Czech Your Math
I am lizard king
I've done a study of a large, but fixed, group of players over several decades.
GOAL: To determine which seasons were most and least difficult for top line forwards and top offensive defensemen to score points.
METHODOLOGY: The concept of the study is simple. It's essentially similar to the method others used in developing "league equivalencies", which has been done for the NHL vs. WHA, NHL vs. minor leagues, and NHL vs. foreign leagues, for various periods. So it's considering "Year X NHL" and "Year X+1 NHL" to basically be different leagues, then examining how players who participated in both performed. It does not necessarily have to be restricted to a certain group of with minimum quality threshold, but some possible reasons for restricting it to higher scoring forwards and defensemen include:
- Such players may be expected to have longer careers, so for each player included there will be more total "player-year"s in each study (decreasing the statistical error in the study).
- Such players produce at a higher level, which is less influenced by random error (variation).
- Such players often have less variation in opportunity (ice time, PP time, etc.), so there results should be less influenced by this.
- Such players are most frequently the subject of comparison. Since the results are derived from such players, the results should be especially applicable to such players, and so particularly useful.
I have continued to add players to the study. The number of players in each season pair (which will usually be less than the number of players in the fixed group which were active at that time):
- From the '47-8 pair of seasons to the '67-8 pair of seasons, it's 32-45 players and an average of ~37 players per pair of seasons. That's an average of about 6 players per team.
- For the '68-9 seasons to the '71-2 seasons, it's 54-62 players and an average of ~53 players or ~4.5 players per team.
- For the '72-3 seasons to '81-82 seasons, it's 72-82 players and an average of ~78 players per pair of seasons or ~4.2 players per team.
- For the '82-83 to '03-4 seasons, it was 79-91 players and an average of ~84 players per pair of seasons or ~3.4 players per team.
Each pair of consecutive seasons was examined separately, the results sorted by % change in adjusted PPG. I looked at several ways to measure the effect, and the results differ significantly depending on which metric is used. I used the median half of players in terms of % change in PPG, since it both includes a full half of the players participating in each season pair and still removes many outliers in both directions that can be caused by irrelevant factors or random error. I believe using the median (middle) half of players to be a good method for obtaining reliable results. This discards the top 1/4 and bottom 1/4 of players in terms of % change in PPG, so that factors such as injury, change in opportunity, change in team or linemates, improvement or decline due to age, etc. are prevented from substantially affecting the results in a harmful fashion.
The method of linking each "year over year" to produce numbers which may be used to compare across longer spans of time is relatively simple math.
Here's what the effective league GPG was for top tiers of players, based on the results of this study:
GOAL: To determine which seasons were most and least difficult for top line forwards and top offensive defensemen to score points.
METHODOLOGY: The concept of the study is simple. It's essentially similar to the method others used in developing "league equivalencies", which has been done for the NHL vs. WHA, NHL vs. minor leagues, and NHL vs. foreign leagues, for various periods. So it's considering "Year X NHL" and "Year X+1 NHL" to basically be different leagues, then examining how players who participated in both performed. It does not necessarily have to be restricted to a certain group of with minimum quality threshold, but some possible reasons for restricting it to higher scoring forwards and defensemen include:
- Such players may be expected to have longer careers, so for each player included there will be more total "player-year"s in each study (decreasing the statistical error in the study).
- Such players produce at a higher level, which is less influenced by random error (variation).
- Such players often have less variation in opportunity (ice time, PP time, etc.), so there results should be less influenced by this.
- Such players are most frequently the subject of comparison. Since the results are derived from such players, the results should be especially applicable to such players, and so particularly useful.
I have continued to add players to the study. The number of players in each season pair (which will usually be less than the number of players in the fixed group which were active at that time):
- From the '47-8 pair of seasons to the '67-8 pair of seasons, it's 32-45 players and an average of ~37 players per pair of seasons. That's an average of about 6 players per team.
- For the '68-9 seasons to the '71-2 seasons, it's 54-62 players and an average of ~53 players or ~4.5 players per team.
- For the '72-3 seasons to '81-82 seasons, it's 72-82 players and an average of ~78 players per pair of seasons or ~4.2 players per team.
- For the '82-83 to '03-4 seasons, it was 79-91 players and an average of ~84 players per pair of seasons or ~3.4 players per team.
Each pair of consecutive seasons was examined separately, the results sorted by % change in adjusted PPG. I looked at several ways to measure the effect, and the results differ significantly depending on which metric is used. I used the median half of players in terms of % change in PPG, since it both includes a full half of the players participating in each season pair and still removes many outliers in both directions that can be caused by irrelevant factors or random error. I believe using the median (middle) half of players to be a good method for obtaining reliable results. This discards the top 1/4 and bottom 1/4 of players in terms of % change in PPG, so that factors such as injury, change in opportunity, change in team or linemates, improvement or decline due to age, etc. are prevented from substantially affecting the results in a harmful fashion.
The method of linking each "year over year" to produce numbers which may be used to compare across longer spans of time is relatively simple math.
Here's what the effective league GPG was for top tiers of players, based on the results of this study:
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