Era Adjusted Goals In a Season

[Czech Your Math]

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.

Yes, this is essentially what happened when the O6 expanded in the late '60s. It's not necessarily unique in terms of the direction of the effect, but the magnitude of the effect is quite unique.

In '67, there were 5.96 GPG.

In '68, while GPG dropped to 5.58, the O6 teams only dropped to 5.87. Their collective GF increased to 3.12 from 2.98. The league-wide decrease was caused by the expansion teams' inability to score goals. O6 teams averaged 3.46 GF & 2.31 GA against expansion teams. When expansion teams played each other, they only averaged 5.05 GPG.

In '69, GPG increased to 5.96. So in terms of difficulty in scoring goals, it was back to where it was two years before, right? Hardly! O6 teams further increased their collective GF to 3.42. This was despite the expansion teams apparently playing a more defensive game: when expansion teams played each other, they averaged only 4.25 GPG. However, when O6 teams played each other, they averaged 3.25 GF (compared to 2.96 in '68 & 2.98 in '67). O6 teams averaged 3.60 GF & 2.42 GA against expansion teams, but more importantly they played 47% of their games against expansion teams (compared to 32% in '68).

From '68 to '75, O6 teams averaged over 12% more GF than the league average in each and every of those 8 seasons (an average of over 14% more, which peaked ~17% in '72 & '74). It then tapered off to a more moderate level, but didn't reach "par" until after the WHA merger.

 

[Czech Your Math]

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.

It doesn't matter why a team is bad. Bad teams skew results regardless of the reason, and this would try to correct this.

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.

What seems to matter most is what proportion of teams are bad and how much worse they are than average. This is much of what the standard deviation, which you mention, captures. During the past to years, the 10 highest "dispersions" (I believe someone used that term for STDEV/MEAN) in GF occurred from '69-'78. I actually used STDEVP, since we are measuring the complete population, and not a random sample. As always, feel free to check my math and methodology.

 

[TheDevilMadeMe]

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.

Gives way too big a boost to players who play on low scoring teams. Low scoring teams are low scoring because of their players.

edit: n/m I think I misunderstood you. You aren't per se giving extra credit to players who play on weaker teams in the same season?

 

[WinterEmpire]

What seems to matter most is what proportion of teams are bad and how much worse they are than average. This is much of what the standard deviation, which you mention, captures. During the past to years, the 10 highest "dispersions" (I believe someone used that term for STDEV/MEAN) in GF occurred from '69-'78. I actually used STDEVP, since we are measuring the complete population, and not a random sample. As always, feel free to check my math and methodology.

Yes absolutely, STD Dev of the population would be the appropriate calculation in this instance, not sample.

Gives way too big a boost to players who play on low scoring teams. Low scoring teams are low scoring because of their players.

edit: n/m I think I misunderstood you. You aren't per se giving extra credit to players who play on weaker teams in the same season?

Well, technically it isn't giving extra credit to players who are on bad teams. It would be more like attempting to normalize a player's goal total based on the assumption that these players have less of an opportunity to prey on weaker teams to boost their goal totals when compared to those who play on the ultra dominant teams. The end goal is to create a formula which removes the effect of disparity between teams and helps normalize the adjusted scoring as if all teams were at parity with each other. I'm sure the sample method I gave is not the be all and end all, but the I believe the core of what I'm aiming for is there.

 

[Averick*]

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.



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.



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

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.

Fair enough but when I looked at the league goals per game averages, the were some noticeable fluctuations in years that didn't involve expansion. That was just eyeballing it though . However, it's easy to make the expansion generalizations and then become myopic because of it.

Also what does the data show for how it affects individual stats?

 

[Averick*]

Yes, this is essentially what happened when the O6 expanded in the late '60s. It's not necessarily unique in terms of the direction of the effect, but the magnitude of the effect is quite unique.

In '67, there were 5.96 GPG.

