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Old
07-21-2010, 04:14 PM
  #26
Doctor No
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Originally Posted by Canadiens1958 View Post
Pythagorean metric disagrees with you very strongly
No. The Pythagorean metric doesn't disagree with me in the slightest. In fact, it agrees with me 100%.

Consider a league where the average goals scored is 200 per season. The incremental value of an additional 50 goals is:

(250)^2 / [(250)^2 + (200)^2] = 61.0% winning percentage.

Now consider a league where the average goals scored is 300 per season. The incremental value of an additional 50 goals is:

(350)^2 / [(350)^2 + (300)^2] = 57.6% winning percentage.

This is using the most basic version of the Pythagorean theorem, but every version supports my claim.

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07-21-2010, 05:03 PM
  #27
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Originally Posted by TheDevilMadeMe View Post
Thanks for taking the time to do this. The numbers using this system do pass the smell test, I think, unlike the previous adjusted points that keep being thrown around.

With the one caveat, of course, that they are only relevant for Top 10 scorers.
Just to be clear, it's not top 10 scorers, it's the top 10% so it's around 60 players used in the 80's and 80 players used in the 00's. But you are absolutely right that it's only relevant for that group. However, this is the group that are mostly discussed here.

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07-21-2010, 05:15 PM
  #28
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Originally Posted by Canadiens1958 View Post
Using your example. You adjusted the scoring because you had an agenda to show nineties scoring in a different light. But did you adjust the resulting goaltending numbers? Defensive numbers? No you did not.
First of all, I did not have an agenda. On the contrary I changed my previous opinion when I saw this new numbers. I use these adjustments to explore and test my preconceived notions rather than try to make them "fit my agenda" (whatever that may be).

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Originally Posted by Canadiens1958
Be it today, 1982-83 or earlier the real value of 50 goals is in the number of wins that can be bought after the goals against are factored out.
Yes, and it's clear that a goal scored in a high scoring environment is less likely to lead to a win than in a low scoring environment. In every game there is one and only one game winning goal. That means the ratio of total goals to game winning goals was lower in the 80s than today.

But you are right of course that comparing players from different eras is fundamentally impossible since it all depends on the surrounding environment. But that is equally true if we use adjusted numbers or try to rank players in any other way. But that does not deter us from trying.

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07-21-2010, 05:24 PM
  #29
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Originally Posted by Rhiessan71 View Post
Ok found what I was looking for.
League scoring average per game:
95/96 = 6.29 goals per game
05/06 = 6.05

I was trying to find a post lockout year that was closest in overall scoring to a relatively healthy 95/96 Mario that was for all intent and purposes still in his prime.

Joe Thornton led the league in scoring in 05/06 with 125 points in 81 games or 1.54 ppg (127 over 82)
Lemieux led the league in scoring in 95/96 with 161 points in 70 games or 2.3 ppg (189 over 82)

This is why I don't believe Mario and Gretzky would actually be capped in the 150-165 range in today's NHL.

You also have to take into account that while the the "Dead puck" era wasn't quite in full swing yet, there was still a hell of a lot more clutching, grabbing and dead puck era crap going on in 95/96 than in 05/06 which to me only makes Mario's totals even more impressive.

It most definitely does not jive with the only 135 adjusted point total for 95/96 in the first chart imo.

Now, I'm not saying those charts aren't a pretty decent indicator for most players.
I just don't think it works well with the freakish anomalies known as Gretzky and Lemieux. They are just too far above anyone else imo.
First of all, that 135 points is for 70 games. Second, Mario's 95/96 season is one of those most punished by the adjustment I made. The reason is that in that season top-end players stood for a much larger share of point totals than in other comparable seasons. Using the adjustment you did (comparable to the "All adj." column) that would be better than any season by Gretzky and I'm not sure I'm buying that.

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07-21-2010, 06:00 PM
  #30
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I still think what you have done is a much better estimate than the other adjusted stats.

