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Adjusted stats - how valuable?

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Old
11-09-2012, 09:39 AM
  #276
Dalton
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Originally Posted by Czech Your Math View Post
Yes, you are correct, it's a matter of probability. If the talent pool is 4x as large as 60 years ago, then if you took the best 2 players from 60 years ago, the odds are there would be ~8 in a more recent season. Maybe there would only be 3 or 4 of that quality... and maybe there would be a dozen or 20 of that quality. However, what is quite improbable is that there would be the same or fewer of that quality with 4x the talent pool.

I think a lot of it has to do with the "aura" surrounding some of the earliest stars of the post-WWII NHL, playing on stacked teams which were consistently Cup contenders (by nature of the much smaller league), who could dominate a much smaller talent pool. The smaller league also limits ice time & PP time to a much smaller group of forwards, which basically means only the top 30 or so forwards had any real chance at high rankings and awards in those O6 seasons.

Think about this: Randomly cut the NHL's talent to 1/4 of its present level. Then condense the remaining 1/4 to 6 teams. The top players remaining would have a much easier time dominating the remaining competition.



Players like Gretzky and Lemieux are going to appear very infrequently and seemingly randomly, because there are so few (if any) other players of that quality. I don't think Sakic or Yzerman are that unique as far as peak/prime adjusted production. There are other players who were in the same range of career adjusted production as well. It's the combination of peak/prime and career that sets them apart, but there will certainly be more players at/above their level IMO. Besides Jagr, who was at a higher level, the closest to matching both their peak/prime and career adjusted production is probably Selanne. He's still (hopefully) still playing and didn't start to play in the NHL until he was 22, so I'd say he's about the equivalent of Sakic & Yzerman in terms of peak/prime and career production (but most would rank them significantly above Selanne based on playoffs, defense, leadership, etc.). The other player with similar peak/prime production who could end up with similar career adjusted numbers is Thornton (who also shares a relatively mediocre playoff record with Selanne), but he'll have to play several more seasons to do so.

Sakic and Yzerman didn't end their careers that long ago, so we must give it time to see who will emerge as the next at their level. It will probably be whichever of Malkin, Crosby and Ovechkin can sustain a long, productive career, as the other contemporary equivalents of Sakic & Yzerman (Lindros, Forsberg) were not able to do so. The difference between Sakic & Yzerman and some other great forwards has more to do with longevity, team success and perceived intangibles than their objective peak/prime production being significantly superior to their potential rivals.
I doubt that. After Orr everyone said you'll never see his like again. But then came Gretzky, Lemieux hot on his tail. This appearance of talent has a lot of factors other than mere population. How many excellent pro athletes take up the game. How many people with the skill set or appropriate intelligences get involved. Again averaging fails.

Lose this mind set.


Last edited by Dalton: 11-09-2012 at 09:46 AM.
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11-09-2012, 10:03 AM
  #277
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Originally Posted by Taco MacArthur View Post
You're in the wrong forum, then:
http://hfboards.hockeysfuture.com/sh....php?t=1237235

This forum is about quantifiable efforts to measure hockey-related issues.

If your claim is that it can't be done, and that everyone should just shut up about it, then there are hundreds of other subforums here that you might enjoy.

Otherwise, feel free to pitch in and help.
Thanx, I'll check it out and try to confine that aspect of my POV there.

I do believe there is a place for math here just not that its strictly a math problem as opposed to a problem in which math is helpful.

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11-09-2012, 10:58 AM
  #278
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Originally Posted by Dalton View Post
This is what I have a problem with. I have 20 students and 2 get As. I have the same class next year. Those two students still deserve As. But 10 students have come to the class from a foreign land rumoured to be really, really good at the subject I'm teaching. The rumours hold out for the most part and 7 of them deserve As.

You would bell curve the class downwards and deny them what they earned. I would give all deserving students an A or whatever grade they earned according to whatever rubric I had been using up to that time.

Giving students a B,C or D when they actually earned an A based on past practices is what's wrong with bell curving or a misplaced belief in averaging. It has deeper implications on society as the study I've referenced suggests.

If you are doing this with raw hockey data then there can be no doubt whatsoever that your interpreted data is in error. You are saying that you would manipulate data to satisfy an irrational urge for normalcy at the expence of truth.
I agree with you that curving isn't the best way to grade a class. It would be better to have an exact standard that's consistently applied, but we don't know what standard to use to equate one season to another. The best estimate so far is based on the mean, which is why the curve (not necessarily bell-shaped) was used as an analogy.

You have to look at the most common alternative, which is just using raw stats. This is the equivalent of having different professors from year to year. One year it's "cool Mr. High" who hands out As & Bs to most of the class... the next year it's "cranky Ms. Low" who relishes failing half the class.

In the context we're speaking of (hockey), using a curve is at least consistent and founded in value. What changes from year to year is the quality of the class.

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11-09-2012, 11:17 AM
  #279
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Originally Posted by Dalton View Post
I think expansion/dilution should be included. In the past some teams- Oilers, Habs, Isles had a lot of talent playing together. Dilution caused by expansion often leaves teams with very little high end talent playing together.

Lemieux and Jagr, Malkin and Crosby, those Detroit wingers. The Pens with their third all-star at center won a cup. Having two or three outstanding players makes a difference these days. It used to be that having an outstanding starting 6 and some excellent guys on the second and third unit was required.
You bring up a good point, but I think there are reasoned arguments on each side. You are focusing on the lack of concentration on the offensive side, while others might point out the dilution on the defensive side. The two factors may offset, or there may be other factors which determine which has more influence in a given era. Expansion in the late 60s & 70s led to increased scoring, despite most expansion teams not being able to score at nearly the rate of most O6 teams.

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Originally Posted by Dalton View Post
Dilution is a factor and another reason why applying a fixed average (AS) fails. Adding players from non-Canadian countries has just served to stem the tide towards mediocrity. Defensive systems also counter dilution. As do rule breaking or bending such as the recent NYR attempt to win by everyone laying down in front of the net when the other team comes calling. That's an increased talent pool?
The Rangers trying to block every shot or teams in the 90s clutching and grabbing are obviously examples of defensive systems. Would it work without a strong (Euro) goalie like Lundqvist? Is it countering dilution or less relative talent compared to other teams? Is it innovation or do these "defensive systems" devolve the game?

I think one factor has been the OT/SO points that came into play. This encourages teams to play for the tie, which means play a stifling defense and avoid giving up goals at all costs. The NHL has probably been short-sighted in using this point system, rather than an alternative which did not reward "playing for the tie."

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Originally Posted by Dalton View Post
AS fails to take into account these changes.

Every tree in every forest is treated the same regardless of the weather or human intervention.
How does raw data take into account any/all of the factors you have mentioned over the course of so many posts? Are you suggesting that relying on raw data is more informative than using adjusted stats as a replacement/supplement to raw data?

Have you taken any steps towards improving adjusted stats? Are you just going to complain, critique, shake your head that "adjusted stats aren't perfect, so they're a failure", and present distracting tangents?


Last edited by Czech Your Math: 11-09-2012 at 11:39 AM.
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11-09-2012, 11:32 AM
  #280
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Originally Posted by Dalton View Post
The difference between the POVs you aren't comfortable with is that they don't come to the debate with a table of stats and an arcane methodology claiming 'I brought math therefore I've won.'