In '68, while GPG dropped to 5.58, the O6 teams only dropped to 5.87. Their collective GF increased to 3.12 from 2.98. The league-wide decrease was caused by the expansion teams' inability to score goals. O6 teams averaged 3.46 GF & 2.31 GA against expansion teams. When expansion teams played each other, they only averaged 5.05 GPG.

In '69, GPG increased to 5.96. So in terms of difficulty in scoring goals, it was back to where it was two years before, right? Hardly! O6 teams further increased their collective GF to 3.42. This was despite the expansion teams apparently playing a more defensive game: when expansion teams played each other, they averaged only 4.25 GPG. However, when O6 teams played each other, they averaged 3.25 GF (compared to 2.96 in '68 & 2.98 in '67). O6 teams averaged 3.60 GF & 2.42 GA against expansion teams, but more importantly they played 47% of their games against expansion teams (compared to 32% in '68).

From '68 to '75, O6 teams averaged over 12% more GF than the league average in each and every of those 8 seasons (an average of over 14% more, which peaked ~17% in '72 & '74). It then tapered off to a more moderate level, but didn't reach "par" until after the WHA merger.

The way expansion happened was not kind to the new teams. It's appropriate to acknowledge a dearth of skill when it comes to goal scoring. But is there also a stylistic element here where the expansion teams tried to muck up games defensively because they recognized they couldn't win by out scoring teams? So is a part of their low scoring games a stylistic preference/necessity?

 

[Uncle Rotter]

So power play goals were not factored into the equation, right?

 

[tombombadil]

I love when Czech gets in on these.

I'm looking forward to some interesting calculations from Winter.

 

[BraveCanadian]

The way expansion happened was not kind to the new teams. It's appropriate to acknowledge a dearth of skill when it comes to goal scoring. But is there also a stylistic element here where the expansion teams tried to muck up games defensively because they recognized they couldn't win by out scoring teams? So is a part of their low scoring games a stylistic preference/necessity?

After the 67 expansion, I personally don't think so.

The have-not teams were getting killed.

If they were trying to play defensively they stunk at that too.

 

[Averick*]

After the 67 expansion, I personally don't think so.

The have-not teams were getting killed.

If they were trying to play defensively they stunk at that too.

It's easy to make this generalization--it might be correct. But what does the data say in terms of how it affected league leading goal scorers?

 

[WinterEmpire]

It's easy to make this generalization--it might be correct. But what does the data say in terms of how it affected league leading goal scorers?

There is no real proof in terms of numerical data as far as I'm aware of, this would certainly be interesting to look into to further strengthen the hypothesis that players benefit/are negatively affected by the relative strength of teams they are on.

However, there are loads of empirical evidence that give this assumption life. There's always that well known Marcel Dionne quote(albeit probably exaggerated on his end).

"It's difficult to say what would have happened, if I had played for the Canadiens", says Dionne. "I was drafted second overall behind Guy Lafleur in 1971. After four years in Detroit, I was traded to the Kings, spending 12 years there. Then I finished mt career in New York, playing for Michel Bergeron in my last year."

"In Montreal, I don't know what would have happened. There's a big difference between playing in Montreal and Los Angeles. Considering the strong teams, loaded with talent the Canadiens had, and that they had a style of play that I adored, with speed and quick puck movement, it's not exaggerating to say I'd have scored a 1000 instead of 731, of course, if they had room for me."

"I always had the satisfaction of a job well done, because by having played for a team as unstable as the Kings, I had to work even harder to have success. One thing's for certain - I showed up to play everynight. Those 1771 points didn't fal from the sky. That total wasn't luck. For sure I might have been fully appreciated in Quebec, and Canada even. Here, we know our hockey. The advantage of playing in Los Angeles was that the pressure was less, maybe even inexistant. I had peace of mind. My career was intimate and private. I liked it like that. There's no way I'd have gotten that in Montreal. Even though, it's very satisfying today that fans remember what I accomplished."

