Refining Adjusted Scoring

[plusandminus]

Scoring distribution within league

The table below shows how many goal certain players scored.
Totally unadjusted what so ever.
r1 is how many goals the teams*1 best player scored.
r2 is how many goals the teams*2 best player scored.
And so on...
Examples:
In 1960-61, the 6th best scorer in the league scored 29 goals, the 12th best scored 24 goals, the 18th best scored 20 goals, and so on.
In 1967-78, the 12th best scorer in the league scored 28 goals, the 24th best scored 24 goals, the 36th best scored 20 goals, and so on.
In 1984-85, the 21th best scorer in the league scored 41 goals, the 42nd best scored 31 goals, the 63th best scored 27 goals, and so on.

Seas|Seas2|Teams|Games|r1|r2|r3|r4|r5|r6|r7|r8|r9|r10|r11|r12|r13|r14|r15|r16
1960|1961|6|70|29|24|20|18|16|15|13|11|10|9|6|5|4|3|2|2
1961|1962|6|70|28|25|22|19|18|15|14|10|8|7|7|5|5|4|3|2
1962|1963|6|70|31|24|22|20|18|16|12|11|8|7|6|5|4|3|2|2
1963|1964|6|70|26|24|21|18|14|12|11|10|8|7|6|5|4|3|2|2
1964|1965|6|70|26|23|21|18|16|14|13|12|9|8|6|5|4|3|2|2
1965|1966|6|70|30|27|22|21|19|16|14|10|8|6|5|4|4|3|2|1
1966|1967|6|70|26|23|20|18|15|13|12|11|11|9|8|6|5|4|3|2
1967|1968|12|74|28|24|20|18|16|14|13|11|9|8|6|5|4|4|3|2
1968|1969|12|76|33|27|25|21|17|15|13|11|10|8|7|5|4|3|2|2
1969|1970|12|76|32|27|23|20|18|16|14|11|10|8|6|5|4|3|3|2
1970|1971|14|78|34|26|22|21|19|17|15|14|11|9|8|6|5|4|3|2
1971|1972|14|78|35|27|23|21|18|16|14|12|11|9|6|6|4|3|3|2
1972|1973|16|78|37|30|27|22|20|17|15|13|11|10|8|7|5|4|3|2
1973|1974|16|78|33|27|24|22|19|17|15|13|11|9|8|6|5|4|3|2
1974|1975|18|80|36|31|26|24|21|18|16|15|13|11|9|8|6|5|4|3
1975|1976|18|80|36|31|26|23|21|19|16|15|13|10|9|8|6|5|4|2
1976|1977|18|80|33|28|25|22|20|18|15|14|13|11|10|9|7|6|4|3
1977|1978|18|80|36|28|24|22|20|18|16|14|12|10|9|7|6|5|4|3
1978|1979|17|80|35|30|27|23|20|18|16|14|13|11|9|8|7|6|5|4
1979|1980|21|80|40|31|27|23|20|17|15|14|12|10|9|8|7|5|5|4
1980|1981|21|80|39|32|28|25|23|20|18|16|14|12|10|9|8|6|5|4
1981|1982|21|80|40|35|32|26|23|21|18|15|13|12|10|9|8|7|5|4
1982|1983|21|80|40|32|28|25|22|19|18|15|14|12|11|8|8|6|6|5
1983|1984|21|80|40|35|29|24|22|20|17|15|13|12|10|9|7|7|6|5
1984|1985|21|80|41|31|27|23|21|19|17|15|14|12|11|10|8|7|6|5
1985|1986|21|80|41|33|29|24|21|20|18|16|15|13|11|10|8|7|6|5
1986|1987|21|80|37|31|27|23|20|18|16|14|13|11|10|9|7|6|6|5
1987|1988|21|80|41|34|27|24|20|17|15|13|11|10|9|8|7|6|5|5
1988|1989|21|80|41|32|27|25|22|18|16|15|13|11|9|8|7|6|5|4
1989|1990|21|80|40|32|28|24|21|18|16|14|12|11|9|8|7|6|5|4
1990|1991|21|80|39|28|24|21|19|17|15|13|12|10|9|8|7|6|5|4
1991|1992|22|80|38|31|26|22|20|18|15|12|11|9|8|7|6|6|5|4
1992|1993|24|84|40|34|28|23|20|18|15|14|12|10|9|8|7|6|5|4
1993|1994|26|84|38|30|25|21|18|16|14|13|12|10|9|7|6|5|5|4
1994|1995|26|48|20|15|13|12|10|9|8|7|6|5|4|4|3|3|2|2
1995|1996|26|82|36|28|23|21|18|16|14|12|10|8|7|7|6|5|4|4
1996|1997|26|82|32|26|22|19|16|14|12|11|10|9|8|7|6|5|4|4
1997|1998|26|82|28|23|19|17|15|13|12|11|9|8|7|6|5|5|4|3
1998|1999|27|82|30|24|20|17|15|13|12|10|9|8|7|6|5|4|4|3
1999|2000|28|82|28|24|21|18|16|14|12|10|10|9|8|7|6|5|4|4
2000|2001|30|82|32|27|21|18|15|13|12|10|9|8|7|6|5|4|4|3
2001|2002|30|82|30|24|20|17|15|13|11|10|9|8|7|6|5|4|4|3
2002|2003|30|82|30|24|20|18|15|13|12|10|9|8|6|6|5|4|4|3
2003|2004|30|82|26|22|19|16|15|13|12|11|9|8|7|6|5|5|4|3
2005|2006|30|82|32|28|23|20|17|15|14|12|10|9|8|7|6|5|4|4
2006|2007|30|82|33|27|22|20|16|14|13|11|10|8|7|6|5|5|4|3
2007|2008|30|82|29|25|21|17|15|13|12|11|9|8|7|6|5|5|4|3
2008|2009|30|82|31|25|22|20|16|15|13|11|10|8|7|6|5|5|4|3
2009|2010|30|82|29|24|21|19|16|14|12|11|10|9|7|6|5|5|4|3
2010|2011|30|82|29|24|21|19|17|14|13|11|10|8|7|6|5|4|4|3