This is not a math problem. This an HR issue. Determining the value of work performed vs peers and making value judgements comparing work done in different social, economic and political times. Hockey has all these variables but they are not reflected in AS in any way whatsoever.
The POV with which I'm not comfortable is that which is not reasonable and open-minded. Probably the biggest problem with all methods used to evaluate players (including AS) is that those using them make no attempt to factor in the very large changes in competition (talent pool) over time, and the increased difficulty that results from having higher quality competition.

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Originally Posted by Dalton View Post
You are assuming that adjusted stats the answer. This is a huge problem in this debate. The assumption that AS is absolutely true and that if you don't buy into that and argue from that POV then you are (fill in the blank).

Hard to have a debate about the value of something when one side won't acknowledge that their value is the debate.
Except they are true, at least in terms of relative value. They are not THE answer. However, they may be the starting point to find the best estimate of the actual possible.

If one cannot reach the summit of a mountain in their first attempt, but plans to try again, does one retreat to base camp or trek all the way down the mountain before making the next attempt? I'm of the group which would go back to base camp. You seem to be of the group which would go back down the entire mountain... if you didn't throw up your arms, declare the entire expedition "useless... complete nonsense", etc. and walk off before you even took a single step up the mountain.

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Originally Posted by Dalton View Post
I doubt that. After Orr everyone said you'll never see his like again. But then came Gretzky, Lemieux hot on his tail. This appearance of talent has a lot of factors other than mere population. How many excellent pro athletes take up the game. How many people with the skill set or appropriate intelligences get involved. Again averaging fails.

Lose this mind set.
The greats don't show up on schedule, I would agree to that. However, it's still a matter of probabilities. I doubt it's an accident that Orr, Gretzky and Lemieux were born towards the end of the population boom and were born less than 18 years apart. It may also not be an accident that they were part of a dynamic time in hockey, when there was more freedom for individual players and scoring was high.

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11-09-2012, 12:17 PM
  #281
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I'll try my best to get this back on track..

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Originally Posted by Czech Your Math View Post
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).

(...)

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.
You report coefficients on each regressor but it's hard to really make sense of the results without the t-statistics. Given the insignificant drop in R-squared when you drop Xn I would assume that 1.05 coefficient is insignificant but I'd like to see the others.

I don't think you can make a judgement on how solid those models are for predicting anything based on R-squared, as that Y series is probably fairly stable. If you regressed Y on a constant you'd get a pretty high R-squared too.

My main takeaway:

Y is adjusted to 6 GPG (HR method), right? If your regression used all the players in the league, by definition you'd get Xg=0, because that's what the adjustment does. You have Xg>0 for the top 5% of players, that means the top guys are further away from the mean in high-scoring seasons than in low-scoring seasons. The adjustment may not bring down the top guys enough in high scoring seasons.

Am I correct?

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11-09-2012, 02:45 PM
  #282
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Originally Posted by barneyg View Post
I'll try my best to get this back on track..

You report coefficients on each regressor but it's hard to really make sense of the results without the t-statistics. Given the insignificant drop in R-squared when you drop Xn I would assume that 1.05 coefficient is insignificant but I'd like to see the others.

No, Xn actually appeared significant to me (Bn was almost 4x SEn). The least significant appeared to be Xp with Bp ~1.5x SEp. What's strange is that the individual correlations were:

Xn = 7%, Xp = 47%, Xe = 27%, and Xg = (-10%)

I thought Xn was coincidentally capturing a lot of the other variables, so I wanted to see what the coefficients looked like without Xn as one of the variables.

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Originally Posted by barneyg View Post
I don't think you can make a judgement on how solid those models are for predicting anything based on R-squared, as that Y series is probably fairly stable. If you regressed Y on a constant you'd get a pretty high R-squared too.
What's the best way to judge models with a relatively stable Y? Just look at the significance of each individual coefficient or is there a better way of judging/comparing models in such cases?


Quote:
Originally Posted by barneyg View Post
My main takeaway:

Y is adjusted to 6 GPG (HR method), right? If your regression used all the players in the league, by definition you'd get Xg=0, because that's what the adjustment does. You have Xg>0 for the top 5% of players, that means the top guys are further away from the mean in high-scoring seasons than in low-scoring seasons. The adjustment may not bring down the top guys enough in high scoring seasons.

Am I correct?
Yes, you seem to understand the process and model well, and are correct in each case. One caveat is that Xg had a small, negative correlation (-10%), but when used as a variable in the models the coefficient became positive and was also the most significant in the 4-variable model (Bg ~7x SEg).

Can you help with this question as well:

http://hfboards.hockeysfuture.com/sh...3#post55604063

I know there must be a way to find a more correct estimate of the difficulty/quality of each season for top players to score points, and I believe using regression will likely yield the most correct estimate possible. Unfortunately, my skills with it are obviously limited, and no one else seems interested in pursuing this avenue, despite my previous suggestions to do so.


Last edited by Czech Your Math: 11-09-2012 at 03:14 PM.
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11-09-2012, 06:10 PM
  #283
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Originally Posted by Czech Your Math View Post
If Bernie Nicholls could score ~150 points, then I'm pretty sure some others since could have done that in the 80s as well. Adjusted stats would suggest these players could have done it (and not just one season):
Nicholls was a very good (IMO bottom-end HHOF caliber) offensive player who centered a star LW (Robitaille) on a second line behind Wayne Gretzky, but still saw plenty of time. He also played RW with Gretzky on the PP and was the triggerman.

Quote:
Definitely- Jagr
Jagr could definitely have done it, although he had a better situation than Yzerman did in terms of offensive help in his prime. Also, Jagr's 149 year was the same as Nicholls' situation (second line, playing with a top center in Francis, Lemieux-Francis-Jagr PP) so that should be accounted for.

Quote:
Probably- Sakic, Forsberg, Selanne, Lindros, Thornton, Ovechkin, Malkin, Crosby...
Arguable. Sakic is the only one on this list who has an adjusted season at or above Nicholls' 124 from 1988-89, although some come close. So "probably" isn't the right word. Thee guys should be in the "Maybe" category.

Quote:
Maybe- Bure, Kariya, etc.
These two were barely outscoring a 30+ Yzerman in the 90s in ACTUAL production. The idea that they would have come near Yzerman's best offensive season is silly. Bure's best seasons in raw production were not even as good, point-wise, as Yzerman's seasons those same years. And nobody is arguing that Yzerman should have done it more than once. If we're including these two, we should probably include Sergei Fedorov, Ron Francis, and Jarome Iginla also.

Yzerman' season, whether the total was inflated by era or not, wa one of the best offensive seasons ever. His linemates certainly didn't post "inflated" numbers (compare to Jagr, Lemieux, Gretzky, Esposito, etc.); this suggests that either Yzerman was just that good, or his linemates were that bad.

Five players have hit 150. Gretzky did it without a 100+ teammate once. Lemieux once. Yzerman once. Nicholls and Esposito were teammates with the Hart trophy winner. That's how singular Yzerman's achievement was; it's something Gretzky and Lemieux themselves only achieved once. And Yzerman did it while also receiving a 1st-place Selke vote as he was double-shifted in a checking role in those days. None of the other four managed that defensive feat while hitting 150.


