Before I start doing anything stupid with my life, I would like to give you a chance to debunk a method for getting improved league equivalencies.

The hypothesis is that:

1) We can crunch the numbers for average production vs age for full season players (down to month of birth, by using season mid point as age) in any given league (at least two seasons per player per league I hope) at least for a 100 players

2) Every measurement point is actually an integral over age:

Production=Integral_from_a1_to_a2{Prodpace(a))da}

3) To get to Prodpace(a)' guess function we first assume the production increase to be linear on average in a given season and plot the production vs a1+[(a2-a1)/2] for all players where a1 is the age of the player when season started, a2 the age of the player when season ended. We fit a best fit polynomial with adequate order to the data set and get Prodpace(a)'.

4) We use the number 2) to adjust for seasonal development for the players through assuming that our data set for Prodpace' is flawed in that we don't know at which age which amount of points was scored in a given season to give us the Production data point of the given player (shifted towards higher age if the prodpace(a)' second derivative is positive, and towards lower age if negative. Thus the dataset ages need to be corrected:

True season age for a given datapoint is x:

integral_from_a1_to_x{prodpace(a)'da}-integral_from_x_to_a2{prodpace(a)'da}=0

Once we have solved x from the equation above we make the correction to the data point plotting the solved x as new age.

(this is an iterative process so trying 3 and 4 again should give even a smaller error for a given point)

5) once we have done 3 and 4 for every data point and we have the development curve adjusted dataset of:

Full season production vs. age of production, we make the final fit to get the prodpace function.

6) now we test this prodpace function against a set of players (NHL prospects vs. players who didn't make it) and see what kind of accuracy we have.

7) We do it for all leagues in the world (at least for 100 players dataset), and once we have that, we check the league equivalencies:

We get at least a hundred players that have moved from a league to another in a given off season, we take the lower league production, extrapolate to startage of the next season, we take the upper league production and interpolate down to startage of the season and divide this adjusted higher league production by adjusted lower league production. We do it for the whole data set.

9) Once we have all these numbers crunched in for all leagues and levels in the world, we should be able to get league equivalency numbers all the way from midgets to slovenian second tier junior. We could have NHL equivalency numbers of 12 year olds (:sarcasm:) and we could project their seasons all the way to their entry to the NHL and their prime.

---

How to use a given leagues prodpace function? You can get a guesstimate of production by plugging midseason age directly in. You get an estimation as accurate as the model is by pluggin the season start age and season end age to the

Production for a given player in a given season = Playerproduction/averageproduction*Integral_from_a1_to_a2{Prodpace( a))da}

How to use league equivalencies?

You have a players production in league 1 how would he do in league 2:

Production in league 2 = league1equivalency/league2equivalency*(production in league 1)

---

Edit:

First glance at literature seems to be that the resulting function might be quite close to this due to skill playing a role:

(The skilled players being the hot ones, wavelength being age, and Power density being the NHL equivalent prodpace function)

First guess at skill factor is [C-exp(-A_n*B*((a-a1)-ln(C-S))], where C is the skill ceiling that can be achieved (1 when normalized to generational players), A_n is a league specific development factor (the higher the league level, the higher A_n), B is a player specific development factor, a factor that accounts for how fast a player can learn, a1 is the age at which the player has entered the league and S is the skill aquired in lower level leagues (or before entering the league in question).

Junior leagues marked in color!

]]>The hypothesis is that:

1) We can crunch the numbers for average production vs age for full season players (down to month of birth, by using season mid point as age) in any given league (at least two seasons per player per league I hope) at least for a 100 players

2) Every measurement point is actually an integral over age:

Production=Integral_from_a1_to_a2{Prodpace(a))da}

3) To get to Prodpace(a)' guess function we first assume the production increase to be linear on average in a given season and plot the production vs a1+[(a2-a1)/2] for all players where a1 is the age of the player when season started, a2 the age of the player when season ended. We fit a best fit polynomial with adequate order to the data set and get Prodpace(a)'.

4) We use the number 2) to adjust for seasonal development for the players through assuming that our data set for Prodpace' is flawed in that we don't know at which age which amount of points was scored in a given season to give us the Production data point of the given player (shifted towards higher age if the prodpace(a)' second derivative is positive, and towards lower age if negative. Thus the dataset ages need to be corrected:

True season age for a given datapoint is x:

integral_from_a1_to_x{prodpace(a)'da}-integral_from_x_to_a2{prodpace(a)'da}=0

Once we have solved x from the equation above we make the correction to the data point plotting the solved x as new age.

(this is an iterative process so trying 3 and 4 again should give even a smaller error for a given point)

5) once we have done 3 and 4 for every data point and we have the development curve adjusted dataset of:

Full season production vs. age of production, we make the final fit to get the prodpace function.

