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Era Adjusted Goals In a Season

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Old
07-25-2013, 09:28 PM
  #1
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Era Adjusted Goals In a Season

Avs fan here. To this point, I've posted exclusively in the Avs forum.

I'm not sure if this has been done before but I've calibrated historical leading goal scorers (in a given season) using 1981 as a baseline year for reference. It's very objecive (as opposed to subjective--no weighting or arbitrary judgment). FWIW, I had a heavy focus on economics during undegrad. And so, I similarly incorporate the idea that the interest rate as the cost of money when scrutinizing the cost of scoring a goal from year to year.

So here it is, including the preface:

I finally did some computations for era adjusted statistics. I used 1981/82 as a baseline year since that is the season when the goals per game was highest. It's also the season that Gretzky had 92 goals. Since that's the baseline year, his 92 is the equivalent of 92. But I also factored in length of season. I ignored the number of games played by goals scored leaders for particular seasons since durability is a part of the game. It also can be come subject to smaller sample size.

So, according to my analysis, the top 5 era adjusted goals per season by an individual player are as follows:

1. Phil Esposito 70/71 --100.18 era adjusted goals
2. Brett Hull 90/91-------99.67 era adjusted goals
3. Gordie Howe 52/53----93.57 era adjusted goals
4. Wayne Gretzky 81/82--92.00 era adjusted goals (baseline year so it's one to one)
5. Alex Ovechkin 07/08---91.47 era adjusted goals


Last edited by Averick*: 07-26-2013 at 08:37 AM.
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07-26-2013, 02:12 AM
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nice work. could you post more? Like, top 20?

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07-26-2013, 08:40 AM
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Originally Posted by tombombadil View Post
nice work. could you post more? Like, top 20?
Thanks. I'll post more tonight. My file is on my laptop at home. I think the 60 from Stamkos from '12 is #10.

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07-26-2013, 09:02 AM
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Can you post the calculations you used to come up with these numbers?

Is there a chance of getting ranking based on per game paces (maybe a minimum of 40 games played or something)? My guess is Lemieux's 3 best seasons in the 90s (69 in 60 in 92-93, 69 in 70 in 95-96 and 35 in 43 in 00-01) will rank pretty well.

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07-26-2013, 09:41 AM
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Originally Posted by hatterson View Post
Can you post the calculations you used to come up with these numbers?

Is there a chance of getting ranking based on per game paces (maybe a minimum of 40 games played or something)? My guess is Lemieux's 3 best seasons in the 90s (69 in 60 in 92-93, 69 in 70 in 95-96 and 35 in 43 in 00-01) will rank pretty well.
I take the goals per game data and unitize each season so it's the equivalent of my baseline year. I then, also, unitize each season to be 80 games, again, like my baseline year, which is 1981/82.

Believe it or not, the hardest part is pinning down how many games were played in a season by each team. That's why I only went back to 1950, I think.

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07-26-2013, 11:45 AM
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Quote:
Originally Posted by hatterson View Post
Can you post the calculations you used to come up with these numbers?

Is there a chance of getting ranking based on per game paces (maybe a minimum of 40 games played or something)? My guess is Lemieux's 3 best seasons in the 90s (69 in 60 in 92-93, 69 in 70 in 95-96 and 35 in 43 in 00-01) will rank pretty well.
I would also like per game. Was thinking Bure's 58 in 74 games would rank very high.
I think Reg Leach's 60 will rate high, too, but those expansion 70's are a little misleading for going by league-wide data (lowest parity)

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07-26-2013, 12:42 PM
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Quote:
Originally Posted by Averick View Post
I take the goals per game data and unitize each season so it's the equivalent of my baseline year. I then, also, unitize each season to be 80 games, again, like my baseline year, which is 1981/82.

Believe it or not, the hardest part is pinning down how many games were played in a season by each team. That's why I only went back to 1950, I think.
So if I'm following you, the calculation would be:

(Goals by player in statistical year) / (NHL average goals per game in statistical year) * (NHL average goals per game in comparison year) / (Games played per team in statistical year) * (Games played per team in comparison year)

Or do you do anything more complex to normalize the data?

