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Adjusted stats - how valuable?

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Old
11-05-2012, 12:49 PM
  #201
Iain Fyffe
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Originally Posted by Rhiessan71 View Post
Overall you're prolly right but again, we deal mostly with outliers and the top 1% here so even a small number will exponentially change the overall picture for these players.
For example, based on the numbers Overpass presented here http://hfboards.hockeysfuture.com/sh...39&postcount=8
Top tier players have a 13.4% increased share of total goals from 1983 compared to 2008.
You take Gretzky's 159 adjusted points from 1983 and that 13.4% increase changes his share so that he would have a projected 180 points in 2008 or a 9.3% increase projecting from 1983 to 2012 equaling 174 point projection.
Suddenly not so insignificant
Not insignificant, but when you say "exponential" I suspect most people would expect the exponent to be more than 1.025...

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11-05-2012, 01:20 PM
  #202
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Quote:
Originally Posted by Rhiessan71 View Post
Overall you're prolly right but again, we deal mostly with outliers and the top 1% here so even a small number will exponentially change the overall picture for these players.
For example, based on the numbers Overpass presented here http://hfboards.hockeysfuture.com/sh...39&postcount=8
Top tier players have a 13.4% increased share of total goals from 1983 compared to 2008.
You take Gretzky's 159 adjusted points from 1983 and that 13.4% increase changes his share so that he would have a projected 180 points in 2008 or a 9.3% increase projecting from 1983 to 2012 equaling 174 point projection.
Suddenly not so insignificant
Obviously this is just a rough example but even at about half that 13.4% at a 7% increase share, it changes that 159 to 170.
First, Overpass' numbers are using the top Y players on each team, not the top (N*Y) players in the league (where N = # of teams). That means as parity between teams increases, the numbers would likely show an increase (since there should be much less parity between top players than 4th liners).

Second, it again depends on the cause, because if the top lines became of higher quality in a manner disproportionate to lower lines, then the numbers would again show an increase, but it would not mean that it was actually any easier for top line players to score adjusted points (in absolute terms). Reflect on the curved-grade classroom with added students as an example.

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11-05-2012, 01:21 PM
  #203
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Originally Posted by Iain Fyffe View Post
Not insignificant, but when you say "exponential" I suspect most people would expect the exponent to be more than 1.025...
Exponential because both the number of points AND the factor by which they are modified are higher than that of an average player.

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11-05-2012, 01:29 PM
  #204
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Originally Posted by Czech Your Math View Post
First, Overpass' numbers are using the top Y players on each team, not the top (N*Y) players in the league (where N = # of teams). That means as parity between teams increases, the numbers would likely show an increase (since there should be much less parity between top players than 4th liners).

Second, it again depends on the cause, because if the top lines became of higher quality in a manner disproportionate to lower lines, then the numbers would again show an increase, but it would not mean that it was actually any easier for top line players to score adjusted points (in absolute terms). Reflect on the curved-grade classroom with added students as an example.
I know, which is why I included the 7% number. Even if OP's numbers are only half right, it's still a significant increase.

Quote:
Obviously this is just a rough example but even at about half that 13.4% at a 7% increase share, it changes that 159 to 170.
Also, to really get picky, one could argue that Gretzky should get double the adjustment as he was producing what 2 average first tier players did


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11-05-2012, 02:14 PM
  #205
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Originally Posted by Rhiessan71 View Post
Exponential because both the number of points AND the factor by which they are modified are higher than that of an average player.
Multiplicative rather than exponential then. To get from 159 to 180 you only need an exponent of 1.025 (ie, 159^1.025 = 180), so calling it exponential is exaggerating the effect.

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11-05-2012, 02:16 PM
  #206
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Originally Posted by Rhiessan71 View Post
Also, to really get picky, one could argue that Gretzky should get double the adjustment as he was producing what 2 average first tier players did
He would already, since you're applying a percentage adjustment to his total. He gains 11 points in your example whereas the average first-tier player as you say would only gain 5 or 6.