 

[WinterEmpire]

So I got the tedious part out of the way and compiled the standard deviation numbers for both GF and GA from the O6 era to now. I was originally only going to focus on GF, but I do believe that team GA stats hold the key to making a more accurate model. Consider a leading goal scorer who happens to play on a dominating team, but what if the variance in GA around the league was fairly low, much lower than the variance in GF? Should this player be as equally 'punished' as one who was able feast of a bunch of very poor teams?

Season|Mean GF|STDEVP GF|CV GF|CV% GF|Mean GA|STDEVP GA|CV GA|CV% GA
1942-43|180.50|13.1116996101|0.0726409951|7.26|180.50|38.8190245455|0.2150638479|21.51
1943-44|204.17|25.4978212577|0.1248872878|12.49|204.17|66.1750624396|0.3241227548|32.41
1944-45|183.83|31.2698825638|0.1700990892|17.01|183.83|41.4745571271|0.2256095583|22.56
1945-46|167.17|18.8539709935|0.1127854696|11.28|167.17|19.5568970499|0.1169904111|11.70
1946-47|189.67|12.2429117815|0.0645496227|6.45|189.67|41.4996653266|0.2188031564|21.88
1947-48|178.43|15.488346874|0.0868041858|8.68|171.29|28.9002114564|0.1687251711|16.87
1948-49|163.00|20.9204843794|0.1283465299|12.83|163.00|26.0832002127|0.1600196332|16.00
1949-50|191.33|21.0686707907|0.1101150041|11.01|191.33|33.9493086168|0.1774354109|17.74
1950-51|189.83|25.28119635|0.133175749|13.32|189.83|47.6284812084|0.2508963014|25.09
1951-52|181.67|20.5318181259|0.1130191823|11.30|181.67|37.048016891|0.2039340379|20.39
1952-53|167.67|24.9710944004|0.1489329686|14.89|167.67|24.2876283093|0.1448566301|14.49
1953-54|168.17|21.8663871933|0.1300280705|13.00|168.17|39.2318606351|0.23329154|23.33
1954-55|176.50|29.6577702016|0.1680326924|16.80|176.50|37.8274591622|0.2143198819|21.43
1955-56|177.33|28.134597128|0.1586537432|15.87|177.33|29.5334085778|0.1665417777|16.65
1956-57|188.33|14.1735277503|0.0752576695|7.53|188.33|29.3011186741|0.1555811611|15.56
1957-58|195.83|27.1748453946|0.138765168|13.88|195.83|20.6915173172|0.1056588118|10.57
1958-59|202.83|27.5706164039|0.1359274432|13.59|202.83|20.8919176291|0.1030004156|10.30
1959-60|206.33|24.6012646468|0.1192306849|11.92|206.33|27.5902559289|0.1337169108|13.37
1960-61|210.17|26.053897128|0.1239677897|12.40|210.17|31.4770639602|0.1497719142|14.98
1961-62|210.67|28.639522032|0.1359470983|13.59|210.67|46.0350108311|0.218520621|21.85
1962-63|208.17|11.739061102|0.0563926074|5.64|208.17|37.5473774791|0.1803717093|18.04
1963-64|194.33|15.5634900399|0.0800865697|8.01|194.33|27.5842144874|0.1419427847|14.19
1964-65|201.33|21.8911448358|0.1087308518|10.87|201.33|34.3252417649|0.1704896114|17.05
1965-66|212.83|23.5896634614|0.1108363201|11.08|212.83|39.7090110121|0.1865732702|18.66
1966-67|208.67|26.6999791927|0.1279551718|12.80|208.67|29.7918706287|0.1427725429|14.28
1967-68|206.33|29.9925916779|0.145359895|14.54|206.33|25.5810259546|0.1239791242|12.40
1968-69|226.50|39.561134126|0.1746628438|17.47|226.50|30.4945350295|0.1346337087|13.46
1969-70|220.75|33.3969185205|0.1512884191|15.13|220.75|33.6455172844|0.1524145743|15.24
1970-71|243.50|51.365288446|0.2109457431|21.09|243.50|47.5901400352|0.1954420535|19.54
1971-72|239.14|45.0743150536|0.1884827989|18.85|239.14|43.7261888556|0.1828454731|18.28
1972-73|255.50|43.4007488415|0.1698659446|16.99|255.50|44.5841900229|0.1744978083|17.45
1973-74|249.31|41.7996990868|0.167659861|16.77|249.31|45.5106014435|0.1825444029|18.25