6) now we test this prodpace function against a set of players (NHL prospects vs. players who didn't make it) and see what kind of accuracy we have.

7) We do it for all leagues in the world (at least for 100 players dataset), and once we have that, we check the league equivalencies:

We get at least a hundred players that have moved from a league to another in a given off season, we take the lower league production, extrapolate to startage of the next season, we take the upper league production and interpolate down to startage of the season and divide this adjusted higher league production by adjusted lower league production. We do it for the whole data set.

9) Once we have all these numbers crunched in for all leagues and levels in the world, we should be able to get league equivalency numbers all the way from midgets to slovenian second tier junior. We could have NHL equivalency numbers of 12 year olds (:sarcasm:) and we could project their seasons all the way to their entry to the NHL and their prime.

---

How to use a given leagues prodpace function? You can get a guesstimate of production by plugging midseason age directly in. You get an estimation as accurate as the model is by pluggin the season start age and season end age to the

Production for a given player in a given season = Playerproduction/averageproduction*Integral_from_a1_to_a2{Prodpace( a))da}

How to use league equivalencies?

You have a players production in league 1 how would he do in league 2:

Production in league 2 = league1equivalency/league2equivalency*(production in league 1)

---

Edit:

First glance at literature seems to be that the resulting function might be quite close to this due to skill playing a role:

(The skilled players being the hot ones, wavelength being age, and Power density being the NHL equivalent prodpace function)

First guess at skill factor is [C-exp(-A_n*B*((a-a1)-ln(C-S))], where C is the skill ceiling that can be achieved (1 when normalized to generational players), A_n is a league specific development factor (the higher the league level, the higher A_n), B is a player specific development factor, a factor that accounts for how fast a player can learn, a1 is the age at which the player has entered the league and S is the skill aquired in lower level leagues (or before entering the league in question).

Junior leagues marked in color!

I have attempted to reproduce the VsX system but instead of applying the rules quoted below in Sturminator's post to point totals (to find a point total benchmark), I applied them to point-per-game numbers to find a point-per-game benchmark for each season since 1926-1927.

Some additional information on my methodology which isn't included in Sturminator's post:

- I only considered players that played**at least** half the games of the season when finding the top few point-per-game scorers

- For each War and Orr years, I took the original benchmark as decided by the original VsX system, then divided it by the number of games in the season to create an artificial point-per-game benchmark.

I changed some key words and colored them red.

The original VsX system thread can be found here: http://hfboards.hockeysfuture.com/sh....php?t=1361409

Take note, when calculating the best 7 years PPG score of players once the benchmarks were established, I disqualified their seasons where they played less than half the games, so those wouldn't count among their best 7 years.

]]>Some additional information on my methodology which isn't included in Sturminator's post:

- I only considered players that played

- For each War and Orr years, I took the original benchmark as decided by the original VsX system, then divided it by the number of games in the season to create an artificial point-per-game benchmark.

I changed some key words and colored them red.

Quote:

Originally Posted by
Sturminator
Allright, I have done the hard work of going through every post-consolidation NHL season and trying to set some kind of benchmark against which we can compare scoring in a VsX percentages system. Before I post the results, my methodology:
1. First preference is to use the 2nd highest point-per-game score. 2. If (3rd PPG score)/(2nd PPG score) < .90, I use the 3rd PPG score, unless... 3. There is a gap of greater than 10% anywhere else in the top-5 (of PPG scores) - following the same method as above: [small #]/[large #] < .90. At that point, I take the first gap, and identify the upper outlier group (top 3 or 4 or 5 above which the gap occurs), and then go down into the PPG scoring table until I reach a number of players which equals: [size of outlier group] * 2. The benchmark is set as an average of the PPG score of these players.4. If any player in the top-5 is more than 7% below the player above him and more than 7% above the player below him, his PPG score is taken as the benchmark. [this is the Bathgate Rule]5.Only players that played half the games in the season are considered in the application of these rules to find the benchmark |

Take note, when calculating the best 7 years PPG score of players once the benchmarks were established, I disqualified their seasons where they played less than half the games, so those wouldn't count among their best 7 years.

Inspired by** Lemieux scoring 5 different ways - what are the odds?**.

Lets take another achievements. I have one.

A goalie has a game with 0 goals in 60 minutes. He stopped 1 shootout in this 60 minutes. And he has a clean sheet also in after-game shutouts.

If im correct, Jaroslav Halak did this last season. So, im now interested, how high is the probability to achieve this.

]]>Lets take another achievements. I have one.

A goalie has a game with 0 goals in 60 minutes. He stopped 1 shootout in this 60 minutes. And he has a clean sheet also in after-game shutouts.

If im correct, Jaroslav Halak did this last season. So, im now interested, how high is the probability to achieve this.