Also in terms of games per year here are the totals in terms of what is on Wikipedia:

The first season of the NHL (after it formed from the NHA) was 17/18

17/18 - 14 in first half of season for 3 teams, 6 for 1 (Montreal Wanderers withdrew after 6 games), 8 for 3 teams in the second half
18/19 - 10 in first half of season, 8 in second half (3 teams)
19/20 - 12 in each half (4 teams)
20/21 - 10 in first half, 14 in second half (4 teams)
21/22 through 23/24 - 24 games (4 teams)
24/25 - 30 games (6 teams)
25/26 - 36 games (7 teams)
26/27 through 30/31 - 44 games (10 teams)
31/32 - 48 games (8 teams)
32/33 through 34/35 - 48 games (9 teams)
35/36 through 37/38 - 48 games (8 teams)
38/39 through 41/42 - 48 games (7 teams)
42/43 through 45/46 - 50 games (6 teams)
46/47 through 48/49 - 60 games (6 teams)
49/50 through 66/67 - 70 games (6 teams)
67/68 through 68/69 - 74 games (12 teams)
69/70 - 76 games (12 teams)
70/71 and 71/72 - 78 games (14 teams)
72/73 and 73/74 - 78 games (16 teams)
74/75 through 77/78 - 80 games (18 teams)
78/79 - 80 games (17 teams)
79/80 through 90/91 - 80 games (21 teams)
91/92 - 80 games (22 teams)
92/93 - 84 games (24 teams)
93/94 - 84 games (26 teams)
94/95 - 48 games (26 teams)
95/96 through 97/98 - 82 games (26 teams)
98/99 - 82 games (27 teams)
99/00 - 82 games (28 teams)
00-01 through 11/12 - 82 games (30 teams) [excluding 04/05 which had 0 games due to lockout]
12/13 - 48 games (30 teams)

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07-26-2013, 01:07 PM
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Quote:
Originally Posted by hatterson View Post
So if I'm following you, the calculation would be:

(Goals by player in statistical year) / (NHL average goals per game in statistical year) * (NHL average goals per game in comparison year) / (Games played per team in statistical year) * (Games played per team in comparison year)

Or do you do anything more complex to normalize the data?

Also in terms of games per year here are the totals in terms of what is on Wikipedia:

The first season of the NHL (after it formed from the NHA) was 17/18

17/18 - 14 in first half of season for 3 teams, 6 for 1 (Montreal Wanderers withdrew after 6 games), 8 for 3 teams in the second half
18/19 - 10 in first half of season, 8 in second half (3 teams)
19/20 - 12 in each half (4 teams)
20/21 - 10 in first half, 14 in second half (4 teams)
21/22 through 23/24 - 24 games (4 teams)
24/25 - 30 games (6 teams)
25/26 - 36 games (7 teams)
26/27 through 30/31 - 44 games (10 teams)
31/32 - 48 games (8 teams)
32/33 through 34/35 - 48 games (9 teams)
35/36 through 37/38 - 48 games (8 teams)
38/39 through 41/42 - 48 games (7 teams)
42/43 through 45/46 - 50 games (6 teams)
46/47 through 48/49 - 60 games (6 teams)
49/50 through 66/67 - 70 games (6 teams)
67/68 through 68/69 - 74 games (12 teams)
69/70 - 76 games (12 teams)
70/71 and 71/72 - 78 games (14 teams)
72/73 and 73/74 - 78 games (16 teams)
74/75 through 77/78 - 80 games (18 teams)
78/79 - 80 games (17 teams)
79/80 through 90/91 - 80 games (21 teams)
91/92 - 80 games (22 teams)
92/93 - 84 games (24 teams)
93/94 - 84 games (26 teams)
94/95 - 48 games (26 teams)
95/96 through 97/98 - 82 games (26 teams)
98/99 - 82 games (27 teams)
99/00 - 82 games (28 teams)
00-01 through 11/12 - 82 games (30 teams) [excluding 04/05 which had 0 games due to lockout]
12/13 - 48 games (30 teams)
Thanks for the info. That's useful for when I get back to this.