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Old
11-09-2012, 07:25 PM
  #284
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Originally Posted by eva unit zero View Post
Nicholls was a very good (IMO bottom-end HHOF caliber) offensive player who centered a star LW (Robitaille) on a second line behind Wayne Gretzky, but still saw plenty of time. He also played RW with Gretzky on the PP and was the triggerman.
Nicholls may not be the best example, but he still hit 150 in a season that was not at the very peak in league gpg.

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Originally Posted by eva unit zero View Post
Jagr could definitely have done it, although he had a better situation than Yzerman did in terms of offensive help in his prime. Also, Jagr's 149 year was the same as Nicholls' situation (second line, playing with a top center in Francis, Lemieux-Francis-Jagr PP) so that should be accounted for.
It was similar to Nicholls, but not the same. First, Jagr actually scored 20 more points at ES than Lemieux in '96 (and more per-game). Also, Jagr's adjusted PP production in '96 was less than in '99, less than in 2000 on a per-game basis, and actually closer to (but slightly ahead of) '98. Because the PP was run through Lemieux, this offset the effect of being on such a great PP unit.

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Originally Posted by eva unit zero View Post
Arguable. Sakic is the only one on this list who has an adjusted season at or above Nicholls' 124 from 1988-89, although some come close. So "probably" isn't the right word. Thee guys should be in the "Maybe" category.
Agreed. I would say "probably could have" or "might have" would be accurate. Those players would have needed to peak during the right stretch of seasons, stayed healthy, etc. to actually do it.

Quote:
Originally Posted by eva unit zero View Post
These two were barely outscoring a 30+ Yzerman in the 90s in ACTUAL production. The idea that they would have come near Yzerman's best offensive season is silly. Bure's best seasons in raw production were not even as good, point-wise, as Yzerman's seasons those same years. And nobody is arguing that Yzerman should have done it more than once. If we're including these two, we should probably include Sergei Fedorov, Ron Francis, and Jarome Iginla also.
Looking at the numbers, Kariya would have needed all the stars to align properly and I shouldn't have listed Bure. Still, to say they barely outscored 30+ y/o Yzerman is a bit of a stretch in terms of peak seasons. Yzerman turned 30 before the '96 season:

'96- Kariya 108, Yzerman 95, Bure only 15 gm
'97- Kariya 99, Yzerman 85, Bure 55 in 63
'98- Bure 90, Yzerman 69, Kariay 31 in 22 gm
'99- Kariya 101, Yzerman 74, Bure 16 in 11 gm
'00- Bure 94, Kariya 86, Yzerman 79
'01- Bure 92, Kariya 67 in 66 gm, Yzerman 52 in 54 gms

I don't think I've downplayed Yzerman's 155 point season in '89 while making the case that other players since may have been able to duplicate ~150 points in at least one season in the 70s, 80s or early 90s.

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11-10-2012, 05:57 AM
  #285
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Originally Posted by Czech Your Math View Post
I agree with you that curving isn't the best way to grade a class. It would be better to have an exact standard that's consistently applied, but we don't know what standard to use to equate one season to another. The best estimate so far is based on the mean, which is why the curve (not necessarily bell-shaped) was used as an analogy.

You have to look at the most common alternative, which is just using raw stats. This is the equivalent of having different professors from year to year. One year it's "cool Mr. High" who hands out As & Bs to most of the class... the next year it's "cranky Ms. Low" who relishes failing half the class.

In the context we're speaking of (hockey), using a curve is at least consistent and founded in value. What changes from year to year is the quality of the class.
This has been disproven in a massive study that included NHL left wingers gs.

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11-10-2012, 07:05 AM
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Originally Posted by Czech Your Math View Post
You bring up a good point, but I think there are reasoned arguments on each side. You are focusing on the lack of concentration on the offensive side, while others might point out the dilution on the defensive side. The two factors may offset, or there may be other factors which determine which has more influence in a given era. Expansion in the late 60s & 70s led to increased scoring, despite most expansion teams not being able to score at nearly the rate of most O6 teams.



The Rangers trying to block every shot or teams in the 90s clutching and grabbing are obviously examples of defensive systems. Would it work without a strong (Euro) goalie like Lundqvist? Is it countering dilution or less relative talent compared to other teams? Is it innovation or do these "defensive systems" devolve the game?

I think one factor has been the OT/SO points that came into play. This encourages teams to play for the tie, which means play a stifling defense and avoid giving up goals at all costs. The NHL has probably been short-sighted in using this point system, rather than an alternative which did not reward "playing for the tie."



How does raw data take into account any/all of the factors you have mentioned over the course of so many posts? Are you suggesting that relying on raw data is more informative than using adjusted stats as a replacement/supplement to raw data?

Have you taken any steps towards improving adjusted stats? Are you just going to complain, critique, shake your head that "adjusted stats aren't perfect, so they're a failure", and present distracting tangents?
I'm not advocating using raw data to compare players across eras. I have suggested and given many examples of using percentages as a way of measuring productivity compared to peers in increasing sets of players to establish a range that a player might have achieved compared to peers in other eras.

I have also suggested using reason to complement mathematical estimates.

Gretzky usually scored more assists than the next best performer got points. Then he added 55-60 goals. I think this is a perfectly reasonable way to look at how he'd do in any other era. That was his talent level. Howe scored just a bit better compared to his peers in his era. What's wrong with these observations? Howe might have got 93-95 goals in Gretzky's 92 goal year if he were the top outlier instead of Gretzky. Math and reason.

To accurately predict what Gretzky or Howe would have actually scored last year is problematic given that their presence in the league changed the way everybody plays. So in effect they would be playing against themselves.

We can look at a measure of their production as a percentage of sets of peers in their eras and apply those to last year and see what shakes out. I did this with Howe and came up with some incredibly high number of goals but since we aren't actually trying to predict that shouldn't be an issue. I think the Howe result of over 300 goals is simply a reflection of just how dominating he was compared to his peers when he scored 49 goals.

Maybe AS shouldn't be trying to set a fixed, realistic looking number to use as a measure. That just makes it look like a prediction. Comparing to peers in their own eras and then comparing those results is a better approach IMHO.

IQ measures are taken against peers in the relevant era. Nobody tries to guess how Newton from the past would fare on an IQ test or physics exam today. Perhaps that is a good example to draw from.

Or maybe a precise definition of what AS is trying to achieve would work here. Honestly it really just looks like an attempt to predict actual GS and that clearly causes confusion. I don't see it as a measure of productivity either. What does 'value of gs' as an example actually mean. What is it trying to do?

GS is productivity. So are sales. Publishing articles, getting out the vote and numerous other examples used in the study I referenced. Ten years ago an individual might achieve a dominant position of productivity compared to peers. Today, the thinking goes, with better training (coming from the success of those 10 years ago), more competition perhaps there may be a few individuals sharing in that top percentile of productivity. But could this not simply be due to the lack of an new dominant outlier? Their appearance is unpredictable.

The lack of a dominant individual should not and cannot justifiably be an argument for devaluing the productivity of those from the past. Does a lack of an Einstein today diminsh his accomplishment? Or is it reasonabe to say that there are many Einsteins today. I say it is not reasonable. Before Einstein or Orr everyone was bunched together at the top simply because those outliers were not present.