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07-21-2010, 06:04 PM
  #31
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Originally Posted by matnor View Post
First of all, that 135 points is for 70 games. Second, Mario's 95/96 season is one of those most punished by the adjustment I made. The reason is that in that season top-end players stood for a much larger share of point totals than in other comparable seasons. Using the adjustment you did (comparable to the "All adj." column) that would be better than any season by Gretzky and I'm not sure I'm buying that.
No, you're absolutely right, my loose interpretation isn't very accurate either.
To me it just reaffirms my point that Lemieux and especially Gretzky simply can't be "boxed" properly.
Using the rest of the league in the formula and applying it to those two suggests to me you're trying to normalize what is in essence the abnormal.
Just like I don't think it's fair to include Gretzky and Lemieux in the formula to determine the rest of the players.
Not only does wide normalization take away from Wayne and Mario but also serves to buff the numbers of the rest.
Know what I'm saying?


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07-21-2010, 06:08 PM
  #32
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Originally Posted by matnor View Post
Just to be clear, it's not top 10 scorers, it's the top 10% so it's around 60 players used in the 80's and 80 players used in the 00's. But you are absolutely right that it's only relevant for that group. However, this is the group that are mostly discussed here.
OH right. Basically your stereotypical "first liners."

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07-21-2010, 06:29 PM
  #33
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Completing the Example

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Originally Posted by Doctor No View Post
No. The Pythagorean metric doesn't disagree with me in the slightest. In fact, it agrees with me 100%.

Consider a league where the average goals scored is 200 per season. The incremental value of an additional 50 goals is:

(250)^2 / [(250)^2 + (200)^2] = 61.0% winning percentage.

Now consider a league where the average goals scored is 300 per season. The incremental value of an additional 50 goals is:

(350)^2 / [(350)^2 + (300)^2] = 57.6% winning percentage.

This is using the most basic version of the Pythagorean theorem, but every version supports my claim.

Let's take the league above to its logical conclusion. Taking the 200 as the average then one should also look at the alternative scenario, the value of giving up 50 less goals. Effectively:

(200)^2 / [(200)^2 + (150)^2] = 64%

Which explains why the NHL coaches went back to a defensive mode.The value of the 50 fewer goals that a team allows is higher than the value of the 50 more goals that it may score. 3% greater expectation of winning at (200/150) than at (250/200). Even at the midpoint (225/175) its 62.3%.

The goal that a team scores is worth less than a goal it prevents, a truism that holds all the time.

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07-21-2010, 06:32 PM
  #34
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Originally Posted by Canadiens1958 View Post
Let's take the league above to its logical conclusion. Taking the 200 as the average then one should also look at the alternative scenario, the value of giving up 50 less goals. Effectively:

(200)^2 / [(200)^2 + (150)^2] = 64%

Which explains why the NHL coaches went back to a defensive mode.The value of the 50 fewer goals that a team allows is higher than the value of the 50 more goals that it may score. 3% greater expectation of winning at (200/150) than at (250/200). Even at the midpoint (225/175) its 62.3%.

The goal that a team scores is worth less than a goal it prevents, a truism that holds all the time.
No kidding. So your argument boils down to "because of this unrelated thing, which happens to be true, your argument is false."

The Pythagorean Theorem does not disagree with what I said (strongly or otherwise). YOU SAID THAT IT DID. The fact that it also supports what you're talking about DOES NOT MAKE WHAT I SAID INCORRECT.

Are we clear?

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07-21-2010, 07:27 PM
  #35
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Originally Posted by Canadiens1958 View Post
Let's take the league above to its logical conclusion. Taking the 200 as the average then one should also look at the alternative scenario, the value of giving up 50 less goals. Effectively:

(200)^2 / [(200)^2 + (150)^2] = 64%

Which explains why the NHL coaches went back to a defensive mode.The value of the 50 fewer goals that a team allows is higher than the value of the 50 more goals that it may score. 3% greater expectation of winning at (200/150) than at (250/200). Even at the midpoint (225/175) its 62.3%.

The goal that a team scores is worth less than a goal it prevents, a truism that holds all the time.
But to "balance your equation" to put it mathematically, you must look at this from your opponents perspective as well. A goal you score may be worth less than one you prevent, but therefore logic dictates that a goal surrendered by the other team is more detrimental to their cause than one they score themselves is beneficial. Since you are only playing one other team, by increasing their chances of losing, you have automatically increased your chances of winning.