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11-05-2012, 02:35 PM
  #207
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Originally Posted by Iain Fyffe View Post
Multiplicative rather than exponential then. To get from 159 to 180 you only need an exponent of 1.025 (ie, 159^1.025 = 180), so calling it exponential is exaggerating the effect.
That's the word I was looking for. Fair enough.

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Originally Posted by Iain Fyffe View Post
He would already, since you're applying a percentage adjustment to his total. He gains 11 points in your example whereas the average first-tier player as you say would only gain 5 or 6.
I know man, I was making a joke in light of Gretzky's total ridiculousness.

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11-05-2012, 04:07 PM
  #208
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I ran a linear regression for '80 to '12 using data that I already had, as follows:

Y = avg. adjusted scoring of top N players (N = # teams in NHL)

Xn = Number of teams in NHL

Xg = Avg. GPG in NHL

Xe = % of top N forwards who were born outside Canada (Canadian trained players from Europe, such as Heatley & Nolan were considered Canadian)

Xp = % of total goals recorded as special teams (PP & SH) goals

Using all 4 variables, the R-squared was 99.8% and the values for each X were as follows:

Xn= 1.05
Xg= 6.77
Xe= 16.4
Xp= 49.4

Using 3 variables (Xn excluded), the R-squared was 99.7% and the values of each X were as follows:

Xg= 7.83
Xe= 39.5
Xp= 92.8

Both appear to be very solid models for predicting the avg. adjusted scoring of the top N players each season. The average for the 32 seasons was 88.95 adj. points with a standard deviation of 3.59. With 4 variables, the predicted Y had a mean of 88.87 with the avg. absolute value of the error being 3.13, and 21/32 seasons had errors of < 1 stdev. With 3 variables, the predicted Y had a mean of 88.71 with the avg. absolute value of the error being 3.86, and 18/32 seasons had errors of < 1 stdev.

It's important to note that in both models there was a positive coefficient for Xg (league GPG), meaning that as league scoring decreased, the model predicted avg. adj. points of the top N players to decrease as well (by ~7-8 points per 1.0 point drop in league scoring).

I did this rather quickly, since I was using data readily available to me. One small flaw is that Xe measures % non-Canadian forwards in top N forwards in points, rather than % non-Canadians in top N players. It would be better if this variable and Y were aligned completely, but given the relatively few defensemen who appear in the top N in scoring, I highly doubt there would be a major effect on the results. If anything, properly aligning Y & Xe may only strengthen the relationship between them, since in more recent years when avg. adj. scoring of top N players has increased, there have been substantially more Euro/US d-men (Lidstrom, Leetch, Zubov, Gonchar, etc.). Still, the actual % of the top N is quite small, so I expect any distortions were relatively minor.

For those who understand this type of study, I certainly welcome comments, suggestions and even follow-up studies which may expand, improve or verify the results. This is what I meant by identifying, analyzing and quantifying various factors that may affect the difficulty of top level players to score adjusted points in various seasons. It can be done, and I have taken a step in that direction. I look forward to others taking further steps forward, instead of steps backward using improper analysis and/or pure speculation.


Last edited by Czech Your Math: 11-06-2012 at 12:34 PM. Reason: spelling
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11-05-2012, 05:48 PM
  #209
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Stats can be read in any way one wants to be.Did Souray produce the greatest single season by a hab Defenceman?Most ppg ever,One of the two top goal seasons ever?He did it with no Hall of Famers.

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11-05-2012, 06:24 PM
  #210
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Originally Posted by thom View Post
Stats can be read in any way one wants to be.Did Souray produce the greatest single season by a hab Defenceman?Most ppg ever,One of the two top goal seasons ever?He did it with no Hall of Famers.
And he was -28. Any argument that focuses on one and only one simple stat is going to be rather seriously flawed, and obviously so.

Stats cannot be read in any way one wants to. That's an oversimplification, because if someone is reading stats in a certain way just because he wants to, it's easy to spot.

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11-05-2012, 07:16 PM
  #211
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Is Souray the greatest pp point man in a single season in canadiens history?Plus and minus is helpful but you need other stats.Considering Souray did not have much help would you not say he was great on the powerplay?

