grabner
F Josh Bailey
D Travis Hamonic

That's really not even close. Islanders win by a small margin on forwards... but Vancouver's D and goaltending absolutely decimates New York. If you add in "remove starting goaltender" to the comparison, the '86 Oilers still have Moog and the Canucks still have Schneider. The Isles would be down to Al Montoya. The '86 Leafs would be reduced from Don Edwards to a young Ken Wregget.

Star players had far more of an influence in the 80s than they do now. That's why people talk about "diluted talent pool" and such. It's not diluted; it's overflowing. The percentage of Canadian players has dropped from 95% to 55%, while the number of teams has risen by nine. That means that there are fewer Canadians in the league than there were even though there are more teams.

3rd liners and 3/4 tweeners from the 80s would struggle to make the league now. 4th liners would be career AHLers. And with the shift to skill over brawn, you see more skilled players sticking on lower lines - teams using the DRW model of two-way skill as the number one priority.

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11-01-2012, 01:41 AM
  #139
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Originally Posted by Iain Fyffe View Post
No that's correct. This means that his stats are divided by a smaller number, since more is taken away from the denominator. And understanding of basic arithmetic tells us that dividing by a smaller number produces a higher result. It isn't complicated.
Yes, once I got the time to sit down (damned kids wanting candy every 2 minutes ) and actually ran the numbers, I saw where I was going wrong. I apologize wholeheartedly.

That still doesn't change my point about averaging and the increasing inaccuracy produced the further away from the median you go.

Like I said, I'll go through all of this and respond.
Obviously I don't want to jump the gun again (and look like an idiot again heh) so I'll make sure I have everything in order before posting.
Most likely on the weekend when I will have the proper time needed.

One thing I will mention right now though is about the previously entered stats about ST goals increasing by 5.3%.
A) That 5.3% doesn't make much ground on the actual % of scoring done by top tier players today compared to the 80's.
B) The Top tier players do not account for 100% of ST scoring.

More at a later date.

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11-01-2012, 04:10 AM
  #140
Czech Your Math
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Originally Posted by Rhiessan71 View Post
That still doesn't change my point about averaging and the increasing inaccuracy produced the further away from the median you go.
It's more complex than saying "top % tiers of players scored comparatively more than bottom tiers in the last two decades than in the 80s, so that proves it's easier for top players to score adjusted points when scoring is lower." The top tier also became of comparatively better quality, so such an effect would also have been expected. That's just one factor and possible explanation when comparing those two eras.

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Originally Posted by Rhiessan71 View Post
One thing I will mention right now though is about the previously entered stats about ST goals increasing by 5.3%.
A) That 5.3% doesn't make much ground on the actual % of scoring done by top tier players today compared to the 80's.
B) The Top tier players do not account for 100% of ST scoring.

More at a later date.
Actually, it appears to me that could be a substantial portion of the observed effect. I believe one or both of the factors mentioned could account for most or all of the change in % of points by the different tiers. One of these would require no further adjustment, the other would require whatever adjustment that is made to allow for the fact that players have different ratios of ES/ST goals/points.

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11-01-2012, 07:41 AM
  #141
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Originally Posted by Czech Your Math View Post
It's hard for me to explain why adjusted stats are useful even when comparing players across the same range of seasons. Basically, as league scoring goes down, it becomes much more difficult to separate from the pack in raw point (not %) terms. So, if one player is 50% better than avg. and then becomes 20% above avg., and the other player is 20% player above avg. and becomes 50% above avg., changes in the league scoring context will distort that in raw point terms:

Year 1
--------
league avg. 50
player A 75 (50% above)
player B 60 (20% above)

Year 2
---------
league avg. 100
player A 120 (20% above)
player B 150 (50% above)

Each player was once 20% above and once 50% above league avg., yet their totals are: Player A 196, Player B 210. Because Player B was better at a time when the league avg. was much higher, he appears to be significantly better than Player B based on a sum of raw point totals over the same seasons, when that wasn't the case.
A possible explanation for this is that they don't do what people think they do. It seems to take a lot more work to defend adjusted stats than to critique them. Of course I'm referring to posters that actually make the effort as opposed to those going for the 'you're too stupid to understand' response.

I disagree with your interpretation of the example you gave.

I would think that the players production was precisely equal. Each produced at a rate 50% better than the league average and also 20% better than the league average.

As for their absolute goals scored well the reality is that the player who scores the most will receive more credit for doing that.

They are different standards of measurement with different goals I think.