1974-75|274.00|53.4114011965|0.1949321212|19.49|274.00|62.7711894281|0.2290919322|22.91
1975-76|272.94|47.4019130207|0.1736687226|17.37|272.94|53.672331194|0.1966419624|19.66
1976-77|265.72|45.893361364|0.1727117927|17.27|265.72|42.6898446882|0.1606559073|16.07
1977-78|263.72|44.7012373127|0.1695012158|16.95|263.72|48.2330057067|0.1828932173|18.29
1978-79|279.82|39.8057567432|0.1422530722|14.23|279.82|37.2072657264|0.1329668945|13.30
1979-80|281.05|31.896374164|0.1134909958|11.35|281.05|33.7772481758|0.1201833636|12.02
1980-81|307.48|29.2910177157|0.0952627183|9.53|307.48|43.5240700211|0.1415526515|14.16
1981-82|321.00|38.525192747|0.1200161768|12.00|321.00|40.9157089404|0.1274632677|12.75
1982-83|309.19|39.1512561954|0.1266250393|12.66|309.19|46.63701682|0.1508358776|15.08
1983-84|315.57|43.1084694237|0.1366044753|13.66|315.57|43.193442435|0.1368737424|13.69
1984-85|310.95|36.9870970944|0.1189477854|11.89|310.95|44.5672057422|0.1433248577|14.33
1985-86|317.48|33.3118297987|0.1049270175|10.49|317.48|45.0297457747|0.1418366074|14.18
1986-87|293.57|22.9524797469|0.0781836293|7.82|293.57|29.5434650393|0.1006346741|10.06
1987-88|297.00|34.0084023231|0.1145064051|11.45|297.00|32.2770742759|0.1086770178|10.87
1988-89|299.33|31.8588155302|0.1064325686|10.64|299.33|39.0644563002|0.1305048651|13.05
1989-90|294.71|26.4199471128|0.0896459669|8.96|294.71|41.7089037624|0.1415231829|14.15
1990-91|276.43|34.7036040787|0.1255427538|12.55|276.43|29.4773059255|0.1066362488|10.66
1991-92|278.32|31.3751296464|0.1127311534|11.27|278.32|31.9351421757|0.114743284|11.47
1992-93|304.63|43.6594897092|0.1433220836|14.33|304.63|42.7549339258|0.140352676|14.04
1993-94|272.35|32.1187008882|0.1179333743|11.79|272.35|39.3083885231|0.1443324533|14.43
1994-95|143.35|20.1779436089|0.1407637601|14.08|143.35|19.6016920535|0.13674376|13.67
1995-96|257.73|36.5866281713|0.1419567725|14.20|257.73|38.74130939|0.1503169742|15.03
1996-97|239.08|19.986385899|0.0835981392|8.36|239.08|30.2348793448|0.126465068|12.65
1997-98|216.31|21.483033074|0.0993170092|9.93|216.31|28.425028558|0.1314101605|13.14
1998-99|215.93|22.4267134461|0.1038629954|10.39|215.93|28.2081232402|0.1306379635|13.06
1999-00|225.21|21.7688459286|0.0966583708|9.67|225.21|33.9204501559|0.1506141142|15.06
2000-01|226.07|30.7646261512|0.1360865209|13.61|226.07|29.6062305755|0.1309623883|13.10
2001-02|214.73|23.7738418342|0.1107133274|11.07|214.73|26.1316325977|0.1216934148|12.17
2002-03|217.67|26.1130022956|0.1199678513|12.00|217.67|27.6939624387|0.1272310679|12.72
2003-04|210.60|23.5267223953|0.1117128319|11.17|210.60|30.0362003811|0.1426220341|14.26
2004-05||||||||
2005-06|252.93|28.9573632931|0.114486149|11.45|252.93|28.9573632931|0.114486149|11.45
2006-07|241.53|26.3726289087|0.1091883615|10.92|241.50|30.9006472424|0.1279529907|12.80
2007-08|228.23|19.0991855556|0.0836827175|8.37|228.23|22.5782835683|0.0989263191|9.89
2008-09|238.83|23.9834433632|0.1004191627|10.04|238.83|23.2150573742|0.097201915|9.72
2009-10|232.90|23.4696257604|0.100771257|10.08|232.90|22.6235128425|0.0971383119|9.71
2010-11|229.00|21.6225191255|0.0944214809|9.44|229.00|25.4780951669|0.1112580575|11.13
2011-12|224.20|23.2800343642|0.1038360141|10.38|224.20|24.8346532088|0.1107700857|11.08
2012-13|130.63|12.9652955573|0.0992495194|9.92|130.63|17.0087885779|0.1302025153|13.02