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11-05-2012, 07:56 PM
  #212
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Stats can be read in any way one wants to be.Did Souray produce the greatest single season by a hab Defenceman?Most ppg ever,One of the two top goal seasons ever?He did it with no Hall of Famers.
Using adjusted points as an indicator of offensive value, his season trailed at least one season by Robinson, Lapointe and Markov. Also, his goals/points were very skewed towards the PP vs. ES. Finally, as Iain pointed out, his plus-minus was horrible (and his adj. plus-minus in comparison to teammates was very bad as well), which indicates his overall ineffectiveness at ES.

Besides those factors, most people do not rate a player's peak based on a single season. I tend to look at a 3-5 season range at least.

I don't think you're going to find too many arguing for Souray as the best Habs' d-man at his peak, or as having the best season of a Habs' d-man.

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Is Souray the greatest pp point man in a single season in canadiens history?Plus and minus is helpful but you need other stats.Considering Souray did not have much help would you not say he was great on the powerplay?
He was one of the best on the PP, at least for that one season. Another indication of this is the Habs' PP% that season, which converted about 5 percentage points higher than league avg.

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11-05-2012, 08:41 PM
  #213
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Originally Posted by thom View Post
Is Souray the greatest pp point man in a single season in canadiens history?Plus and minus is helpful but you need other stats.Considering Souray did not have much help would you not say he was great on the powerplay?
You've moved the goalposts significantly here - you went from single greatest season by a defenceman to greatest PP point man.

He was good on the PP, but in that season he did benefit from a very high scoring percentage from the blueline, and he didn't ring up all that many assists, so the goals by themselves may not be enough.

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11-05-2012, 10:27 PM
  #214
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Originally Posted by Czech Your Math View Post
Using all 4 variables, the R-squared was 99.8% and the values for each X were as follows:

Xn= 1.05
Xg= 6.77
Xe= 16.4
Xp= 49.4

Using 3 variables (Xn excluded), the R-squared was 99.7% and the values of each X were as follows:

Xg= 7.83
Xe= 39.5
Xp= 92.8
Let me just explain this process to those unfamiliar with it. Each model calculates coefficient values for each variable, which together produce the least total error (actually it's a sum of the square of each error). The equation for the first (4 variable) model is:

Y = 1.05*Xn + 6.77*Xg + 16.4*Xe + 49.4*Xp

or

Avg. Adj. Pts. of Top N Players = (1.05 * # Teams) + (6.77 * League Avg. GPG) + (16.4 * Ratio of non-Canadian Top N to Total Top N) + (49.4 * Ratio of PP & SH Goals to Total Goals)

In the second (3 variable) model, the coefficient values of Xe and Xp increase dramatically, as a result of Xn being excluded. This is because in the first model, Xn captured a lot of the effect present in Xe and Xp. IOW, in most of the same seasons where there was an increase in teams (due to expansion), there was also an increased representation by Euro/US players in the top N scorers, and an increased number of PP opportunities. I would think that a lot of the effects causes by increased non-Canadian players and increased PP opportunities was mistakenly attributed to the increase in the number of teams, because they each had increased values in most of the same seasons.

Here's what the second model would predict:

A) For each .10 increase in league gpg, a .78 increase in avg. adj. pts. of top N scorers

B) For each 10 percentage point increase in top N forwards which were non-Canadian (e.g. from 20% to 30%), a 3.95 increase in avg. adj. pts. of top N scorers

C) For each 1.0 percentage point increase (e.g. from 22% to 23%) in PP/SH goals as a % of total goals, a .49 increase in the avg. adj. pts. of top N scorers

There may be some small rounding or other errors present in each of the variables, but these shouldn't significantly affect the results. There are some alternative models that could be studied, but I would guess the most interesting modifications would be to the quality of the Y variable (using different quality or quantity of tiers), rather than to the X variables (I can't think of many other important X variables, except maybe a variable that measures parity between teams and/or players).