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Old
07-21-2010, 09:48 PM
  #36
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Originally Posted by Kyle McMahon View Post
But to "balance your equation" to put it mathematically, you must look at this from your opponents perspective as well. A goal you score may be worth less than one you prevent, but therefore logic dictates that a goal surrendered by the other team is more detrimental to their cause than one they score themselves is beneficial. Since you are only playing one other team, by increasing their chances of losing, you have automatically increased your chances of winning.
Yes, any given goal has a zero-sum value when comparing two opponents within the same game. But for a given team, the "Pythagorean metric" states that, on average, a goal prevented is more valuable than a goal scored. Let's translate that to a specific game situation.

Add a single goal to a team's seasonal total. Randomly select which game that goal will be added to. Then remove a single goal from that team's (original) seasonal total. The goal that was removed is (very very slightly) more likely to make a difference in the outcome of a game than the goal that was added, because an added goal may just tack on an extra goal in a blowout. This slight advantage adds up when you are talking 50 goals added vs 50 goals prevented.

The fact that there is a limit on goal prevention but there is no limit on goal scoring means that on average, a goal prevented is slightly more valuable than a goal scored.

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07-21-2010, 10:42 PM
  #37
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Originally Posted by overpass View Post
Yes, any given goal has a zero-sum value when comparing two opponents within the same game. But for a given team, the "Pythagorean metric" states that, on average, a goal prevented is more valuable than a goal scored. Let's translate that to a specific game situation.

Add a single goal to a team's seasonal total. Randomly select which game that goal will be added to. Then remove a single goal from that team's (original) seasonal total. The goal that was removed is (very very slightly) more likely to make a difference in the outcome of a game than the goal that was added, because an added goal may just tack on an extra goal in a blowout. This slight advantage adds up when you are talking 50 goals added vs 50 goals prevented.

The fact that there is a limit on goal prevention but there is no limit on goal scoring means that on average, a goal prevented is slightly more valuable than a goal scored.
Why is this the case? The removed goal may be taken away from a blowout as well, or from a game that would be lost regardless.

If I'm understanding correctly, you're basically saying, take a team with a 200 GF/100 GA ratio. Going to 201/100 gives a very slightly lower expected win% than going to 200/99. Alright, I understand this, and yes it works when isolating a single team. But like in a single game, is this balance not off-set by an opponent's end of season expected win % being slightly changed for the worse? Therefore ever so slightly increasing the chances of being ahead of them in the standings?

I'll run the numbers...

Example A:
200 GF / 100 GA team = 80% expected win %
100 GF / 200 GA team = 20% expected win %

Net total is even, with a total 100 % expected winning %

With a random goal added:

Example B:
201 GF / 100 GA = 80.16%
100 GF / 201 GA = 19.84%

One taken away:

Example C:
200 GF / 99 GA = 80.32%
99 GF / 200 GA = 19.68%

Hmmm...alright, it appears you are correct. Though you could also say that the value of scoring another goal in Example C is equal to the same value as preventing an extra one in Example B...now I'm just confused. And perhaps I didn't use the correct mathematical model to demonstrate the point I was trying to make...

Edit: I just had another thought. Throwing in one extra goal is guaranteed to increase your odds of winning in every game, so its value is always divided amongst 82 games. But if you recorded five shutouts for example, the value of an extra goal prevented would divide amongst 77 games, since you cannot prevent another goal in a game in which you allowed zero to begin with. This is just illustrating your point that there is a limit on GA, but not on GF. Perhaps now I am on the right track.


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Old
07-21-2010, 11:17 PM
  #38
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Simple

Kyle,

The simplest approach is to look at a .500 team over the course of a season. A .500 team that has exactly the same number of wins as loses and has scored exactly as many goals as it has given up. No loser points or ties.

If the team is to improve(>.500) which approach should it favour, one that will allow it to score x more goals while keeping the GA at the exact same number or reduce the number of goals allowed by x while scoring exactly the number of goals?

Regardless of what your starting point is where GF = GA and regardless of what the x is the Pythagorean Expectation will always show that the x reducing the number of goals allowed has more value - generates more win potential than if the x is applied to goals for.

That is why defense is the prevailing choice of coaches in any sport.


Last edited by Canadiens1958: 07-21-2010 at 11:18 PM. Reason: Addition
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07-21-2010, 11:25 PM
  #39
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Quote:
Originally Posted by Canadiens1958 View Post
Kyle,

The simplest approach is to look at a .500 team over the course of a season. A .500 team that has exactly the same number of wins as loses and has scored exactly as many goals as it has given up. No loser points or ties.