Scoring 49 goals in 70 games compared to 92 in 80. Obviously 92 goals is the greater achievement but if we want compare the players production compared to their peers in any season we see that 49 in 70 was a little bit better. At worst they are comparable.

I would also remind that this is not a math question. We are talking about evaluating and predicting production. In that sense we could be talking about any measurable human activity as easily as goals or points.

Is 20% of %100,000 in sales 10 years ago better or worse than 20% of $1,000,000 in sales last year? The actual numbers are different but the productivity is identical. If a salesperson achieved exactly 20% every year then predicting would appear pretty straight forward.

We have a study that shows us that outliers play a large role in determining averages. Hockey GS among left wingers were used in the HR study. It's like a fractal. Outliers influence the averages regardless of the sample size. Teams, divisions, seasons all the same. Using averages results in errors of several magnitudes higher than not using them.

In some seasons the sum of production of all the players is an outlier. Averaging seasons would result in errors several magnitudes above not using means or normalization. Averaging seasons is not a loop hole. This is why I proposed comparing production across eras as a means of comparing production. There is no average worker in a sense. There are outliers and then the rest. The rest are always below the average because of the outliers influence on the averages. Summing the production shouldn't change this. The mere fact of using an average to calculate production should lower the outliers performance at the high end and increase everyone elses by definition. The 'average' worker's production is actually below the average production of all workers because of the effect of the outliers on the average. The outliers production is not only above the average but is sometimes way above the average. This difference is unpredictable and can get unpredictably large. Just look at seasons with very few players.

Selanne scored 52 in 97/98
Howe scored 49 in 52/53

I'll post my numbers in case I made an error.

First I need the average goals per game in each season-
52/53=1006/210=4.79
97/98=5624/1230=4.57

Now I multiply the gs of each player by 6 and divide by the gpg in their respective seasons.

Selanne=68
Howe=61

Did I do that correctly?

But comparing their actual productivity as a percentage of the work done or results achieved by all the workers we get dramatically different results.

Howe's production in his season is equivalent to 626 goals among the top 5% in 97/98.
Selanne's production in his season is equivalent to 16 goals among the top 5% in 52/53.

Of course these are not expected results in the real world but it does a much better job of comparing the players real productivity.

I think people started this adjusted thing to actually predict what each player might score in each other's season's as a means of comparing them. Criticism has moved everyone away from this original line of thinking. Unfortunate because I believe it is the source of the debate. Adjusted scoring was meant to predict, It doesn't so supporters are trying to salvage it as something else that they are having trouble explaining instead of moving on.

I think you have to look at another route to achieve prediction. Not math or logic but reasoning. They are different.

Howe outscored his next best producer by a bit more than 50% So in Selanne's season he probably gets about 79 or 80 goals.

Selanne matched his best competitor which suggest he gets 49 too in Howe's season. But OTOH Selanne is just grouped with a bunch of scorers in the 50 goal range. I think it's more likely Selanne gets 30+ goals. Maybe 32.

Howe just spanked his competition but Selanne didn't.

Of course we can down and dirty utilizing available stats such as STs gs to enhance the debate.

Honestly I think this is the best we can do.

I don't believe adjusted stats have any role anymore now that it seems to be accepted by all that they don't do what they were originally intended to do- predict.


Last edited by Dalton: 11-01-2012 at 08:42 AM.
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11-01-2012, 11:08 AM
  #142
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No one's trying to "predict" anything. No one would ever use a player's adjusted stats to predict what they will do in the future, and in the case of comparing it to players past, obviously you can't "predict" what Howe would do in 1998 or what Selanne would do in 1952, as those years are long past. Your entire case against adjusted stats all along has been based on straw men - making this about something it's not. Normalization, bell curves, and now predictions.

They are nothing more than a tool to help evaluate whether one player's production in one season is more, less, or about as impressive/statistically significant as another player's production in another season.

I feel for you; you have wasted a lot of time on this argument.

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11-01-2012, 11:18 AM
  #143
Iain Fyffe
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Originally Posted by Rhiessan71 View Post
That still doesn't change my point about averaging and the increasing inaccuracy produced the further away from the median you go.
That's the claim, yes. Looking forward to the evidence that it's more than simply an assertion.

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Originally Posted by Dalton View Post
It seems to take a lot more work to defend adjusted stats than to critique them.
It does if the criticisms are imagined things that take no effort to come up with (because they are assertions, rather than conclusions based on research, which take effort).