Fun with graphs, the season to season coeffecients of variance, also known as 'dispersion', for team GF and GA.

Next step is the incorporate this data with the Era adjusted goal totals in a meaningful way.

 

[tombombadil]

i hope you have that graph pinned in post-its to the inside of a shed in the back yard, Russel Crowe!

(Please keep it coming, btw)

 

[Averick*]

So I got the tedious part out of the way and compiled the standard deviation numbers for both GF and GA from the O6 era to now. I was originally only going to focus on GF, but I do believe that team GA stats hold the key to making a more accurate model. Consider a leading goal scorer who happens to play on a dominating team, but what if the variance in GA around the league was fairly low, much lower than the variance in GF? Should this player be as equally 'punished' as one who was able feast of a bunch of very poor teams?

Season|Mean GF|STDEVP GF|CV GF|CV% GF|Mean GA|STDEVP GA|CV GA|CV% GA
1942-43|180.50|13.1116996101|0.0726409951|7.26|180.50|38.8190245455|0.2150638479|21.51
1943-44|204.17|25.4978212577|0.1248872878|12.49|204.17|66.1750624396|0.3241227548|32.41
1944-45|183.83|31.2698825638|0.1700990892|17.01|183.83|41.4745571271|0.2256095583|22.56
1945-46|167.17|18.8539709935|0.1127854696|11.28|167.17|19.5568970499|0.1169904111|11.70
1946-47|189.67|12.2429117815|0.0645496227|6.45|189.67|41.4996653266|0.2188031564|21.88
1947-48|178.43|15.488346874|0.0868041858|8.68|171.29|28.9002114564|0.1687251711|16.87
1948-49|163.00|20.9204843794|0.1283465299|12.83|163.00|26.0832002127|0.1600196332|16.00
1949-50|191.33|21.0686707907|0.1101150041|11.01|191.33|33.9493086168|0.1774354109|17.74
1950-51|189.83|25.28119635|0.133175749|13.32|189.83|47.6284812084|0.2508963014|25.09
1951-52|181.67|20.5318181259|0.1130191823|11.30|181.67|37.048016891|0.2039340379|20.39
1952-53|167.67|24.9710944004|0.1489329686|14.89|167.67|24.2876283093|0.1448566301|14.49
1953-54|168.17|21.8663871933|0.1300280705|13.00|168.17|39.2318606351|0.23329154|23.33
1954-55|176.50|29.6577702016|0.1680326924|16.80|176.50|37.8274591622|0.2143198819|21.43
1955-56|177.33|28.134597128|0.1586537432|15.87|177.33|29.5334085778|0.1665417777|16.65
1956-57|188.33|14.1735277503|0.0752576695|7.53|188.33|29.3011186741|0.1555811611|15.56
1957-58|195.83|27.1748453946|0.138765168|13.88|195.83|20.6915173172|0.1056588118|10.57
1958-59|202.83|27.5706164039|0.1359274432|13.59|202.83|20.8919176291|0.1030004156|10.30
1959-60|206.33|24.6012646468|0.1192306849|11.92|206.33|27.5902559289|0.1337169108|13.37
1960-61|210.17|26.053897128|0.1239677897|12.40|210.17|31.4770639602|0.1497719142|14.98
1961-62|210.67|28.639522032|0.1359470983|13.59|210.67|46.0350108311|0.218520621|21.85
1962-63|208.17|11.739061102|0.0563926074|5.64|208.17|37.5473774791|0.1803717093|18.04
1963-64|194.33|15.5634900399|0.0800865697|8.01|194.33|27.5842144874|0.1419427847|14.19
1964-65|201.33|21.8911448358|0.1087308518|10.87|201.33|34.3252417649|0.1704896114|17.05
1965-66|212.83|23.5896634614|0.1108363201|11.08|212.83|39.7090110121|0.1865732702|18.66
1966-67|208.67|26.6999791927|0.1279551718|12.80|208.67|29.7918706287|0.1427725429|14.28
1967-68|206.33|29.9925916779|0.145359895|14.54|206.33|25.5810259546|0.1239791242|12.40
1968-69|226.50|39.561134126|0.1746628438|17.47|226.50|30.4945350295|0.1346337087|13.46
1969-70|220.75|33.3969185205|0.1512884191|15.13|220.75|33.6455172844|0.1524145743|15.24
1970-71|243.50|51.365288446|0.2109457431|21.09|243.50|47.5901400352|0.1954420535|19.54
