By The NumbersHockey Analytics... the Final Frontier. Explore strange new worlds, to seek out new algorithms, to boldly go where no one has gone before.

Improving Adjusted Scoring and Comparing Scoring of Top Tier Players Across Eras

I have now somewhat repeated your study, doing it for all seasons from 1948-49 to 2010-11. I use factual points per game for players being 23-27 years old during the first of the two seasons compared, and they should have played at least 40 games during each of the two seasons and scored at least 15 points during each two (to avoid extreme point per game changes). Only Canadian forwards, about 20 per season during O6 and then at least 40 per season from that onwards.
Results are preliminary so far, but a few notes. There seem to have been a large increase between 1971-72-73 (WHA started, NHL expanded from 12 to 14 teams using a balanced schedule meaning getting to play 12 more easy games). The 1973-74-75 also seem to indicate a change (NHL going from 16 to 18 teams, and Washington allowing 446 goals in 80 games, while WHA still existing).

I have now somewhat repeated your study, doing it for all seasons from 1948-49 to 2010-11. I use factual points per game for players being 23-27 years old during the first of the two seasons compared, and they should have played at least 40 games during each of the two seasons and scored at least 15 points during each two (to avoid extreme point per game changes). Only Canadian forwards, about 20 per season during O6 and then at least 40 per season from that onwards.
Results are preliminary so far, but a few notes. There seem to have been a large increase between 1971-72-73 (WHA started, NHL expanded from 12 to 14 teams using a balanced schedule meaning getting to play 12 more easy games). The 1973-74-75 also seem to indicate a change (NHL going from 16 to 18 teams, and Washington allowing 446 goals in 80 games, while WHA still existing).

Are the increases in actual or adjusted PPG?

There were distinct increases in '73 and '75, after a huge increase in '68. After '76, there appeared 6 successive decreases.

There were distinct increases in '73 and '75, after a huge increase in '68. After '76, there appeared 6 successive decreases.

Do you think ages 23-27 is a bit restrictive?

Actual Points per game.
Yes, the increase in 1973 and also 1975 I can see, but not necessarily 1968. I will look more into it later. It's bedtime now.
I don't think ages 23-27 is too restrictive. But I'll look more into that too to see if there is some kind of unbalance (for example far more 23 year olds than 27 year olds).
Problem with players <23 years old is that they naturally tend to increase their scoring by pretty much from season to season, while players above 30 tends to steadily decrease.

Actual Points per game.
Yes, the increase in 1973 and also 1975 I can see, but not necessarily 1968.

When the number of teams doubles overnight, the average quality of players of any age group is going to decrease substantially, so their collective PPG should drop significantly. This is why I used a fixed group of players.

I've added quite a few post-expansion players since I posted this thread. The data has been updated to reflect this. I need to add some more players, particularly since the last lockout, but so far it appears adjusted points have become slightly more difficult since the lockout.

I wanted to include a list of players and how many seasons were used for each, to give an idea of how few seasons were deducted. These are the players included born through 1973 (SP= season pairs used, which will be at least 1 less than years used):

This is from a study I did about changes in PPG for the better players from season to season:

This is how the average of different tiers of players scored, using simple adjusted data (schedule, league gpg, assist/goal ratio), where N = number of teams in NHL (1st N = 1 to N, 2nd N = N+1 to 2N, etc.):

These are the same tiers using adjusted gpg from my study:

Note: Adjusted to 6.00 gpg, 1.667 assists/goal and 82 games.

Y was the average adjusted points of the top N players (N = number of teams).

Xn = number of teams
Xf = standard deviation of teams' GF
Xa = standard deviation of teams' GA
Xe = percent of top N forwards which were non-Canadian
Xg = league GPG
Xp = ratio of special teams goals to all goals

The new results are:

B = 82
Mn = (0.44)
Mf = 87
Ma = (18)
Me = 8.1
Mg = (.74)
Mp = 42

R^2 = .56

All variables appear significant, with Xa having the lowest t-score of ~4.8 (Ma/SEa = .73, N^.5 = 6.6).

I think this model holds a lot of promise, with R^2 > .5, all variables significant, and I thought this was interesting as well:

Standard deviation of Y (avg. adjusted points of top N players) was 3.86, and only 3/44 predicted values of Y varied from the actual value by more than this (the highest deviation was ~1.6 std dev). Each of those three predicted values was lower than the actual value, possibly in part due to some of the best players being in the league and having strong seasons (Orr, Espo, etc. in '72... Lemieux, Jagr, etc. in '96 & '97).

Some of the varaibles may improve with further refinement. It may be useful to define a variable that will somehow capture the effect of having so much top talent in the league, but not exactly sure what the best and fairest way to do that might be. Any suggestions welcome.

For those not familiar with regression, this is what the model suggests at this stage:

For each additional team, Y decreases by .44
For each 1 % point increase in standard deviation of teams' GF, Y increases by .87
For each 1 % point increase in standard deviation of teams' GA, Y decreases by .18
For each 10 % point increase in % of non-Canadians in top N, Y increases by .81
For each .10 increase in league GPG, Y decreases by .07
For each 1 % point increase in special teams goals as % of total goals, Y increases by .42

Last edited by Czech Your Math: 11-17-2012 at 02:32 PM.