First, I adjust for the apparent reality that its harder to score league wide in some seasons more so than others. So to make them apples to apples, I did two calculations relative to my base year of 1982.

My first step was to convert other years goals per game avg to my base year, which is 8.02. I divide 8.02 by the league avg from other years. Then I multiply the league leaders raw # of goals from those years by this number.

The second part involved making other seasons the equivalent of 80 games, which is the # of games from my base year. I, once again divide my base year # by the number of games in other years. I then multiply my product in the a above paragraph by this number.

That's all I did.

I should also add that I d/led my league avg data from hockeyreference by putting it in text and then excel.

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07-26-2013, 02:56 PM
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Quote:
Originally Posted by Averick View Post
Thanks for the info. That's useful for when I get back to this.

First, I adjust for the apparent reality that its harder to score league wide in some seasons more so than others. So to make them apples to apples, I did two calculations relative to my base year of 1982.

My first step was to convert other years goals per game avg to my base year, which is 8.02. I divide 8.02 by the league avg from other years. Then I multiply the league leaders raw # of goals from those years by this number.

The second part involved making other seasons the equivalent of 80 games, which is the # of games from my base year. I, once again divide my base year # by the number of games in other years. I then multiply my product in the a above paragraph by this number.

That's all I did.

I should also add that I d/led my league avg data from hockeyreference by putting it in text and then excel.
Just an observation - Hockey Reference's goals for/game season averages also count shootout goals. Unless you took that into account in your calculations, you will slightly underestimate adjusted goals scored by post-lockout players.

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07-26-2013, 06:24 PM
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So here it is, as promised, the top 20:

Code:
Rank	Year	Player	Era Adjusted Goals
1	1970-71	Phil Esposito	100.184
2	1990-91	Brett Hull	             99.671
3	1952-53	Gordie Howe	93.567
4	1981-82	Wayne Gretzky	92.000
5	2007-08	Alex Ovechkin	91.472
6	1988-89	Mario Lemieux	91.136
7	1983-84	Wayne Gretzky	88.546
8	1971-72	Phil Esposito	88.419
9	1973-74	Phil Esposito	87.397
10	2011-12	Steven Stamkos	85.982
11	1995-96	Mario Lemieux	85.969
12	1955-56	Gordie Howe	85.136
13	1992-93	Mogilny/Selanne	83.956
14	1951-52	Gordie Howe	82.844
15	1999-00	Pavel Bure	82.512
16	2000-01	Pavel Bure	82.213
17	1968-69	Bobby Hull	82.155
18	1965-66	Bobby Hull	81.406
19	1991-92	Brett Hull	             80.661
20	1966-67	Bobby Hull	79.969


Last edited by Averick*: 07-26-2013 at 07:08 PM.
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07-26-2013, 06:30 PM
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Originally Posted by VinnyC View Post
Just an observation - Hockey Reference's goals for/game season averages also count shootout goals. Unless you took that into account in your calculations, you will slightly underestimate adjusted goals scored by post-lockout players.
I'm treating this like it all comes out in the wash. In some ways, it's easier to score goals in different years or different eras. In some ways it's harder. Im not trying to make this an exercise in quantifying how all the ways it's easier or harder. Like I said, it all comes out in the wash and is revealed in the goals per game when considering how easy or difficult it was at various points in time.

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07-26-2013, 09:09 PM
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Quote:
Originally Posted by Averick View Post
I'm treating this like it all comes out in the wash. In some ways, it's easier to score goals in different years or different eras. In some ways it's harder. Im not trying to make this an exercise in quantifying how all the ways it's easier or harder. Like I said, it all comes out in the wash and is revealed in the goals per game when considering how easy or difficult it was at various points in time.
What he's saying is that the more recent seasons have goals counted that aren't the same as the goals that you're counting.