We see these outliers because of their dominant productivity. The performance of the whole era they belonged to also has higher value because of their presence. Outliers change everything. Einstein opened a whole new way of thinking that accelerated schievements in Physics that persists today just as Orr changed the way d-men play forever. Both can be seen as having built on the work of previous outliers. In a very real sense these outliers made their eras outliers.

When you average eras so that their achievements are all equal, as a method of comparing them, you devalue the achievements of the eras and the outliers that led the way.

Gretzky was a superb offensive machine as Newton and Liebnitz were superb mathematicians. Nothing is going on today that compares to those eras. The unintended consequence of averaging the eras to compare them is to devalue the accomplishments of the outliers themselves. Hence averaging necessarily reduces the output of the best while increasing the output of the rest.

Removing the outliers does not solve this problem since they impacted the productivity of all their peers. Everybody learned something about offence from Gretzky and math from Gauss. You cannot remove their impact on their era by just removing their accomplishments.

I conclude that you can only really look at an outliers productivity in the context of the era they achieved. If anything their productivity should be increased to reflect the fact that their presence increased the productivity of their peers thus closing the true gap between them and their peers. I don't think its fair to reduce the value of their peers though.

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11-10-2012, 02:17 PM
  #287
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I'm not advocating using raw data to compare players across eras. I have suggested and given many examples of using percentages as a way of measuring productivity compared to peers in increasing sets of players to establish a range that a player might have achieved compared to peers in other eras.
Honestly, most of your % work was too confusing more me to follow. Some of it seemed very similar to adjusted stats though.

The problem with strictly using performance vs. peer group is that the quality of the peer group has changed substantially over time. The quality and depth of Howe's peers during his prime was likely much less than those during Gretzky's prime, etc.

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Originally Posted by Dalton View Post
I have also suggested using reason to complement mathematical estimates.
I definitely agree with that.

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Originally Posted by Dalton View Post
We can look at a measure of their production as a percentage of sets of peers in their eras and apply those to last year and see what shakes out. I did this with Howe and came up with some incredibly high number of goals but since we aren't actually trying to predict that shouldn't be an issue. I think the Howe result of over 300 goals is simply a reflection of just how dominating he was compared to his peers when he scored 49 goals.
Again, the quality (and distribution) of the peer group makes all the difference. The same quality of performance will appear much more dominating against a lesser quality group of peers.

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Originally Posted by Dalton View Post
Maybe AS shouldn't be trying to set a fixed, realistic looking number to use as a measure. That just makes it look like a prediction. Comparing to peers in their own eras and then comparing those results is a better approach IMHO.
The units aren't really important, but using a "realistic looking" number gives some kind of reference point... it's as good as any.

The peer comparison tells us nothing of comparative value. As far as comparing performances from different seasons, it doesn't tell us much unless we can confidently estimate the magnitude and nature of the change in quality of the peer groups.


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Originally Posted by Dalton View Post
Or maybe a precise definition of what AS is trying to achieve would work here. Honestly it really just looks like an attempt to predict actual GS and that clearly causes confusion. I don't see it as a measure of productivity either. What does 'value of gs' as an example actually mean. What is it trying to do?
I see two main uses for adjusted stats:

1. It gives a value estimate, based on the fixed proportion of production vs. scoring environment. 30 goals in a 6.00 gpg league should have about the same value as 40 goals in a 8.00 gpg league or 20 goals in a 4.00 gpg league. AS is perfect at this relatively simple function.

2. it is a potential starting point for comparing players' seasons, but it is complicated by many factors which affect the difficulty of attaining various levels of adjusted production in each season.

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Originally Posted by Dalton View Post
The lack of a dominant individual should not and cannot justifiably be an argument for devaluing the productivity of those from the past.
Be careful when using terms like "devaluing", because adjusted stats are very clear and useful when it comes to the value of production in each season. Where it's not so clear is when trying to determine which player-season was of higher quality/difficulty.

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Originally Posted by Dalton View Post
We see these outliers because of their dominant productivity. The performance of the whole era they belonged to also has higher value because of their presence. Outliers change everything. Einstein opened a whole new way of thinking that accelerated schievements in Physics that persists today just as Orr changed the way d-men play forever. Both can be seen as having built on the work of previous outliers. In a very real sense these outliers made their eras outliers.

When you average eras so that their achievements are all equal, as a method of comparing them, you devalue the achievements of the eras and the outliers that led the way.

Gretzky was a superb offensive machine as Newton and Liebnitz were superb mathematicians. Nothing is going on today that compares to those eras. The unintended consequence of averaging the eras to compare them is to devalue the accomplishments of the outliers themselves. Hence averaging necessarily reduces the output of the best while increasing the output of the rest.

Removing the outliers does not solve this problem since they impacted the productivity of all their peers. Everybody learned something about offence from Gretzky and math from Gauss. You cannot remove their impact on their era by just removing their accomplishments.

I conclude that you can only really look at an outliers productivity in the context of the era they achieved. If anything their productivity should be increased to reflect the fact that their presence increased the productivity of their peers thus closing the true gap between them and their peers. I don't think its fair to reduce the value of their peers though.
Most great accomplishment were achieved by standing on the shoulders of giants, that is true.

All I'm saying is that just because standard physics becomes inadequate when studying the very big (cosmology) or the very small (quantum physics), is no reason to discard it. Similarly, just because simple adjusted stats don't automatically tell us which player-season was of higher quality... or may have increased error when dealing with extreme outliers... does not mean they are inherently flawed and practically useless. They are perfectly good as a measure of value. I don't see any measure at this point that can tell us with nearly absolute confidence how production in different seasons varied in quality/difficulty. More study should be done in this area if that is the goal, but in the meantime I believe adjusted stats are as good as any metric in helping to assess that.

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11-10-2012, 07:12 PM
  #288
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Originally Posted by Czech Your Math View Post
Oates scored 142 in '93, which was very kind to high scoring players, didn't miss any of the 84 games, and played with Brett Hull.
Joe Juneau and Dmitri Kvartalnov, actually. He was a Bruin that year. Traded partway through the previous season.

Quote:
Nicholls scored 150 in '89, which again was a season that seemed to help high scoring players, missed only one game, and played on the same team as Gretzky, Robitaille, etc. Again, these players were mostly in the right place at the right time for their peak seasons (although put Hull & Oates in '82, and Oates likely hits 150), not superior to all players since.
Give Oates a full season in 1990-91 at the pace he was scoring and he hits 150. There's no question Oates was capable of the mark; their numbers together and apart are why I say that he had far more impact on Hull's numbers than Hull did on his. LaFontaine is obviously one to consider given his 148 with Mogilny in 1992-93.

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However, that's not the only way a player can put up an amazing total. Someone still needs to explain Maruk's 136 point campaign. He fit 2/3 criteria ('82 was THE peak season, and he didn't miss a game), but the only big name teammate was Gartner who scored only 80 points that year. Maruk never hit 100 points again, either before or after that season. I guess that sort of contradicts the whole "high scoring seasons help lower tier players more than higher scoring players" hypothesis.