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11-06-2012, 03:22 AM
  #215
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Originally Posted by Iain Fyffe View Post

Indeed.


Well said.
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Originally Posted by Czech Your Math View Post

Good explanation, perhaps your will sink in better than mine seemed to have.



Another good explanation, again hope it sinks in for some.
I must have been having a good day back on Friday. Usually it's me thinking you guys are eloquently stating what I can't!

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11-06-2012, 06:58 PM
  #216
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Thank you!

And yes, I realise no system is going to be perfect. Which is why you don't just base comparisons on ONE system and you certainly don't abandon common sense in the process.

I am still going to continue to drive home the point that not all tiers of players are going to be affected equally in a harsher scoring environment.
I saw it all through minor hockey. As we got older, coaching sunk in better as we could better understand the implementation of systems and positioning.
As this happened, the lesser talented players found it increasingly harder to score while the more talented players were having a lot less trouble maintaining their production.
As a result, our team scoring became less spread out between all lines and more concentrated on the top lines. Our total goals scored decreased but that decrease was in no way, shape or from an equal decrease between all players.
This is reality and IMO, exactly the same thing has happened in the NHL over the last 30 years.

So you can continue to say that scoring has decreased between all players equally and I will continue to call ********

The Math aside, you KNOW this makes a hell of a lot of sense.
I'm not sure how anyone can argue against this unless they somehow have a vested interest. How does Russian goal scorers coming over make it more difficult for Lemieux and Gretzky to put up points? The Euro/Russia defencemen have been pretty mediocre, aside from Lidstrom.

Of course if the league gets tougher, Chris Nilan and the gang are going to be hurt more than the top point getters and to think otherwise is pretty absurd and baseless imo.

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11-06-2012, 08:14 PM
  #217
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Originally Posted by habsfanatics View Post
I'm not sure how anyone can argue against this unless they somehow have a vested interest. How does Russian goal scorers coming over make it more difficult for Lemieux and Gretzky to put up points? The Euro/Russia defencemen have been pretty mediocre, aside from Lidstrom.

Of course if the league gets tougher, Chris Nilan and the gang are going to be hurt more than the top point getters and to think otherwise is pretty absurd and baseless imo.
I don't think saying that only someone having a "vested interest" could argue against it is fair.
I think sometimes people can get so caught up in the numbers and the math that they let common sense, among other observations, drop by the wayside.

The old saying "Can't see the forest for the trees" has been used in this thread.

There have always been and will continue to be players that defy the numbers.

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11-06-2012, 08:19 PM
  #218
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Originally Posted by habsfanatics View Post
I'm not sure how anyone can argue against this unless they somehow have a vested interest. How does Russian goal scorers coming over make it more difficult for Lemieux and Gretzky to put up points? The Euro/Russia defencemen have been pretty mediocre, aside from Lidstrom.
You seem to be missing the concept of adjusted stats. Basically, the increased competition increases the difficulty of the "curve", since disproportionately more high scoring forwards should (other things being equal) increase the league avg. GPG, which would lower adjusted stats for any given level of raw production.

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Originally Posted by habsfanatics View Post
Of course if the league gets tougher, Chris Nilan and the gang are going to be hurt more than the top point getters and to think otherwise is pretty absurd and baseless imo.
I can see arguments going both ways. The argument as to top players would be disproportionately adversely affected would probably be as follows. Three main reasons often cited for the decrease in league scoring in the 90s, and their possible implications are:

1. More defensive systems/coaching- These probably focus more on preventing the top lines from scoring, since they tend to do most of the scoring.

2. Lack of rules enforcement- Clutch and grab, hook and hold type play that was allowed in that era may hurt top players more, since it neutralizes those players' speed and skill, while lower line players may get more garbage goals and be used to that type of playing style (since they may play that way themselves more than top line players do).

3. Better/bigger goalie equipment- Larger coverage of the net due to larger goalie equipment and quicker reactions allowed by lighter equipment may hurt top players more, since they have much better aim and can "pick corners" and deke goalies more effectively. Players who may be getting a large % of goals in front of the net, off their stick or bodies, or who are throwing pucks blindly and/or randomly at the net and hoping to get lucky, may be less affected by such changes.