If the team is to improve(>.500) which approach should it favour, one that will allow it to score x more goals while keeping the GA at the exact same number or reduce the number of goals allowed by x while scoring exactly the number of goals?

Regardless of what your starting point is where GF = GA and regardless of what the x is the Pythagorean Expectation will always show that the x reducing the number of goals allowed has more value - generates more win potential than if the x is applied to goals for.

That is why defense is the prevailing choice of coaches in any sport.
The only problem with this theory is that you could have 0 GA and never win a game if you don't score.

Yes defense improves your odds but at the end of the day you still need to score more than your opposition no matter what the GA.

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07-22-2010, 12:24 AM
  #40
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Quote:
Originally Posted by Canadiens1958 View Post
Kyle,

The simplest approach is to look at a .500 team over the course of a season. A .500 team that has exactly the same number of wins as loses and has scored exactly as many goals as it has given up. No loser points or ties.

If the team is to improve(>.500) which approach should it favour, one that will allow it to score x more goals while keeping the GA at the exact same number or reduce the number of goals allowed by x while scoring exactly the number of goals?

Regardless of what your starting point is where GF = GA and regardless of what the x is the Pythagorean Expectation will always show that the x reducing the number of goals allowed has more value - generates more win potential than if the x is applied to goals for.

That is why defense is the prevailing choice of coaches in any sport.
Yes, I understand this part of the concept clearly.

I think I'm starting to wrap my head around some of my own questions now after much thought...

When a goal is taken away, the number of total goals in the league is reduced, which increases the individual value of a single goal in relation to the starting point. Your GF total has remained the same, but its value has increased. Meanwhile somebody else has been robbed of a goal, which is now slightly more valuable.

When a goal is added, the value of a goal is reduced. You gain less of an advantage, and the surrendering team is less punished.

So the net effect on the league is still the same, but from an individual coach's perspective, one is better than the other, which was your point to begin with. And now it's time to give my overheating brain a rest...

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Old
07-22-2010, 12:26 AM
  #41
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It's a step in the right direction, yet there are many more steps and improvements that can be made. League-wide scoring is one way to adjust, the scoring of the top 10% is another, and there are countless other possibilities.

Many recognize that the top scorers in the '80s scored less on an adjusted basis than did those of the '70s or than those in more recent years. It's important to explore the reasons for that, which can be vastly different for each era.

The '70s saw drastic expansion and talent concentrated among a few O6 powers. This greatly inflated the adjusted numbers of all the top scorers. The dead puck era saw gradual, yet significant expansion, coinciding with an increasing influx of overseas talent. This talent was not evenly distributed between positions and skill levels, but especially concentrated among top end forwards. This produces a substantial compression effect among top scorers.

As an example of the effect of overseas talent, take the '96 season:

The first liners (26 teams x 3 = top 78 scorers) scored an average of 81.1 points. The top 78 North American scorers averaged 72.9 points. The top 78 scorers averaged 11% higher when including overseas players, that's a very substantial difference. If you calculated the difference in the '80s, it's likely about 1%.

I don't see how one can lump the 70's with the 90's, they were completely different in terms of effects (change in actual scoring levels) and causes (drastic expansion and talent dilution/decompression as opposed to gradual expansion and talent influx/compression). The 70's featured an increase in scoring, despite the presence of at least 50% of the teams/players being inferior and unable to score at anywhere near the pace of the best established teams/players. The 90's featured the largest influx of scoring talent in modern history, yet there was a substantial reduction in league-wide scoring. They are totally different eras.

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07-22-2010, 01:26 AM
  #42
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Quote:
Originally Posted by Canadiens1958 View Post
Kyle,

The simplest approach is to look at a .500 team over the course of a season. A .500 team that has exactly the same number of wins as loses and has scored exactly as many goals as it has given up. No loser points or ties.

If the team is to improve(>.500) which approach should it favour, one that will allow it to score x more goals while keeping the GA at the exact same number or reduce the number of goals allowed by x while scoring exactly the number of goals?

Regardless of what your starting point is where GF = GA and regardless of what the x is the Pythagorean Expectation will always show that the x reducing the number of goals allowed has more value - generates more win potential than if the x is applied to goals for.

That is why defense is the prevailing choice of coaches in any sport.
To your last point, defense is easier to teach than offense as well.