However, I have no doubt that more bird shot will be sprayed into the sky in the hopes of actually hitting something.
Ryan Walter scored 87 points that year also, finishing second. Also noticeable is defenseman Darren Veitch (67 games, 53 points), who was actually a very skilled offensive defenseman. He comprised all of Washington's back-end offense, and played only ten games the next season - Maruk only scored 81 points. Veitch had played 59 in the year before (his rookie year), when Maruk scored 97. Looking at this, it seems like there was a sort of connection between the two, and with Veitch missing 70 games in 1982-83, Maruk's production dropped back to pre-Veitch levels.

So maybe if an already highly skilled player (Maruk was always at/above PPG with Washington) connects well with another talented player (Stamkos/Lecavalier with St.Louis, maybe?) and the league' scoring booms, it could happen. But that kind of connection is rare. Veitch certainly didn't connect with Yzerman that way despite performing well in Detroit (103pt in 153GP from the 1986 deadline through the end of the 87-88 season).

You can't simply take one example and say "anyone could have done it in that era" because 2nd-place career scorer Mark Messier has a career high of 129 points, and he was Gretzky's LW in 81-82 but posted a line of 50-38-88. It was his only 50-goal season.

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11-10-2012, 07:34 PM
  #289
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Originally Posted by eva unit zero View Post
Joe Juneau and Dmitri Kvartalnov, actually. He was a Bruin that year. Traded partway through the previous season.

Give Oates a full season in 1990-91 at the pace he was scoring and he hits 150. There's no question Oates was capable of the mark; their numbers together and apart are why I say that he had far more impact on Hull's numbers than Hull did on his. LaFontaine is obviously one to consider given his 148 with Mogilny in 1992-93.
Thanks for correction, forgot that Oates did that in Boston. Yes, that makes it even more impressive. It also only makes me more convinced that other players could have hit ~150 at least once, because I definitely believe there were better players as good or better than Oates & Lafontaine in their peaks/primes... and at least 10% better than Maruk... and 25% better point producers than Clarke, who spent much of his energy on defense & fighting and in the penalty box.

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Originally Posted by eva unit zero View Post
Ryan Walter scored 87 points that year also, finishing second. Also noticeable is defenseman Darren Veitch (67 games, 53 points), who was actually a very skilled offensive defenseman. He comprised all of Washington's back-end offense, and played only ten games the next season - Maruk only scored 81 points. Veitch had played 59 in the year before (his rookie year), when Maruk scored 97. Looking at this, it seems like there was a sort of connection between the two, and with Veitch missing 70 games in 1982-83, Maruk's production dropped back to pre-Veitch levels.
I'm not going to give much credence to the "Ryan Walter effect", esp. as Maruk outscored him by ~50 points. If Maruk could basically score 136 on his own, that doesn't exactly dissuade me from believing Sakic, Selanne, Forsberg, etc. and Ovechkin, Malkin, Crosby, etc. wouldn't have a good chance at some point if they played ~80s. I doubt anyone would have said "Ovechkin was pretty great that year... but then he did play with Ryan Walter." (no offense Mr. Walter).

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Originally Posted by eva unit zero View Post
So maybe if an already highly skilled player (Maruk was always at/above PPG with Washington) connects well with another talented player (Stamkos/Lecavalier with St.Louis, maybe?) and the league' scoring booms, it could happen. But that kind of connection is rare. Veitch certainly didn't connect with Yzerman that way despite performing well in Detroit (103pt in 153GP from the 1986 deadline through the end of the 87-88 season).

You can't simply take one example and say "anyone could have done it in that era" because 2nd-place career scorer Mark Messier has a career high of 129 points, and he was Gretzky's LW in 81-82 but posted a line of 50-38-88. It was his only 50-goal season.
I just don't see Gartner-Walter-Veitch as a Trottier-Potvin or Lemieux/Gretzky-Coffey type of set up. Gartner's a HOFer, but he wasn't exactly an elite point producer in his peak/prime years.

I didn't say anyone, I mentioned several of the greatest offensive players of the past 20 years... really some of the best in history... when players like Brett Hull, Bure, Fedorov, St. Louis, Iginla, Stamkos, etc. don't even make the "possible" list, then it's a rather select group who are given a good chance of possibly doing so. Messier would be around that level of adjusted peak/prime point production, not in the Sakic/Ovechkin group. If Messier could score 129 at age 29, w/o Gretzky, when there were many higher scoring seasons than that in the 80s... then again I believe there are better point producers who may have hit 150.

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11-10-2012, 11:01 PM
  #290
Iain Fyffe
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Originally Posted by Dalton View Post
AS fails to take into account these changes.

Every tree in every forest is treated the same regardless of the weather or human intervention.
Just like raw stats. Adjusted stats do not take everything into account, but they take some things into account that raw stats do not, which gives them their value.

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This is not a math problem.
You made it a math problem by making claims about the math that are simply wrong.

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Originally Posted by Dalton View Post
You are assuming that adjusted stats the answer. This is a huge problem in this debate. The assumption that AS is absolutely true and that if you don't buy into that and argue from that POV then you are (fill in the blank).
Massive misrepresentation. Many of us have discussed the flaws in the system, while pointing out that many of the flaws you say it has are not actually real.

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Again averaging fails.

Lose this mind set.
Again averaging does not mean what you seem to think it means. Lose this mindset.

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Originally Posted by Dalton View Post
This has been disproven in a massive study that included NHL left wingers gs.
Once again, that study does not say what you claim it says. We've been over this.

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Originally Posted by Dalton View Post
To accurately predict what Gretzky or Howe would have actually scored last year is problematic given that their presence in the league changed the way everybody plays.
Indeed, but since adjusted scoring does not make such predictions, it's not much of a problem. Again, we've been over this before.

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Originally Posted by Dalton View Post
Maybe AS shouldn't be trying to set a fixed, realistic looking number to use as a measure. That just makes it look like a prediction. Comparing to peers in their own eras and then comparing those results is a better approach IMHO.
Since adjusted scoring uses a player's results when playing against peers in their own era, this is exactly what adjusted scoring does. "Comparing to peers in their own eras and then comparing those results" is an excellent, succinct statement of what adjusted scoring does.

So what's the issue?

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Originally Posted by Dalton View Post
The unintended consequence of averaging the eras to compare them is to devalue the accomplishments of the outliers themselves. Hence averaging necessarily reduces the output of the best while increasing the output of the rest.
This is mathematically false. It would be the result if adjusted scoring actually normalized results, but of course, as we've been over and over again, adjusted scoring does not normalize.

Some of the best players have their output increased, and some decreased. Some of the lesser-tier players have their output increased, and some decreased. You're still hung up on the idea that normalization occurs. It does not.

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Originally Posted by Dalton View Post
I conclude that you can only really look at an outliers productivity in the context of the era they achieved. If anything their productivity should be increased to reflect the fact that their presence increased the productivity of their peers thus closing the true gap between them and their peers.
And indeed adjusted scoring does do this in a very small way. If you think it should be more, please provide something other that "it should be more".