A quick conclusion. It was much easier for top scorers to score many goals in the early 1980s. 30 goals of today, would correspond to about 40 goals in the early 1980s. Thus, 50 goals in the early 1980s would correspond to say 37 goals today.
If so, we should be as impressed by 37 goal scorers today, as we were with the 50 goal scorers of the early 1980s.

 

[plusandminus]

Doing the same for points:

Seas|Seas2|Teams|Games|r1|r2|r3|r4|r5|r6|r7|r8|r9|r10|r11|r12|r13|r14|r15|r16
1960|1961|6|70|70|58|52|45|39|35|33|31|29|25|20|17|15|11|9|8
1961|1962|6|70|69|60|53|46|43|40|37|30|25|23|20|17|15|12|11|9
1962|1963|6|70|67|61|53|43|39|35|32|27|25|24|21|19|16|13|11|9
1963|1964|6|70|71|56|53|45|37|31|28|25|23|21|19|18|14|12|9|5
1964|1965|6|70|64|52|46|43|39|37|33|28|26|22|19|17|17|13|12|10
1965|1966|6|70|72|56|51|48|43|36|34|31|27|23|20|18|16|14|10|8
1966|1967|6|70|63|52|46|42|40|37|35|33|30|25|23|19|16|15|11|9
1967|1968|12|74|66|54|49|44|40|36|33|29|26|23|20|19|16|13|11|9
1968|1969|12|76|77|63|54|48|44|40|35|31|28|25|22|19|16|14|12|8
1969|1970|12|76|70|59|54|47|42|38|34|32|27|24|22|19|16|14|11|9
1970|1971|14|78|73|63|55|50|45|41|37|33|31|27|25|21|19|16|14|12
1971|1972|14|78|75|64|55|49|45|41|37|33|29|25|23|20|17|15|12|11
1972|1973|16|78|84|73|60|53|48|43|39|36|33|30|26|21|19|17|14|11
1973|1974|16|78|77|67|56|52|46|42|37|34|31|29|25|22|18|16|14|12
1974|1975|18|80|80|71|63|58|50|44|41|37|34|31|28|26|21|18|16|13
1975|1976|18|80|86|71|63|57|50|47|42|38|35|31|27|24|21|18|15|12
1976|1977|18|80|80|64|57|53|48|45|41|38|33|30|27|24|22|20|16|14
1977|1978|18|80|79|66|60|54|49|44|40|37|33|30|25|22|19|18|17|14
1978|1979|17|80|83|70|61|56|51|45|41|37|34|31|27|25|23|20|18|15
1979|1980|21|80|85|73|65|58|50|45|41|37|34|32|26|23|21|19|17|15
1980|1981|21|80|86|73|66|62|58|53|49|43|38|33|30|26|24|21|18|16
1981|1982|21|80|92|80|72|67|59|53|47|43|39|35|31|27|24|21|19|16
1982|1983|21|80|86|76|69|63|55|50|44|40|37|33|31|28|24|22|18|16
1983|1984|21|80|92|79|69|61|55|51|45|42|37|33|31|28|24|21|20|17
1984|1985|21|80|95|74|66|61|55|50|44|41|38|33|31|28|25|22|20|18
1985|1986|21|80|87|76|69|64|58|53|45|42|39|35|32|28|26|23|21|18
1986|1987|21|80|81|73|66|59|51|49|44|40|36|32|28|26|22|20|18|16
1987|1988|21|80|89|77|67|59|52|48|41|37|33|30|26|25|22|19|18|16
1988|1989|21|80|88|77|68|62|54|47|44|41|37|31|28|24|21|18|17|15
1989|1990|21|80|92|76|69|62|54|48|42|39|35|30|26|24|21|18|17|15
1990|1991|21|80|86|70|62|54|47|43|40|35|32|29|26|23|22|18|16|15