Quote:
Originally Posted by Dalton View Post
Scoring 49 goals in 70 games compared to 92 in 80. Obviously 92 goals is the greater achievement but if we want compare the players production compared to their peers in any season we see that 49 in 70 was a little bit better. At worst they are comparable.
Obviously 92 goals is the greater achievement? Aren't you missing a whole lot of context before being able to make a claim like that?

Quote:
Originally Posted by Dalton View Post
I would also remind that this is not a math question. We are talking about evaluating and predicting production.
...by using math. Evaluating, yes. Predicting, no. See below.

Quote:
Originally Posted by Dalton View Post
We have a study that shows us that outliers play a large role in determining averages. Hockey GS among left wingers were used in the HR study. It's like a fractal. Outliers influence the averages regardless of the sample size. Teams, divisions, seasons all the same. Using averages results in errors of several magnitudes higher than not using them.
Are you referring to the study you linked to? It doesn't say you shouldn't use averages. It says that outliers should not automatically be disregarded when calculating the average, and that human performance should not be assumed to be a normal distribution. Adjusted scoring does neither of these things.

Quote:
Originally Posted by Dalton View Post
In some seasons the sum of production of all the players is an outlier.
You don't know what outlier means, if you make this claim. We discussed this earlier in the thread. There is no strict mathematical definition of what value would constitute an outlier in a particular case, but if a study suggests an entire season's worth of data is an outlier, then said study should rightly be criticized for that.

Quote:
Originally Posted by Dalton View Post
The mere fact of using an average to calculate production should lower the outliers performance at the high end and increase everyone elses by definition.
And yet, it doesn't. So perhaps you're not as clear on what's happening as you think you are?

In a season with 5 GPG against an arbitrary base of 6 GPG, everyone's production will be increased (everyone with more than 0 goals, that is). Those below the season average are pulled toward the average, while everyone above the average is pushed away from it.

Quote:
Originally Posted by Dalton View Post
The 'average' worker's production is actually below the average production of all workers because of the effect of the outliers on the average.
This has nothing to do with outliers, it has to do with the shape of the curve. As I've said, in a power-law curve the "zero" results are not outliers; only very high results could be considered outliers (and they're not necessarily outliers), and due to the small number of such results they have a very small effect on the calculation of the average.

If I'm reading you correctly, you're saying the mode is less than the mean in a power-law curve? That's true, but obviously not a problem since we should be using a power-law curve, yes? It's something that shows up in the raw data as well.

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Originally Posted by Dalton View Post
Did I do that correctly?
It's a bit late to be asking if you understand the very basic concept of adjusted scoring, isn't it? If you're not sure, perhaps you should study it some more before trying to discuss the finer points.

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Originally Posted by Dalton View Post
I think people started this adjusted thing to actually predict what each player might score in each other's season's as a means of comparing them.
That's not a prediction. A prediction would be using the adjusted scoring number to guess what the player might do in a season that hasn't happened yet. Adjusted scoring is not intended to make predictions any more raw scoring is.

Adjusted scoring is a means of more fairly comparing two players' seasons when they were different scoring levels etc. No more than that.

Quote:
Originally Posted by Dalton View Post
Criticism has moved everyone away from this original line of thinking. Unfortunate because I believe it is the source of the debate. Adjusted scoring was meant to predict
Prove it, then. Adjusted scoring was first done, I believe, in Total Hockey. This is, of course, a historical encyclopaedia of the NHL. It seems pretty clear to me that the system was developed to allow a player from 1929-30 to be more fairly compared with one from 1989-90. In fact, we don't actually have to guess why they did it, because they tell us why they did it:

Quote:
Originally Posted by Total Hockey (2nd Ed), p. 613
In preparing Total Hockey we set out to create a reliable method of comparing players from disparate eras.
Emphasis added. A method for comparison, not prediction.

Quote:
Originally Posted by Dalton View Post
I don't believe adjusted stats have any role anymore now that it seems to be accepted by all that they don't do what they were originally intended to do- predict.
What are you saying now? That some people don't understand what they're intended to do, so now "all" have "accepted" that they're useless? You're digging yourself deeper here. This statement is flatly false.

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11-01-2012, 01:57 PM
  #144
Czech Your Math
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Quote:
Originally Posted by Dalton View Post
A possible explanation for this is that they don't do what people think they do. It seems to take a lot more work to defend adjusted stats than to critique them.
It's generally easier to destroy than create.

Many claim any perceived flaw means that adjusted stats are incompletely invalidated. They claim one of Mona Lisa's hairs is out of place, and that proves to them that the painting should be burned and we should go back to looking at stick figures. One of the stripes on the airplane looks crooked, so it's back to horses and buggies.