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11-07-2012, 03:09 PM
  #219
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Originally Posted by Czech Your Math View Post
You seem to be missing the concept of adjusted stats. Basically, the increased competition increases the difficulty of the "curve", since disproportionately more high scoring forwards should (other things being equal) increase the league avg. GPG, which would lower adjusted stats for any given level of raw production.



I can see arguments going both ways. The argument as to top players would be disproportionately adversely affected would probably be as follows. Three main reasons often cited for the decrease in league scoring in the 90s, and their possible implications are:

1. More defensive systems/coaching- These probably focus more on preventing the top lines from scoring, since they tend to do most of the scoring.

2. Lack of rules enforcement- Clutch and grab, hook and hold type play that was allowed in that era may hurt top players more, since it neutralizes those players' speed and skill, while lower line players may get more garbage goals and be used to that type of playing style (since they may play that way themselves more than top line players do).

3. Better/bigger goalie equipment- Larger coverage of the net due to larger goalie equipment and quicker reactions allowed by lighter equipment may hurt top players more, since they have much better aim and can "pick corners" and deke goalies more effectively. Players who may be getting a large % of goals in front of the net, off their stick or bodies, or who are throwing pucks blindly and/or randomly at the net and hoping to get lucky, may be less affected by such changes.

In every level of hockey I've ever played when the competition gets more difficult it tends to hurt those that were fringe to begin with and those at the top remain relatively unchanged. We're talking about the top 1% of players here generally. It is my opinion that they are unfairly dropped into the same pool of players that aren't the best. The cream rises to the top and there is no way in hell that the decline in scoring is spread evenly from the top all the way down to the fringe. Sometimes numbers can't be substituted for common sense.

I get the idea behind adjusted stats, but I believe they have some pretty big holes.


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11-07-2012, 03:58 PM
  #220
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In every level of hockey I've ever played when the competition gets more difficult it tends to hurt those that were fringe to begin with and those at the top remain relatively unchanged. We're talking about the top 1% of players here generally. It is my opinion that they are unfairly dropped into the same pool of players that aren't the best. The cream rises to the top and there is no way in hell that the decline in scoring is spread evenly from the top all the way down to the fringe. Sometimes numbers can't be substituted for common sense.

I get the idea behind adjusted stats, but I believe they have some pretty big holes.
The 1% is a "special case" compared to the rest of the NHL... but then NHL players are a "special case" compared to the group of players which at some time played a relatively high level of organized hockey, such as collegiate, junior, minor league, etc.

I understand your skepticism, but to say that it's purely "common sense" is quite assumptive IMO.

The very top NHL players are best compared to those of similar ability/performance, but as we know, as one gets farther to the extreme of the spectrum, there are fewer and fewer players who are somewhat comparable.

I believe there are some ways to study this that haven't been fully explored, but it will take some time and effort on the parts of people who understand the problem, the factors involved, and the techniques that are most likely to yield an eventual (at least partial) solution to improving the comparison of players across different seasons/eras.

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11-07-2012, 04:31 PM
  #221
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Originally Posted by Czech Your Math View Post
The 1% is a "special case" compared to the rest of the NHL... but then NHL players are a "special case" compared to the group of players which at some time played a relatively high level of organized hockey, such as collegiate, junior, minor league, etc.

I understand your skepticism, but to say that it's purely "common sense" is quite assumptive IMO.

The very top NHL players are best compared to those of similar ability/performance, but as we know, as one gets farther to the extreme of the spectrum, there are fewer and fewer players who are somewhat comparable.

I believe there are some ways to study this that haven't been fully explored, but it will take some time and effort on the parts of people who understand the problem, the factors involved, and the techniques that are most likely to yield an eventual (at least partial) solution to improving the comparison of players across different seasons/eras.
No one is saying that Adjusted Stats are insignificant or completely devoid of value.
AGAIN, it's when people use them at the expense of everything else available that they become an issue.