1991|1992|22|80|86|75|65|58|51|46|40|36|31|28|25|22|19|17|16|14
1992|1993|24|84|97|82|74|63|54|48|43|38|33|30|27|24|21|19|17|15
1993|1994|26|84|85|73|64|55|50|43|39|35|31|28|25|23|20|18|16|14
1994|1995|26|48|44|38|33|29|26|23|20|19|17|15|13|12|11|9|8|7
1995|1996|26|82|85|68|60|53|46|41|36|32|29|26|23|20|18|16|14|12
1996|1997|26|82|77|61|53|48|42|37|34|31|28|25|22|21|18|16|14|13
1997|1998|26|82|66|55|48|43|39|35|31|28|25|23|21|18|17|15|13|11
1998|1999|27|82|65|56|50|45|40|36|32|30|27|23|20|17|15|14|12|10
1999|2000|28|82|70|59|51|45|40|36|33|30|27|25|22|20|17|16|13|12
2000|2001|30|82|76|63|53|47|40|36|32|29|26|23|21|19|17|15|13|11
2001|2002|30|82|67|59|50|45|41|36|32|28|25|23|21|18|16|14|13|10
2002|2003|30|82|69|59|51|45|40|35|32|29|26|23|20|18|16|14|12|11
2003|2004|30|82|65|53|48|43|39|34|31|29|26|24|21|19|17|15|12|11
2005|2006|30|82|79|66|58|52|46|40|37|34|30|27|24|22|20|17|15|13
2006|2007|30|82|78|64|57|51|44|39|35|31|28|26|23|21|18|16|14|12
2007|2008|30|82|72|61|53|46|40|37|33|30|26|24|21|18|17|15|13|11
2008|2009|30|82|73|60|53|48|44|40|36|32|28|26|23|20|18|16|14|12
2009|2010|30|82|70|58|52|47|42|38|34|31|28|24|22|20|17|15|14|13
2010|2011|30|82|66|57|51|46|43|39|35|31|28|25|22|20|17|16|14|12

Looks pretty similar.


I intend to do this for adjusted stats later, probably not tonight. Perhaps ideal adjusted stats would make each row look fairly similar to each other.

 

[plusandminus]

I have now done the adjusted ones too. (I adjusted only for length_of_league_schedule and league_total_goals_per_game. I tried both the "halving" and the "non-halving" mentioned yesterday.)
It does not look "good enough" for me to want to post it yet. I'll look more into the adjustment methods. (It may not be "my fault". Scoring distribution within teams may be a factor.)

 

[Czech Your Math]

I have now done the adjusted ones too. (I adjusted only for length_of_league_schedule and league_total_goals_per_game. I tried both the "halving" and the "non-halving" mentioned yesterday.)
It does not look "good enough" for me to want to post it yet. I'll look more into the adjustment methods. (It may not be "my fault". Scoring distribution within teams may be a factor.)

Definitely wouldn't "halve" to do basic adjustment. Can you just post what you have with full adjustment?

 

[Czech Your Math]

fixed tiers

This is adjusted to 6.0 GPG and shows the average of tiers of 6 players each (top scorers 1-6, 7-12, 13-18, etc.):