Quote:
Originally Posted by Dalton View Post
Of course I'm referring to posters that actually make the effort as opposed to those going for the 'you're too stupid to understand' response.
I, and others, have certainly made the effort to explain the foundation (value proportional to scoring context) and methodology (formulas) for adjusted stats. Specifically, while I prefaced my explanation of comparing players across the same range of seasons with the cautionary "this is difficult to explain" (and even more difficult to grasp if you do not fully understand the foundation and reasoning for adjusted stats), I still did my best to explain it by use of a simplified example.

Quote:
Originally Posted by Dalton View Post
I disagree with your interpretation of the example you gave.

I would think that the players production was precisely equal. Each produced at a rate 50% better than the league average and also 20% better than the league average.

As for their absolute goals scored well the reality is that the player who scores the most will receive more credit for doing that.

They are different standards of measurement with different goals I think.
I agree with your bolded statement. One would expect the two players to have roughly equal production over the combined two seasons, yet they wouldn't. The reason is that the scoring context changed substantially.

The player who scored more absolute goals will get more credit by people who don't understand that his goals didn't have more value than the other player's goals. Raw data's goal is to record the data as directly and simply as possible. There is no other goal or refinement present in the raw data.

---------------------

There are various problems with comparing a player's production to a vary small subset of his peers (say the top 10 finishers or similar group):

- as has been pointed out ITT, comparative scoring between tiers can change and the reasons for that change should determine whether/how to further adjust for that fact (e.g., the top 10 players' adjusted scoring may increase simply due to being of comparative higher quality than before)

- the data for a very small subset is much more likely to vary substantially due to random factors, or for reasons that are more difficult to assess and properly adjust for

- the link between the adjusted data and value is broken

Simple adjusted data is built on the premise that goals win games, and that the value of a player's goal/point production is fixed in proportion to the average gpg in the season in which he was playing. Any deviation that does not explicitly and directly factor in the scoring context will distort the direct link to value which has been established. IMO simple adjusted stats should not be excluded in the quest for "new & improved" adjusted stats.

There are so many factors to consider for "new & improved" adjusted stats, that I'm not sure if/when there will be substantial agreement as to the proper method to obtain such. There was a thread in HoH about "Why would Gretzky still dominate today?" Well over 500 posts by many of the more knowledgeable posters and wide range of opinions on just how dominant Gretzky would be in today's NHL. That's just one player hypothetically placed in one different era. What about every player in any era? Coming to some sort of consensus on that will be incredibly difficult, but that doesn't mean it isn't worth attempting.

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11-01-2012, 02:55 PM
  #145
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Quote:
Originally Posted by Dalton View Post
This difference is unpredictable and can get unpredictably large. Just look at seasons with very few players.

Selanne scored 52 in 97/98
Howe scored 49 in 52/53

I'll post my numbers in case I made an error.

First I need the average goals per game in each season-
52/53=1006/210=4.79
97/98=5624/1230=4.57

Now I multiply the gs of each player by 6 and divide by the gpg in their respective seasons.

Selanne=68
Howe=61

Did I do that correctly?
The numbers for 1997-98 are wrong - the average goals per game should be 5.28.

So Selanne would have about 59 adjusted goals.

Not it makes a huge difference.

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11-01-2012, 04:44 PM
  #146
Hardyvan123
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Originally Posted by Rhiessan71 View Post
Half right.
When comparing middle tier players across era's they are more valuable than raw stats.
When comparing top tier players across era's they most certainly are not more valuable than raw stats.
That does not mean that raw stats don't still hold some value in the first example nor does that mean that adjusted stats don't still hold some value in the second example though.

Comparing players from different eras is not about ONLY using one or the other. You use both as well as anything else you can get your hands on.
Sure but what do raw stats of say the top goal scorers in 80 compared to 09 tell us?

Not very much. that's why the use of adjusted stats is way more meaningful to compare those 2 groups of players.

Your hangup on adjusted stats has more to do with your arguments about Wayne that it does with logic or even math.

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11-01-2012, 04:56 PM
  #147
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Jean Belliveau was playing in the Quebec senior league and making over 20 thousand a year.The Owners of the habs had to buy the league to get Jean to play for Montreal.Their are dozens of examples of players like jean.The vancouver team in the sixties might have made the playoffs in the nhl they were that good
Dozens who could play and NHL game or two or heck even partial seasons?

Or dozens that could excel like Jean did?

More likely the former.

Also what Vancouver team are you talking about?

The one that was so so to average in the WHL in the 60's?