It's not that goals are easier/harder to score in the current era - it's that the totals you're using to normalize are counting apples plus oranges, and you only want apples.

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07-27-2013, 01:20 AM
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Originally Posted by Taco MacArthur View Post
What he's saying is that the more recent seasons have goals counted that aren't the same as the goals that you're counting.

It's not that goals are easier/harder to score in the current era - it's that the totals you're using to normalize are counting apples plus oranges, and you only want apples.
I know what he's saying. Like I said, it all comes out in the wash as the macro level data, ie the goals per game data draws the relationship.

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07-27-2013, 03:24 AM
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I posted this on the history board in response to your post there, but this is the more appropriate thread to discuss it in detail.

Whatever calculation is used here HAS to be missing a factor related to expansion. There is no way that only 1 of the top 14 seasons of all time (you have 2 players at "#13) happened before the 1967 expansion.

Edit: Maybe it's a dumb question, but did you adjust goal totals to the number of games in a season?

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07-27-2013, 11:38 AM
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Originally Posted by TheDevilMadeMe View Post
I posted this on the history board in response to your post there, but this is the more appropriate thread to discuss it in detail.

Whatever calculation is used here HAS to be missing a factor related to expansion. There is no way that only 1 of the top 14 seasons of all time (you have 2 players at "#13) happened before the 1967 expansion.

Edit: Maybe it's a dumb question, but did you adjust goal totals to the number of games in a season?
yep, he did adjust to number of games in a season.

I think what this raw data (adjusted to scoring average of league) suggests, is that parity was high pre-1967, and is high again.

We already knew this, yes, but that is where the fault (which there isn't technically a fault because these are objective numbers) lies. Expansion teams don't score as many goals, and give up way too many, compared to a median(?)

I'm not as smart as most of the guys on this board, and I'm not just saying that, but I believe everyone has insight to offer, and it hit me that these numbers could use adjusting based off of a certain amount of teams. Perhaps, playoff teams numbers ONLY included in the calculations. Or maybe even top 8 teams, top 4 in the 06.

Even the great Bobby Orr's playoff numbers look human, and I don't think it's just because playoff play gets tighter, I think it has a lot to do with playing the Flyers and Habs instead of the Golden Seals and Canucks.

On a slightly side note - whereas I feel that the HOH boys tend to overvalue the oldtimers, I agree that this undervalues them. I am of the mind that a top end athlete is a top end athlete, and that any crunching of numbers or verbal parlay should result in an even spread of top players from all eras, and that the size of the gaps between the top guys and the field reflects league structure more than individual, mind-blowing greatness.

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07-28-2013, 03:27 AM
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In regards to the previous post. If we wanted to account for parity, perhaps what is needed instead of just eliminating certain teams from the calculation is to weigh the numbers by an extra variable that measures the relative scoring strength of a team to the rest of the league that year.

For example:
Number of standard deviations away the team's total goals scored is from the league mean.

Those players who played in relative parity, would be unaffected while those who played in the expansion era would be properly adjusted to have a lower number. Additionally players who were on bad teams during these high variance seasons would deservedly get a boost.

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07-28-2013, 07:25 AM
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Quote:
Originally Posted by WinterEmpire View Post
In regards to the previous post. If we wanted to account for parity, perhaps what is needed instead of just eliminating certain teams from the calculation is to weigh the numbers by an extra variable that measures the relative scoring strength of a team to the rest of the league that year.

For example:
Number of standard deviations away the team's total goals scored is from the league mean.

Those players who played in relative parity, would be unaffected while those who played in the expansion era would be properly adjusted to have a lower number. Additionally players who were on bad teams during these high variance seasons would deservedly get a boost.
I like this idea a lot.

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07-28-2013, 05:09 PM
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The trouble with (ad hoc) parity adjustments is that the idea is you're trying to account for the strength of the player pool. The goal is admirable, trying to extract a quantum of comparable skill. Fact is that any expansion diluted year should see an uptick of scoring for the better players and team... eventually things equalize and talent pools get bigger.