Year 1-6 7-12 13-18 19-24 25-30 31-36
-------------------------------------
2011 103 85 80 77 73 71
2010 109 93 87 79 74 73
2009 104 90 83 80 76 75
2008 108 95 89 84 79 77
2007 109 97 89 84 80 77
2006 107 92 86 82 77 75
2004 99 91 85 80 76 71
2003 111 98 88 85 79 75
2002 96 87 84 80 78 76
2001 111 96 89 86 83 81
2000 97 87 81 78 76 73
1999 117 100 86 80 73 71
1998 104 94 84 80 75 72
1997 107 92 86 83 78 71
1996 124 101 93 87 80 77
1995 110 94 86 82 75 73
1994 104 91 85 81 77 74
1993 114 98 86 80 76 71
1992 103 89 81 76 71 68
1991 110 89 81 76 71 66
1990 104 86 81 77 73 69
1989 124 82 75 72 70 66
1988 110 88 77 74 70 66
1987 101 80 73 69 66 64
1986 114 84 76 68 65 62
1985 111 82 79 74 69 64
1984 106 84 75 72 68 66
1983 104 83 74 70 66 63
1982 113 84 74 70 68 66
1981 105 85 78 70 66 62
1980 106 86 81 75 70 67
1979 109 83 75 70 66 62
1978 104 84 77 71 68 66
1977 102 84 77 72 67 63
1976 104 92 82 76 71 66
1975 112 87 78 72 69 66
1974 106 83 78 74 70 66
1973 101 89 83 78 73 70
1972 116 88 78 73 67 62
1971 118 78 73 67 64 61
1970 101 81 76 70 66 62
1969 112 88 78 71 66 61
1968 98 84 75 68 64 60
1967 87 68 57 53 49 46
1966 92 71 63 57 52 46
1965 93 70 59 55 51 47
1964 101 79 69 60 50 43
1963 91 75 69 56 50 43
1962 90 73 66 57 53 48
1961 96 76 63 57 49 45
1960 91 79 62 55 49 44
1959 102 76 68 61 51 46
1958 94 73 64 59 53 49
1957 103 72 61 55 52 48
1956 105 76 67 57 53 46
1955 100 78 65 57 50 46
1954 93 71 64 57 52 46
1953 104 70 61 56 52 44
1952 94 74 65 59 55 51
1951 94 76 57 53 50 46
1950 92 71 63 58 54 49
1949 97 75 66 61 53 48
1948 90 79 67 57 51 45
1947 96 78 68 60 53 46
1946 95 80 69 59 52 46

Notice how every tier jumps substantially in 1968 with first expansion. More teams = more opportunities for ice time = higher scoring and more of it.

There is another significant jump in the tiers around 1993, which is when the influx of overseas talent really began to be pronounced. The top tier really ends up being about the same as in the 80's (except a couple years with more PPs), since Gretzky was slowing down. However, the other tiers generally sustain their jumps higher, as would be expected with the deeper forward talent.

 

[plusandminus]

Definitely wouldn't "halve" to do basic adjustment. Can you just post what you have with full adjustment?

I don't want to, yet. I've posted a number of tables the last week, and suspect people might become tired of me doing it. Plus that things tend to get misinterpreted or overinterpreted, resulting me being accused of things. The preliminary observations from it seems to be that scoring distribution within teams changes too, in a way that makes one ponder whether to use different adjustments for different tiers (which I don't think would be a very good solution).

Regarding your last post, I think you obviously see the decreasing trend if looking from 2010-11 to 1960-61. There are more teams in the league these day, which means more players. That is why I yesterday focused the xth players based on how many teams.

 

[Czech Your Math]

I don't want to, yet. I've posted a number of tables the last week, and suspect people might become tired of me doing it. Plus that things tend to get misinterpreted or overinterpreted, resulting me being accused of things. The preliminary observations from it seems to be that scoring distribution within teams changes too, in a way that makes one ponder whether to use different adjustments for different tiers (which I don't think would be a very good solution).

Regarding your last post, I think you obviously see the decreasing trend if looking from 2010-11 to 1960-61. There are more teams in the league these day, which means more players. That is why I yesterday focused the xth players based on how many teams.

It's your choice, but wouldn't let others' opinions influence your decision. This thread is meant as a resource for data and ideas, although haven't seen as much of either as there could be. I definitely agree that the tiers should be mostly/entirely based on number of teams.

If someone has the database and resources and would like to continue the Year over Year study, I would be happy to go over the methodology and answer any questions. Otherwise I will continue it, but it will take a while until it's finished.

Another thing I tried with limited success was using multivariable linear regression. It worked somewhat using averages (like the tiered data presented), but I had hoped to use it on a more extensive basis and it did not work for some reason.

My idea was using variables like this:

each season = 0 or 1 (1 if it is that season)
each top player = 0 or 1 (1 if it is that player)
% change in # teams = for example going from 12 to 14 teams would be (14/12)-1 or .167... can also time-lag this to see if it has an effect past the immediate season

The dependent variable would be the (adjusted?) points for each top player-season. Does anyone have any ideas along these lines?