1971-72|239.14|45.0743150536|0.1884827989|18.85|239.14|43.7261888556|0.1828454731|18.28
1972-73|255.50|43.4007488415|0.1698659446|16.99|255.50|44.5841900229|0.1744978083|17.45
1973-74|249.31|41.7996990868|0.167659861|16.77|249.31|45.5106014435|0.1825444029|18.25
1974-75|274.00|53.4114011965|0.1949321212|19.49|274.00|62.7711894281|0.2290919322|22.91
1975-76|272.94|47.4019130207|0.1736687226|17.37|272.94|53.672331194|0.1966419624|19.66
1976-77|265.72|45.893361364|0.1727117927|17.27|265.72|42.6898446882|0.1606559073|16.07
1977-78|263.72|44.7012373127|0.1695012158|16.95|263.72|48.2330057067|0.1828932173|18.29
1978-79|279.82|39.8057567432|0.1422530722|14.23|279.82|37.2072657264|0.1329668945|13.30
1979-80|281.05|31.896374164|0.1134909958|11.35|281.05|33.7772481758|0.1201833636|12.02
1980-81|307.48|29.2910177157|0.0952627183|9.53|307.48|43.5240700211|0.1415526515|14.16
1981-82|321.00|38.525192747|0.1200161768|12.00|321.00|40.9157089404|0.1274632677|12.75
1982-83|309.19|39.1512561954|0.1266250393|12.66|309.19|46.63701682|0.1508358776|15.08
1983-84|315.57|43.1084694237|0.1366044753|13.66|315.57|43.193442435|0.1368737424|13.69
1984-85|310.95|36.9870970944|0.1189477854|11.89|310.95|44.5672057422|0.1433248577|14.33
1985-86|317.48|33.3118297987|0.1049270175|10.49|317.48|45.0297457747|0.1418366074|14.18
1986-87|293.57|22.9524797469|0.0781836293|7.82|293.57|29.5434650393|0.1006346741|10.06
1987-88|297.00|34.0084023231|0.1145064051|11.45|297.00|32.2770742759|0.1086770178|10.87
1988-89|299.33|31.8588155302|0.1064325686|10.64|299.33|39.0644563002|0.1305048651|13.05
1989-90|294.71|26.4199471128|0.0896459669|8.96|294.71|41.7089037624|0.1415231829|14.15
1990-91|276.43|34.7036040787|0.1255427538|12.55|276.43|29.4773059255|0.1066362488|10.66
1991-92|278.32|31.3751296464|0.1127311534|11.27|278.32|31.9351421757|0.114743284|11.47
1992-93|304.63|43.6594897092|0.1433220836|14.33|304.63|42.7549339258|0.140352676|14.04
1993-94|272.35|32.1187008882|0.1179333743|11.79|272.35|39.3083885231|0.1443324533|14.43
1994-95|143.35|20.1779436089|0.1407637601|14.08|143.35|19.6016920535|0.13674376|13.67
1995-96|257.73|36.5866281713|0.1419567725|14.20|257.73|38.74130939|0.1503169742|15.03
1996-97|239.08|19.986385899|0.0835981392|8.36|239.08|30.2348793448|0.126465068|12.65
1997-98|216.31|21.483033074|0.0993170092|9.93|216.31|28.425028558|0.1314101605|13.14
1998-99|215.93|22.4267134461|0.1038629954|10.39|215.93|28.2081232402|0.1306379635|13.06
1999-00|225.21|21.7688459286|0.0966583708|9.67|225.21|33.9204501559|0.1506141142|15.06
2000-01|226.07|30.7646261512|0.1360865209|13.61|226.07|29.6062305755|0.1309623883|13.10
2001-02|214.73|23.7738418342|0.1107133274|11.07|214.73|26.1316325977|0.1216934148|12.17
2002-03|217.67|26.1130022956|0.1199678513|12.00|217.67|27.6939624387|0.1272310679|12.72
2003-04|210.60|23.5267223953|0.1117128319|11.17|210.60|30.0362003811|0.1426220341|14.26
2004-05||||||||
2005-06|252.93|28.9573632931|0.114486149|11.45|252.93|28.9573632931|0.114486149|11.45
2006-07|241.53|26.3726289087|0.1091883615|10.92|241.50|30.9006472424|0.1279529907|12.80
2007-08|228.23|19.0991855556|0.0836827175|8.37|228.23|22.5782835683|0.0989263191|9.89
2008-09|238.83|23.9834433632|0.1004191627|10.04|238.83|23.2150573742|0.097201915|9.72
2009-10|232.90|23.4696257604|0.100771257|10.08|232.90|22.6235128425|0.0971383119|9.71
2010-11|229.00|21.6225191255|0.0944214809|9.44|229.00|25.4780951669|0.1112580575|11.13
2011-12|224.20|23.2800343642|0.1038360141|10.38|224.20|24.8346532088|0.1107700857|11.08
2012-13|130.63|12.9652955573|0.0992495194|9.92|130.63|17.0087885779|0.1302025153|13.02