That being said, what has already been done here is good because it attempts to put scoring in the same context, but we still have to admit that they are still within the individual contexts of their seasons. So, when addressing parity, one is then trying to normalize in regards to an ideal competition level within that group that would presumably be comparable across age groups.

So basically, its hard to leap into addressing parity vis a vis scoring figures and other stats... its function on goal scoring and the rest is a function of talent pool depth which is harder to measure.

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07-28-2013, 08:17 PM
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Quote:
Originally Posted by WinterEmpire View Post
In regards to the previous post. If we wanted to account for parity, perhaps what is needed instead of just eliminating certain teams from the calculation is to weigh the numbers by an extra variable that measures the relative scoring strength of a team to the rest of the league that year.

For example:
Number of standard deviations away the team's total goals scored is from the league mean.

Those players who played in relative parity, would be unaffected while those who played in the expansion era would be properly adjusted to have a lower number. Additionally players who were on bad teams during these high variance seasons would deservedly get a boost.
please do. as i said, I am not advanced.

Would this angle undervalue a player, as his own contributions would weigh heavily on his teams' scoring? or is that accounted for in your fancy-talk? (i'm not being sarcastic)

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07-28-2013, 10:29 PM
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Quote:
Originally Posted by WinterEmpire View Post
In regards to the previous post. If we wanted to account for parity, perhaps what is needed instead of just eliminating certain teams from the calculation is to weigh the numbers by an extra variable that measures the relative scoring strength of a team to the rest of the league that year.

For example:
Number of standard deviations away the team's total goals scored is from the league mean.

Those players who played in relative parity, would be unaffected while those who played in the expansion era would be properly adjusted to have a lower number. Additionally players who were on bad teams during these high variance seasons would deservedly get a boost.
Expansion is a slippery slope. How long into a teams tenure do you attribute their being bad to expansion and unfavorable expansion rules? And then how long do you wait before you can start calling it bad management? The other thing is that if a more established team hits hard times, it's not as readily questioned as much as it is if an expansion team struggles.

Another thing that needs to be mentioned about the general idea that, by default, expansion means diluting talent. This isn't necessarily the case. You have to also look at it in relation to the talent pool available. If ten times the number of kids play organized hockey in 1965 than was the case in 1945, expansion could be more in line with an expanding talent pool.

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07-28-2013, 10:41 PM
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Code:
Seq      Year          Goals per Game
45	1967-68	NHL	5.58
46	1966-67	NHL	5.96
47	1965-66	NHL	6.08
48	1964-65	NHL	5.76
49	1963-64	NHL	5.56
50	1962-63	NHL	5.94
51	1961-62	NHL	6.02
52	1960-61	NHL	6
53	1959-60	NHL	5.9
54	1958-59	NHL	5.8
Here is another issue. Above is the range of years leading up to the expansion of 1967/68. Scoring actually went down leaguewide in the year of expansion. It became more difficult to score goals according to the macro level data.

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07-28-2013, 10:53 PM
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Quote:
Originally Posted by Averick View Post
Code:
Seq      Year          Goals per Game
45	1967-68	NHL	5.58
46	1966-67	NHL	5.96
47	1965-66	NHL	6.08
48	1964-65	NHL	5.76
49	1963-64	NHL	5.56
50	1962-63	NHL	5.94
51	1961-62	NHL	6.02
52	1960-61	NHL	6
53	1959-60	NHL	5.9
54	1958-59	NHL	5.8
Here is another issue. Above is the range of years leading up to the expansion of 1967/68. Scoring actually went down leaguewide in the year of expansion. It became more difficult to score goals according to the macro level data.
this is where parity comes in, though. Some teams(new, weak teams) are scoring very little, dragging down the league average, making those on the established teams, whose numbers went up by beating on new teams, look even better against the league average.