Defense comes down to systems and team play, while offense is a much more creative and instinctive and a less predictible factor that coaches can influence.

I know this from both playing and coaching sports, I can't create better eye hand coordination but i can aply angles on defense and we can play systems in preventing teams from gaining the line are the most obvious examples here.

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07-22-2010, 01:36 AM
  #43
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Quote:
Originally Posted by Czech Your Math View Post
It's a step in the right direction, yet there are many more steps and improvements that can be made. League-wide scoring is one way to adjust, the scoring of the top 10% is another, and there are countless other possibilities.

Many recognize that the top scorers in the '80s scored less on an adjusted basis than did those of the '70s or than those in more recent years. It's important to explore the reasons for that, which can be vastly different for each era.

The '70s saw drastic expansion and talent concentrated among a few O6 powers. This greatly inflated the adjusted numbers of all the top scorers. The dead puck era saw gradual, yet significant expansion, coinciding with an increasing influx of overseas talent. This talent was not evenly distributed between positions and skill levels, but especially concentrated among top end forwards. This produces a substantial compression effect among top scorers.

As an example of the effect of overseas talent, take the '96 season:

The first liners (26 teams x 3 = top 78 scorers) scored an average of 81.1 points. The top 78 North American scorers averaged 72.9 points. The top 78 scorers averaged 11% higher when including overseas players, that's a very substantial difference. If you calculated the difference in the '80s, it's likely about 1%.

I don't see how one can lump the 70's with the 90's, they were completely different in terms of effects (change in actual scoring levels) and causes (drastic expansion and talent dilution/decompression as opposed to gradual expansion and talent influx/compression). The 70's featured an increase in scoring, despite the presence of at least 50% of the teams/players being inferior and unable to score at anywhere near the pace of the best established teams/players. The 90's featured the largest influx of scoring talent in modern history, yet there was a substantial reduction in league-wide scoring. They are totally different eras.
Some really good points here and I think that the point of the discussion is that adjusted stats are a better starting point in comaring player A's season from lets say 1982 to player B's season in 2005.

The "actual " stats in any given year can only be used to compare players within that given year, along with other factors like team style for instance.

Adjusted stats either from the hockey reference site or as listed here give a much better template and starting point in comparing the 2 above mentioned players in some context.

There is no agenda other than trying to get a somewaht objective starting point to compare different players seasons to each other over time and need to be used in conjunction with as much information about the particlaur players and teams and league during those seasons as well.

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07-22-2010, 01:44 AM
  #44
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Adjustments

Quote:
Originally Posted by Czech Your Math View Post
It's a step in the right direction, yet there are many more steps and improvements that can be made. League-wide scoring is one way to adjust, the scoring of the top 10% is another, and there are countless other possibilities.

Many recognize that the top scorers in the '80s scored less on an adjusted basis than did those of the '70s or than those in more recent years. It's important to explore the reasons for that, which can be vastly different for each era.

The '70s saw drastic expansion and talent concentrated among a few O6 powers. This greatly inflated the adjusted numbers of all the top scorers. The dead puck era saw gradual, yet significant expansion, coinciding with an increasing influx of overseas talent. This talent was not evenly distributed between positions and skill levels, but especially concentrated among top end forwards. This produces a substantial compression effect among top scorers.

As an example of the effect of overseas talent, take the '96 season:

The first liners (26 teams x 3 = top 78 scorers) scored an average of 81.1 points. The top 78 North American scorers averaged 72.9 points. The top 78 scorers averaged 11% higher when including overseas players, that's a very substantial difference. If you calculated the difference in the '80s, it's likely about 1%.

I don't see how one can lump the 70's with the 90's, they were completely different in terms of effects (change in actual scoring levels) and causes (drastic expansion and talent dilution/decompression as opposed to gradual expansion and talent influx/compression). The 70's featured an increase in scoring, despite the presence of at least 50% of the teams/players being inferior and unable to score at anywhere near the pace of the best established teams/players. The 90's featured the largest influx of scoring talent in modern history, yet there was a substantial reduction in league-wide scoring. They are totally different eras.

Re the characterization of the 1970's - the NHL powers in the 1970's included the Flyers, Sabres, Islanders who were not O6 teams. The Canadiens and Bruins were O6 teams that were still powers.

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07-22-2010, 02:04 AM
  #45
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Why are people still coming out with versions of adjusted points, when the version on hockey-reference.com works fine?