Fun with graphs, the season to season coeffecients of variance, also known as 'dispersion', for team GF and GA.

Next step is the incorporate this data with the Era adjusted goal totals in a meaningful way.

Kudos on your research. That's some really great information.

But previously I raised a question about goal disparity being partly a function of stylistic choices. Part of the goal disparity could be a function of the less talented teams recognize they lacked the talent to win high scoring games, so they embraced a more defensive style. The std devs doesn't provide the panaplea of reasons for the disparity. And relative to goal scoring leaders, it seems yo have had little to no impact. From 65-68, the league leaders in goals scored had 42, 54, 52, and 44 goals consecutively.

 

[WinterEmpire]

Kudos on your research. That's some really great information.

But previously I raised a question about goal disparity being partly a function of stylistic choices. Part of the goal disparity could be a function of the less talented teams recognize they lacked the talent to win high scoring games, so they embraced a more defensive style. The std devs doesn't provide the panaplea of reasons for the disparity. And relative to goal scoring leaders, it seems yo have had little to no impact. From 65-68, the league leaders in goals scored had 42, 54, 52, and 44 goals consecutively.

Right, goal scoring alone doesn't provide the full picture. This is why I now believe it's important to also consider the defensive disparity between teams as recognized by GA.

Standard deviations and their related calculations aren't supposed to represent the reason for disparity, they are statistical proof of disparity themselves. More of a 'what happened' as opposed to 'why it is'. Is using Goal Scoring/Defending deviations the best representation of this? Perhaps/perhaps not, but I think it is the most accurate high level approach we can use to determine this.