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11-11-2012, 02:13 AM
  #291
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Originally Posted by Czech Your Math View Post
Thanks for correction, forgot that Oates did that in Boston. Yes, that makes it even more impressive. It also only makes me more convinced that other players could have hit ~150 at least once, because I definitely believe there were better players as good or better than Oates & Lafontaine in their peaks/primes... and at least 10% better than Maruk... and 25% better point producers than Clarke, who spent much of his energy on defense & fighting and in the penalty box.
I'm not disputing that it might have been possible for others to do it. But the fact remains that Yzerman did it, on a team where he had basically no offensive support; arguably less even than Maruk did. That's a pretty incredible feat. As I said before; it has been achieved three times without another player on the team cracking 100. Once each by Gretzky, Lemieux, and Yzerman. And further reducing the impact of Nicholls' and Esposito's 150+ seasons is the fact that the years they did it, they played with the Hart trophy winner.

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I'm not going to give much credence to the "Ryan Walter effect", esp. as Maruk outscored him by ~50 points. If Maruk could basically score 136 on his own, that doesn't exactly dissuade me from believing Sakic, Selanne, Forsberg, etc. and Ovechkin, Malkin, Crosby, etc. wouldn't have a good chance at some point if they played ~80s. I doubt anyone would have said "Ovechkin was pretty great that year... but then he did play with Ryan Walter." (no offense Mr. Walter).
How many points does a prime Yzerman score in 1982? He posted 155, 137, and 127 with pretty shoddy linemates. He was clearing 100 despite rolling in Murray's "three first-line center" system before 1992-93 saw a move back to more reliance on Yzerman and ultimately Carson being dealt.

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I just don't see Gartner-Walter-Veitch as a Trottier-Potvin or Lemieux/Gretzky-Coffey type of set up. Gartner's a HOFer, but he wasn't exactly an elite point producer in his peak/prime years.

I didn't say anyone, I mentioned several of the greatest offensive players of the past 20 years... really some of the best in history... when players like Brett Hull, Bure, Fedorov, St. Louis, Iginla, Stamkos, etc. don't even make the "possible" list, then it's a rather select group who are given a good chance of possibly doing so. Messier would be around that level of adjusted peak/prime point production, not in the Sakic/Ovechkin group. If Messier could score 129 at age 29, w/o Gretzky, when there were many higher scoring seasons than that in the 80s... then again I believe there are better point producers who may have hit 150.
Messier's 129 is his only season that comes close to comparing to Iginla's 2002 or 2008 in adjusted points. That season was also only a shade lower scoring than 1988-89, and Messier's 129 is a huge outlier for him - he was really a 105 (give or take) guy and not a 130 guy. Comparable to Maruk's huge year, in that a huge offensive year came out of nowhere, and then he went back to his "normal" production.

A far a adjusted points, only a handful of seasons since 1932 adjust to or above 124 points with a 6 GPG average (124 is what Nicholls adjusts to) that weren't already 150+ seasons. Those seasons? Phil Esposito in 1968-69, 1971-72, and 1973-74; Bobby Orr in 1969-70; Mario Lemieux 1996-97; Jaromir Jagr 1995-96, 1998-99, and 2000-01; and Joe Sakic in 2000-01. Malkin last year, Ovechkin in 2008, Crosby in 2007, and Selanne in 1999 adjust to 122 for basically as close as you get. Crosby in 2010-11 had 71 in 41, so he was on pace to break the mark. But "on pace" doesn't do it. And adjusted numbers are only an estimate; we have to still consider that Nicholls' 124 is pushed down by the presence of Lemieux's 199, Gretzky's 168, and Yzerman's 155. If you replace those three in calculations with "average" players based on the remaining players in the league, how does Nicholls adjust then?

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11-11-2012, 02:23 PM
  #292
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Originally Posted by eva unit zero View Post
I'm not disputing that it might have been possible for others to do it. But the fact remains that Yzerman did it, on a team where he had basically no offensive support; arguably less even than Maruk did. That's a pretty incredible feat. As I said before; it has been achieved three times without another player on the team cracking 100. Once each by Gretzky, Lemieux, and Yzerman. And further reducing the impact of Nicholls' and Esposito's 150+ seasons is the fact that the years they did it, they played with the Hart trophy winner.
You keep citing Yzerman's great '89 season, but I don't recall having said one thing negative ITT about Yzerman or his great season, so I'm not sure what you think this proves.

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Originally Posted by eva unit zero View Post
How many points does a prime Yzerman score in 1982? He posted 155, 137, and 127 with pretty shoddy linemates. He was clearing 100 despite rolling in Murray's "three first-line center" system before 1992-93 saw a move back to more reliance on Yzerman and ultimately Carson being dealt.
Value-wise it equates to ~171 points in '82. My best guess based on ES/PP points is that Yzerman may have scored ~163 points in '82 if he had similar circumstances to '89.

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Originally Posted by eva unit zero View Post
A far a adjusted points, only a handful of seasons since 1932 adjust to or above 124 points with a 6 GPG average (124 is what Nicholls adjusts to) that weren't already 150+ seasons. Those seasons? Phil Esposito in 1968-69, 1971-72, and 1973-74; Bobby Orr in 1969-70; Mario Lemieux 1996-97; Jaromir Jagr 1995-96, 1998-99, and 2000-01; and Joe Sakic in 2000-01. Malkin last year, Ovechkin in 2008, Crosby in 2007, and Selanne in 1999 adjust to 122 for basically as close as you get. Crosby in 2010-11 had 71 in 41, so he was on pace to break the mark. But "on pace" doesn't do it. And adjusted numbers are only an estimate; we have to still consider that Nicholls' 124 is pushed down by the presence of Lemieux's 199, Gretzky's 168, and Yzerman's 155. If you replace those three in calculations with "average" players based on the remaining players in the league, how does Nicholls adjust then?
One wouldn't need to score 124 adjusted points in '89 to have a chance at 150 at some point in the 80s.

I don't know what you mean by "pushed down". Intuitively, other higher scoring seasons makes Nicholls' season a bit less impressive. I may be understanding what you're asking, but if you removed those top 3 players' seasons, then it would lower the league avg. and increase Nicholls' adjusted PPG that season.

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11-11-2012, 10:40 PM
  #293
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Originally Posted by Iain Fyffe View Post
Again averaging does not mean what you seem to think it means.
*rimshot*

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Originally Posted by Czech Your Math View Post
You keep citing Yzerman's great '89 season, but I don't recall having said one thing negative ITT about Yzerman or his great season, so I'm not sure what you think this proves.

Value-wise it equates to ~171 points in '82. My best guess based on ES/PP points is that Yzerman may have scored ~163 points in '82 if he had similar circumstances to '89.

One wouldn't need to score 124 adjusted points in '89 to have a chance at 150 at some point in the 80s.

I don't know what you mean by "pushed down". Intuitively, other higher scoring seasons makes Nicholls' season a bit less impressive. I may be understanding what you're asking, but if you removed those top 3 players' seasons, then it would lower the league avg. and increase Nicholls' adjusted PPG that season.
Mike Bossy had an adjusted 108 in 1982, and Gretzky 156. That suggests that 110 is the mark for the 81-82 season. And in that case, Milan Hejduk and Vincent Lecavalier are members of the 150+ club. Lindros is in a couple times also. Plus a bunch of the guys you mentioned.

But Mark Messier - whose career high points season just barely misses it - played that year and only posted 50-38-88 while on Gretzky's LW, as I said. That's an adjusted 38-26-64; Messier's fifth-worst season, after his rookie year and his last three years. Ye, he was even better than that in Vancouver. So clearly the "drag and drop" argument doesn't work; different players work better in different eras and situations. For example, Derian Hatcher in the DPE. He wouldn't/didn't work well in the 80s/early 90s and didn't after the DPE.