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11-01-2012, 07:14 PM
  #148
Rhiessan71
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Originally Posted by Hardyvan123 View Post
Sure but what do raw stats of say the top goal scorers in 80 compared to 09 tell us?

Not very much. that's why the use of adjusted stats is way more meaningful to compare those 2 groups of players.

Your hangup on adjusted stats has more to do with your arguments about Wayne that it does with logic or even math.
No, my hangup with Adjusted Stats has always been how they are used far to often as the ONLY form of comparison with the exclusion of everything else between players of different era's.
If AS is going to be used that exclusively with that much weight, it better be extremely god damned accurate!

And because this actually seems right to you....

Raw Career PpG: Bourque-.98 Lidstrom-.73
ADJ Career PpG: Bourque-.88 Lidstrom-.76
Raw 10year(92-01) in the league together: Bourque-.86 Lidstrom-.73
Adj 10year(92-01) in the league together: Bourque-1.00 Lidstrom-.66
Raw remaining years: (80-91)Bourque-1.07 (02-12)Lidstrom-.73
ADJ remaining years: (80-91)Bourque-.78 (02-12)Lidstrom-.78

So despite Bourque through 79/80-90/91 leading his team in scoring multiple times, despite having a top 10 along with multiple top 20 league scoring finishes, despite what your actual eyes tell you, despite Bourque doing this with a hell of a lot less offensive support than Lidstrom and despite Bourque being clearly better offensively in all other data...that an 01/02-11/12 Lidstrom that includes 3 of the 4 worst offensive years of his entire career was exactly equal to 79/80-90/91 Bourque offensively?

Nothing wrong there

Sorry but somewhere along the line, Adjusted stats is breaking down and breaking down bigtime.

On a scale of 1-10(10 of course being the most value), what value would say AS's has when comparing Bourque's first 12 years with Lidstrom's last 10?
For me, it's about 2, maybe 3 at the most.


Last edited by Rhiessan71: 11-01-2012 at 07:38 PM.
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Old
11-01-2012, 07:36 PM
  #149
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Originally Posted by Rhiessan71 View Post
No, my hangup with Adjusted Stats has always been how they are used far to often as the ONLY form of comparison with the exclusion of everything else between players of different era's.
If AS is going to be used that exclusively with that much weight, it better be extremely god damned accurate!

And because this actually seems right to you....

Raw Career PpG: Bourque-.98 Lidstrom-.73
ADJ Career PpG: Bourque-.88 Lidstrom-.76
Raw 10year(92-01) in the league together: Bourque-.86 Lidstrom-.73
Adj 10year(92-01) in the league together: Bourque-1.00 Lidstrom-.66
Raw remaining years: (80-91)Bourque-1.07 (02-12)Lidstrom-.73
ADJ remaining years: (80-91)Bourque-.78 (02-12)Lidstrom-.78

So despite Bourque through 79/80-90/91 leading his team in scoring multiple times, despite having a top 10 along with multiple top 20 league scoring finishes, despite what your actual eyes tell you, despite Bourque doing this with a hell of a lot less offensive support than Lidstrom and despite Bourque being clearly better offensively in all other data...that an 01/02-11/12 Lidstrom that includes 3 of the 4 worst offensive years of his entire career was exactly equal to 79/80-90/91 Bourque offensively?

Nothing wrong there

Sorry but somewhere along the line, Adjusted stats is breaking down and breaking down bigtime.
Ok, so what's the alternative? Using raw data instead of adjusted stats seems to me to result in two conclusions: Either players' offensive numbers from prior to 67-68 and after 92-93 are brushed aside because they significantly inferior to the numbers put up between 67-68 and 92-93 OR we can't compare players from different eras at all because it's apples and oranges. Neither seems to me to be a very satisfactory answer.

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11-01-2012, 07:44 PM
  #150
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Ok, so what's the alternative? Using raw data instead of adjusted stats seems to me to result in two conclusions: Either players' offensive numbers from prior to 67-68 and after 92-93 are brushed aside because they significantly inferior to the numbers put up between 67-68 and 92-93 OR we can't compare players from different eras at all because it's apples and oranges. Neither seems to me to be a very satisfactory answer.
No, as I just showed, you take EVERYTHING into account and for the love of god, use common sense.
If you're investigating a crime with 6 witnesses and 5 of the witnesses have similar stories while the 6th witness doesn't...

And for the record, I'm not saying that Adjusted Stats is always that "6th witness".


Last edited by Rhiessan71: 11-01-2012 at 08:06 PM.
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