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07-28-2013, 11:04 PM
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Originally Posted by tombombadil View Post
this is where parity comes in, though. Some teams(new, weak teams) are scoring very little, dragging down the league average, making those on the established teams, whose numbers went up by beating on new teams, look even better against the league average.
The avg went down almost .4 goals a game. So the drop of .4 is because the new teams are so bad that they're offsetting the surge in scoring of the established teams?

I have a question for you. Do you think there are some years where there were really bad teams that were similarly dragging down the average?

My point is that there are some years, that don't involve expansion, where there are some really bad teams. In the end, does it matter why a team is bad (expansion or otherwise)?

BTW, the league leading goal scorer went from 52 goals the year before expansion to 44 during the year of expansion.


Last edited by Averick*: 07-28-2013 at 11:09 PM.
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07-29-2013, 12:03 AM
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Originally Posted by Averick View Post
Expansion is a slippery slope. How long into a teams tenure do you attribute their being bad to expansion and unfavorable expansion rules? And then how long do you wait before you can start calling it bad management? The other thing is that if a more established team hits hard times, it's not as readily questioned as much as it is if an expansion team struggles.

Another thing that needs to be mentioned about the general idea that, by default, expansion means diluting talent. This isn't necessarily the case. You have to also look at it in relation to the talent pool available. If ten times the number of kids play organized hockey in 1965 than was the case in 1945, expansion could be more in line with an expanding talent pool.
This isn't about just accounting for expansion though. Yes, expansion years usually coincide with a decrease in league wide parity. But this variable is meant to account for any year where there is a large disparity in team scoring talent for whatever reason. The assumption is that any year in which there are there a handful of a very bad teams, these would over inflate the the goal scoring totals of certain players in comparison to years in which talent is more evenly spread around the league.

Quote:
Originally Posted by Averick View Post

Here is another issue. Above is the range of years leading up to the expansion of 1967/68. Scoring actually went down leaguewide in the year of expansion. It became more difficult to score goals according to the macro level data.
Right, the average scoring went down, but as Tom mentioned before this could very well likely be because of those new expansion teams who did poorly bring down the goal total average. Standard deviations show us a better picture of what the goal scoring spread is like.

Quote:
Originally Posted by Averick View Post
The avg went down almost .4 goals a game. So the drop of .4 is because the new teams are so bad that they're offsetting the surge in scoring of the established teams?

I have a question for you. Do you think there are some years where there were really bad teams that were similarly dragging down the average?

My point is that there are some years, that don't involve expansion, where there are some really bad teams. In the end, does it matter why a team is bad (expansion or otherwise)?

BTW, the league leading goal scorer went from 52 goals the year before expansion to 44 during the year of expansion.
It doesn't matter why a team is bad. Bad teams skew results regardless of the reason, and this would try to correct this.

Just for a quick peak at the numbers

Code:
Season             GF Totals                                  Mean(Average)          Std Deviation    # Std Dev leading team is away from mean

65-66              240,239,221,208,195,174               212.83333                    25.84118      1.0513

66-67             264,212,204,202,188,182               208.66667                    29.24836       1.89184

67-68(expan)   259,245,236,226,212,209,                206.33333                  31.32624       1.68123
                     200,195,191,177,173,153

68-69             303,280,271,239,234,231,219,         226.5                          41.32026     1.85139
                      204,189,189,185,174
I just think it would be worthwhile to run the numbers and see what kind of results we get, I'll do it when I have the time in the next couple of days.


Last edited by WinterEmpire: 07-29-2013 at 12:11 AM.
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07-29-2013, 01:25 AM
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It seems the OP is calculating what I would term "simple adjusted" scoring, in this case applied to goals scored.

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Originally Posted by VinnyC View Post
Just an observation - Hockey Reference's goals for/game season averages also count shootout goals. Unless you took that into account in your calculations, you will slightly underestimate adjusted goals scored by post-lockout players.
Yes, if you don't subtract shootout goals, then they are counted in the team totals (and therefor league averages), but not in the individual totals.

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