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11-12-2012, 01:09 AM
  #294
Rhiessan71
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Thanks for correction, forgot that Oates did that in Boston. Yes, that makes it even more impressive. It also only makes me more convinced that other players could have hit ~150 at least once, because I definitely believe there were better players as good or better than Oates & Lafontaine in their peaks/primes... and at least 10% better than Maruk... and 25% better point producers than Clarke, who spent much of his energy on defense & fighting and in the penalty box.
You realise that both Oates and Lafontaine both played 84 games that year right?
On an 80's 80 game sched, Lafontaine only has a 141 raw and an adjusted 113 point season and Oates only has a 135 raw and 110 points adjusted.

And of course it's not at all suspicious that both of these guys just happen to have a spike in their scoring in the same year while members of the same division.
Hmmm...I wonder if something changed in their division that year like say...the 398 goal allowing Senator's coming in that both of them piled up 14 points in 7 games each against.
It's not like the scoring of the existing 5 teams in the Adam's division didn't spike by a whopping 23% from 91/92 to 92/93 or anything.

Took me all of 3 seconds to figure that out by looking at the story the raw numbers were saying.
But hey, lets just look at the Adjusted stats numbers without any other context and conclude those seasons were worth 150 in the 80's despite that the reasons they even scored that much that year (4 extra games and 7 games to beat the crap out of the Sens) wouldn't have even been in the mix for them.

So tell me, at the end of the day, which information would you consider more valuable in gauging the actual worth of Oates and Patty's 92/93 seasons? The story Adjusted Stats is telling you or the story the raw data is telling you?
Do you think AS's is giving you an accurate "value" of their points that year?

And again, I'm not doing this to bash AS's. Just stop trying to use them as the be end all or base so much, if not all of your final answers on them so often.
They definitely have their place but it sure as hell is not always going to be at the front of the line.


Last edited by Rhiessan71: 11-12-2012 at 02:04 AM.
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11-12-2012, 12:53 PM
  #295
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No, Xn actually appeared significant to me (Bn was almost 4x SEn). The least significant appeared to be Xp with Bp ~1.5x SEp. What's strange is that the individual correlations were:

Xn = 7%, Xp = 47%, Xe = 27%, and Xg = (-10%)

I thought Xn was coincidentally capturing a lot of the other variables, so I wanted to see what the coefficients looked like without Xn as one of the variables.
What are the correlations between those variables? I'd assume Xp is strongly correlated with them if it becomes the least significant variable once the others are included. That said, with 30 data points any t-stat above ~2 will be significant and the t-statistic on Bp seems to be 1.5*5.5 = 8.25 (square root of 30 = 5.5).


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What's the best way to judge models with a relatively stable Y? Just look at the significance of each individual coefficient or is there a better way of judging/comparing models in such cases?
I'm not an econometrician (I don't play one on TV either), but I know that R-square doesn't mean squat when no intercept is included in the model. Was there one in yours?

I have seen a measure such as 'incremental R-square' i.e. (new-old)/old where 'new' is the R2 from the full model and 'old' is the one with only an intercept or something.

In models with stable time series, people often calculate first differences i.e. Y'(1985) = Y(1985) - Y(1984) and run the model on those changes instead of the level. It changes the narrative because 'last year' is the benchmark for each observation but since your objective is often 'what makes Y change' it works. There's a deeper econometric(al?) reason that justifies first differences as well.

I'll try to find time to look at the other thread too.

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11-12-2012, 03:03 PM
  #296
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You realise that both Oates and Lafontaine both played 84 games that year right?
On an 80's 80 game sched, Lafontaine only has a 141 raw and an adjusted 113 point season and Oates only has a 135 raw and 110 points adjusted.
Wait... so it's okay to adjust for schedule?

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And of course it's not at all suspicious that both of these guys just happen to have a spike in their scoring in the same year while members of the same division.
Hmmm...I wonder if something changed in their division that year like say...the 398 goal allowing Senator's coming in that both of them piled up 14 points in 7 games each against.
It's not like the scoring of the existing 5 teams in the Adam's division didn't spike by a whopping 23% from 91/92 to 92/93 or anything.

Took me all of 3 seconds to figure that out by looking at the story the raw numbers were saying.
But hey, lets just look at the Adjusted stats numbers without any other context and conclude those seasons were worth 150 in the 80's despite that the reasons they even scored that much that year (4 extra games and 7 games to beat the crap out of the Sens) wouldn't have even been in the mix for them.
You really showed me. It took me a whole 3 minutes to look at the game logs for Oates & Lafontaine that season. They each scored 14 points in 7 games vs. Ottawa:

Lafontaine
total: 1.76 PPG (148 Pts)
vs. all but Ottawa: 1.74 PPG (146 Pts/84)

Oates
total: 1.69 PPG (142)
vs. all but Ottawa: 1.66 PPG (140/84)

So their PPGs increased by 1.2-1.7% due to Ottawa being in their division... yet league scoring increased by over 4% from '92. You've really convinced me now that no players since could match or surpass their totals!

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So tell me, at the end of the day, which information would you consider more valuable in gauging the actual worth of Oates and Patty's 92/93 seasons? The story Adjusted Stats is telling you or the story the raw data is telling you?
Do you think AS's is giving you an accurate "value" of their points that year?
It depends on what you mean by "value." If you want to examine how valuable their seasons were in terms of offensive contribution to winning, then adjusted points (or adj. goals created) would be about as perfect an indicator as possible.

If you want to determine whether Lafontaine's 148 in '93 was "better" or "more difficult" than, say, Ovechkin's '08 season... then adjusted stats are to me the best starting point, before looking at other factors which may influence those numbers.

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Originally Posted by Rhiessan71 View Post
And again, I'm not doing this to bash AS's. Just stop trying to use them as the be end all or base so much, if not all of your final answers on them so often.
They definitely have their place but it sure as hell is not always going to be at the front of the line.
They are the be all & end all in terms of calculating actual offensive value. They are the base for further adjustment and/or examination, as the best estimate before further info is included. They are at the front of the line, because they are objective numbers which reflect actual value and the best starting place forf estimating quality/difficulty of individual seasons. Those are basically my opinions on the matter, and you're free to disagree, and you often do.

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11-12-2012, 03:15 PM
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What are the correlations between those variables? I'd assume Xp is strongly correlated with them if it becomes the least significant variable once the others are included. That said, with 30 data points any t-stat above ~2 will be significant and the t-statistic on Bp seems to be 1.5*5.5 = 8.25 (square root of 30 = 5.5).
I haven't calculated cross-correlations between the variables, but would expect all 4 to have substantial correlations to one another (including negative correlations with Xg), because the changes in each variable are relatively contemporaneous (all of them tended to occur in the 90s... after the 80s and relatively constant after 90s).

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I'm not an econometrician (I don't play one on TV either), but I know that R-square doesn't mean squat when no intercept is included in the model. Was there one in yours?
I was trying to include an intercept [using LINEST in Excel with paramaters (Y range, X ranges, false, true) ], but the intercept calculated as zero. I'll have to check that again, perhaps the false should be a true (but I thought it said that parameter was B = 0, so I entered that as false).