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07-22-2010, 02:06 AM
  #46
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Not Really

Quote:
Originally Posted by Hardyvan123 View Post
To your last point, defense is easier to teach than offense as well.

Defense comes down to systems and team play, while offense is a much more creative and instinctive and a less predictible factor that coaches can influence.

I know this from both playing and coaching sports, I can't create better eye hand coordination but i can aply angles on defense and we can play systems in preventing teams from gaining the line are the most obvious examples here.
Not really, all you have shown is that most coaches do not know how to teach offense.

The accepted truism in football was that you could not teach offense until Don Coryell and Bill Walsh showed that it was possible.

Your line about angles illustrates this quite readily, just a question of finding the appropriate angles that will shred your defense. Peyton Manning did this a few years ago on a Sunday night against a new, revolutionary Denver defense. Took a couple of series then shredded them for seven or eight scoring drives. Rest of the NFL saw how it was done and goodbye new Denver defense.

Hockey is rather simple if a forward understands defense then he understands offense since they mirror each other.

If you explain to a kid that the key to defense is preventing a certain angle to the net then any kid that is moderately alert figures out that that the key to offense is taking that angle to the net when on offense. This reciprocal relationship holds in all the other aspects of hockey. If you tell players to force the other team's players to the useless ice or perimeter in the defense zone then the players should be astute enough to understand that when they are in the offensive zone then they have to avoid the useless ice and perimeter and crash the crease and the slot.

Getting the players to apply these facts or pay the price is another matter.

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07-22-2010, 02:06 AM
  #47
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Originally Posted by seventieslord View Post
Why are people still coming out with versions of adjusted points, when the version on hockey-reference.com works fine?
Not sure as it's only a starting point, an important basis to compare to be sure, not the end point of comparing players

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07-22-2010, 02:52 AM
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TheDevilMadeMe
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Originally Posted by seventieslord View Post
Why are people still coming out with versions of adjusted points, when the version on hockey-reference.com works fine?
As shown in the latest Forsberg thread, they tend to overrate the top scorers of lower scoring eras and underrate the top scoreres of higher scoring eras. Basically, first line players scored a higher percentage of their team's goals in the dead puck era than they did in the 1980s, so adjusting their numbers to overall league scoring levels overrates their totals.

The example was Glen Murray scoring almost 150 adjusted points in the 1980s.

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07-22-2010, 03:11 AM
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Hardyvan123
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Originally Posted by TheDevilMadeMe View Post
As shown in the latest Forsberg thread, they tend to overrate the top scorers of lower scoring eras and underrate the top scoreres of higher scoring eras. Basically, first line players scored a higher percentage of their team's goals in the dead puck era than they did in the 1980s, so adjusting their numbers to overall league scoring levels overrates their totals.

The example was Glen Murray scoring almost 150 adjusted points in the 1980s.
Glen Murray had a career year in 02-03 where he was 5th in goals with 44 (leader had 50) and 7th in points with 92 (leader had 106, Forsberg actually).

It was a fluke in the sense that adjsuted points never gave him more than 86 again after his career high of 111.

More invesitigation of the scoring patterns of 1st line players in the dead puck era is in order though, there may be more at play than the 1st line guys "being better" than other 1st line guys in other seasons.

If anyone was actually awake durign the "Dead Puck" era please feel free to jump in.

(Just a joke, hopefully guys will relax and not jump all over it...lol)

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07-22-2010, 03:56 AM
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seventieslord
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Originally Posted by TheDevilMadeMe View Post
As shown in the latest Forsberg thread, they tend to overrate the top scorers of lower scoring eras and underrate the top scoreres of higher scoring eras. Basically, first line players scored a higher percentage of their team's goals in the dead puck era than they did in the 1980s, so adjusting their numbers to overall league scoring levels overrates their totals.

The example was Glen Murray scoring almost 150 adjusted points in the 1980s.
Hmm. I completely avoided that thread.

What seems to raise the red flag for you, is the notion that Glen Murray would have scored almost 150 points in the 1980s. That sounds silly, I get it. But I suppose he did have one season that could have been nearly as impressive statistically as 150 points in the 1980s. (I don't know of a system that says that he did, though. hockey-reference.com says he had 111 adjusted points, and Dionne's 126 from 1984-85 adjusts to 113)

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