When someone bases their entire argument purely on what AS's says then we/I have a problem and it happens far too often.

You keep taking an extremist view every time someone has the slightest issue with AS's.
99% of the time the issue isn't even with AS's themselves, it's the value being assigned to them or that they are the only thing being used, that is.
Far too often I hear the response..."You don't agree because just don't understand them" when the reality is that one doesn't even have to fully understand them to understand what they are saying compared to everything else.
There's a difference between understanding AS's and understanding their value or weight in the equation.


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11-07-2012, 05:02 PM
  #222
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No one is saying that Adjusted Stats are insignificant or completely devoid of value.
AGAIN, it's when people use them at the expense of everything else available that they become an issue.

When someone bases their entire argument purely on what AS's says then we/I have a problem and it happens far too often.

You keep taking an extremist view every time someone has the slightest issue with AS's.
99% of the time the issue isn't even with AS's themselves, it's the value being assigned to them or that they are the only thing being used, that is.
Far too often I hear the response..."You don't agree because just don't understand them" when the reality is that one doesn't even have to fully understand them to understand what they are saying compared to everything else.
There's a difference between understanding AS's and understanding their value or weight in the equation.
I understand your position, because I feel very similar about common ways of evaluating players:

- awards, which are tallying of votes, usually by sportswriters: to me these are often mistaken, biased, and based on reputation (since they don't see most players for more than a few games at most), and there are drastic differences in competition for awards in different eras

- ranking amongst their peers: usually this totally ignores the drastic differences in competition during various seasons/eras, so that Howe & Richard's rankings are deemed just as valid as those of the past 2-3 decades

- the good ole "eye test": do I even have to explain that this is as subjective as it gets, and does little to get closer to any reasoned consensus in most cases?

- Cup counting and the like: of course, when one points out that playing in a 6 team league with two rounds of playoffs is going to lead to a lot more Cups for most top individual players, it is usually summarily dismissed as irrelevant

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11-07-2012, 05:05 PM
  #223
habsfanatics
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Originally Posted by Rhiessan71 View Post
No one is saying that Adjusted Stats are insignificant or completely devoid of value.
AGAIN, it's when people use them at the expense of everything else available that they become an issue.

When someone bases their entire argument purely on what AS's says then we/I have a problem and it happens far too often.

You keep taking an extremist view every time someone has the slightest issue with AS's.
99% of the time the issue isn't even with AS's themselves, it's the value being assigned to them or that they are the only thing being used, that is.
Far too often I hear the response..."You don't agree because just don't understand them" when the reality is that one doesn't even have to fully understand them to understand what they are saying compared to everything else.
There's a difference between understanding AS's and understanding their value or weight in the equation.
Agreed, I think they're neat and fun to ponder, but I have reservations about how they get thrown about around here. They are far from perfect and they do help a bit with context.

The defenders usually substitute you don't agree with "you don't understand". I understand fine, I also understand that when discussing the top 1% certain things don't apply.

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11-07-2012, 05:08 PM
  #224
Chalupa Batman
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Originally Posted by habsfanatics View Post
The defenders usually substitute you don't agree with "you don't understand". I understand fine, I also understand that when discussing the top 1% certain things don't apply.
It's not fair to paint all people with the same brush here (as in "the defenders"...).

Particularly when there are a fair number of detractors who will say "I don't care what your numbers say, I know what I saw and I'm not changing my mind." That's a pretty quick conversation ender.

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11-07-2012, 05:11 PM
  #225
SaintPatrick33
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Quote:
Originally Posted by Czech Your Math View Post
- ranking amongst their peers: usually this totally ignores the drastic differences in competition during various seasons/eras, so that Howe & Richard's rankings are deemed just as valid as those of the past 2-3 decades
Got to disagree with you there: Howe and Richard played when talent was distilled down to six teams. One can make a valid point about how players from Europe increased the talent pool, but you have to qualify that with the fact that that talent has been spread over five times as many teams which pretty much makes it a wash.

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