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In models with stable time series, people often calculate first differences i.e. Y'(1985) = Y(1985) - Y(1984) and run the model on those changes instead of the level. It changes the narrative because 'last year' is the benchmark for each observation but since your objective is often 'what makes Y change' it works. There's a deeper econometric(al?) reason that justifies first differences as well.

I'll try to find time to look at the other thread too.
Yes, I thought about calculating differences first, as I did in an unrelated model. Do you think % (ratio) differences would be better than raw differences?

Please do look at my other post if you have time at some point. It's not a whole thread, just a post with questions in a stick thread titled "Ideas for Future Studies" on this (BTN) sub-forum. I think the model I was trying to create, or a similar, workable version of such, would be the best solution in the longer term, but obviously we need a model where coefficients will generate.

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11-12-2012, 04:12 PM
  #298
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Wait... so it's okay to adjust for schedule?
When you're trying to project an 84 game season total into an 80 game season total...



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You really showed me. It took me a whole 3 minutes to look at the game logs for Oates & Lafontaine that season. They each scored 14 points in 7 games vs. Ottawa:

Lafontaine
total: 1.76 PPG (148 Pts)
vs. all but Ottawa: 1.74 PPG (146 Pts/84)

Oates
total: 1.69 PPG (142)
vs. all but Ottawa: 1.66 PPG (140/84)

So their PPGs increased by 1.2-1.7% due to Ottawa being in their division... yet league scoring increased by over 4% from '92. You've really convinced me now that no players since could match or surpass their totals!
There's more to it than that though. Take 3 more seconds and look over the teams in the Adam's division that year. It wasn't just Oates, the Bruins and Lafontaine, the Sabres. Look at the amount of players also on the Habs, Nords and Whalers that posted career years or pretty much matched their previous career years in 92/93. I'm not just talking about slightly better than their norm kinda thing either, most of them spiked well above anything they had done before or after.
It's like 2-4 players per team for pete's sake and again, Adam's division scoring increased by 23% not the league 4%.
Sundin(21% better), Ricci(39%), Lafontaine(41%), Mogilny(19%), Damphousse (3%), Muller(matched his career high), Lebeau(38%), Oates(23%), Juneau(42%), Sanderson(33%), Cassels(25%), Zalapski(14%).
The list goes on and on for that year in that division.
You can't just ignore this many concentrated anomalies. It has to be accounted for before you can simply say Adam's and Pat's season are worth 150 in the 80's because the value Adjusted Stats assigns those points, says so.
That's ridiculous, seriously.


Quote:
It depends on what you mean by "value." If you want to examine how valuable their seasons were in terms of offensive contribution to winning, then adjusted points (or adj. goals created) would be about as perfect an indicator as possible.

If you want to determine whether Lafontaine's 148 in '93 was "better" or "more difficult" than, say, Ovechkin's '08 season... then adjusted stats are to me the best starting point, before looking at other factors which may influence those numbers.



They are the be all & end all in terms of calculating actual offensive value. They are the base for further adjustment and/or examination, as the best estimate before further info is included. They are at the front of the line, because they are objective numbers which reflect actual value and the best starting place forf estimating quality/difficulty of individual seasons. Those are basically my opinions on the matter, and you're free to disagree, and you often do.
But you're not just using them as a starting point are you! You're using them as the start and the finish and THAT is my whole problem with it all in the first place.

Again, for hopefully the last time...it's not so much the math or the value that AS's assigns that is flawed(even though it most certainly is in the way it handles the top 1% and outliers). It's the value that AS's gets in the equation far too often, that is.
There has to be context!


You keep saying there are all these indications that it could be done yet ignore the indicators that say it wouldn't like Dionne, Lafleur, Bossy and Stastny who are as good or better than anyone you mentioned and each of them had better help and sometimes far superior circumstances to do it but didn't.


Last edited by Rhiessan71: 11-12-2012 at 04:24 PM.
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Old
11-12-2012, 04:29 PM
  #299
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Originally Posted by Rhiessan71 View Post
When you're trying to project an 84 game season total into an 80 game season total...
AS adjusts for season length; each game is calculated as a percentage of the season. The season could be 20 games or 100 games, and two player with adjusted 70 points would be considered to have had equivalent performances by that measure, before considering things such as teammates, missed games, etc.

Yzerman' 87-88 and 93-94 seasons are good examples of "missed games" years. He posted 50-52-102 in 64 games in 87-88 before wrecking his knee on a goal post in that 64th game. Pro-rated to 80, it' 63-65-128 (and fourth in scoring). Adjusted stats give us 42-43-85 for those 64 games; pro-rated to 53-54-107 in a full 80. In 1993-94, he posted 24-58-82 in 58; pro-rated to 35-84-119 (and 3rd in scoring) in 84, adjusted to 22-53-75. Pro-rate the AS to 84 and he's at 32-77-109; his third best year for AS after 89 and 93.


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11-12-2012, 04:45 PM
  #300
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Originally Posted by Rhiessan71 View Post
When you're trying to project an 84 game season total into an 80 game season total...
All I said was that based on such production as Lafontaine & Oates
in '93 (and other player-seasons) that I see ~150 points as attainable by some more recent players at some point(s) in their career. Laftonaine scoring 141/80 doesn't really change my opinion.

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Originally Posted by Rhiessan71 View Post
There's more to it than that though. Take 3 more seconds and look over the teams in the Adam's division that year. It wasn't just Oates, the Bruins and Lafontaine, the Sabres. Look at the amount of players also on the Habs, Nords and Whalers that posted career years or pretty much matched their previous career years in 92/93. I'm not just talking about slightly better than their norm kinda thing either, most of them spiked well above anything they had done before or after.
It's like 2-4 players per team for pete's sake and again, Adam's division scoring increased by 23% not the league 4%.

The list goes on and on for that year in that division.
You can't just ignore this many concentrated anomalies. It has to be accounted for before you can simply say Adam's and Pat's season are worth 150 in the 80's because the value Adjusted Stats assigns those points, says so.
That's ridiculous, seriously.
You attributed the increase for Oates & Lafontaine to Ottawa's presence, but this reason appears to have been refuted. There were other reasons that many stars saw increases in their PPG that season. Oates & Lafontaine's production equates to ~135-140+/80 at the height of the 80s in terms of value, the only question is what is the fairest estimate of the quality/difficulty of that level of production in comparison to ~150 in '82. Simple adjusted stats are the best estimate, the agreed upon base summit, until higher ground is reached. Until the direction and magnitude of changes due to various reasons are determined, I don't see how one can properly arrive at a better estimate. I believe that at some point better estimates may be calculated.

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But you're not just using them as a starting point are you! You're using them as the start and the finish and THAT is my whole problem with it all in the first place.

Again, for hopefully the last time...it's not so much the math or the value that AS's assigns that is flawed. It's the value that AS's gets in the equation far too often, that is.
There has to be context!
I give value to other things besides adjusted points. It seems the detractors of adjusted stats look for flaws in its context and disagree with the significance others may place on them in their evaluations of forwards, yet they weight much more flawed (IMO) data with almost no thought to the vast differences in context for rankings, awards, team success, etc. I'm not ranking players based on a single season of adjusted stats, but based on multiple seasons in multiple categories.

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