Finally, your statement regarding how this had no impact on goal scoring leaders by using the year to year goal scoring leader totals as proof. Are you implying that goal scoring, if disparity had an effect on it, would had to have been sole direct dependency of it? Because otherwise, you cannot conclusively say anything about how year-to-year top goal scoring totals relate to the effect of disparity. Individual goal scoring is determined by a multitude of factors, most of which have no quantifiable measure. I believe that disparity is just one of those many factors. One that can be accurately modeled and applied to scoring totals to provide an interesting and previously unseen point of view.

 

[Czech Your Math]

Right, goal scoring alone doesn't provide the full picture. This is why I now believe it's important to also consider the defensive disparity between teams as recognized by GA.

Standard deviations and their related calculations aren't supposed to represent the reason for disparity, they are statistical proof of disparity themselves. More of a 'what happened' as opposed to 'why it is'. Is using Goal Scoring/Defending deviations the best representation of this? Perhaps/perhaps not, but I think it is the most accurate high level approach we can use to determine this.

Finally, your statement regarding how this had no impact on goal scoring leaders by using the year to year goal scoring leader totals as proof. Are you implying that goal scoring, if disparity had an effect on it, would had to have been sole direct dependency of it? Because otherwise, you cannot conclusively say anything about how year-to-year top goal scoring totals relate to the effect of disparity. Individual goal scoring is determined by a multitude of factors, most of which have no quantifiable measure. I believe that disparity is just one of those many factors. One that can be accurately modeled and applied to scoring totals to provide an interesting and previously unseen point of view.

I like your approach. The data suggests to me that the standard deviation in GF is much more influential than that of GA, in terms of the difficulty for top players to score.

My previous basic attempts at regression may provide some food for thought:

Adjusting Adjusted Points for Top Players Using Regression

The factors that seem most important, at least in the period studied (post-O6 expansion):

- disparity, esp. in team GF
- the effect of the presence of non-Canadians in the top tier
- expansion (number of teams & fraction of teams in their first 1-2 seasons)
- power play opportunities

 

[Averick*]

Right, goal scoring alone doesn't provide the full picture. This is why I now believe it's important to also consider the defensive disparity between teams as recognized by GA.

Standard deviations and their related calculations aren't supposed to represent the reason for disparity, they are statistical proof of disparity themselves. More of a 'what happened' as opposed to 'why it is'. Is using Goal Scoring/Defending deviations the best representation of this? Perhaps/perhaps not, but I think it is the most accurate high level approach we can use to determine this.

Finally, your statement regarding how this had no impact on goal scoring leaders by using the year to year goal scoring leader totals as proof. Are you implying that goal scoring, if disparity had an effect on it, would had to have been sole direct dependency of it? Because otherwise, you cannot conclusively say anything about how year-to-year top goal scoring totals relate to the effect of disparity. Individual goal scoring is determined by a multitude of factors, most of which have no quantifiable measure. I believe that disparity is just one of those many factors. One that can be accurately modeled and applied to scoring totals to provide an interesting and previously unseen point of view.

I've looked at the data too. But I wasn't looking at from the myopic view of the effect of expansion on scoring. And I can tell you that some random years produce big fluctuations. This is why it was correct for Czech to focus on standard deviations in a more limited scope of this discussion. But again, no one has answered my question about style of play choices. I'm guessing it was a likely factor but also hard to pin down and quantify. We all know that expansion represented a bunch of cast-offs. That doesnt mean it was easier to score for individual players. As a matter of fact, the stats support the idea they have minimal effect.

I've enjoyed this discussion immensely. Sadly, it only pertains to a couple of years in the late 60s. But I've enjoyed watching you guys zero in on relevant data.


Overall, there's been a lot of give and take in this thread. I've agreed with many of the comments but, that's partly because they've strayed from the original theses of translating difficultiy in scoring to individual scoring leaders. As I've mentioned before, the focus seems to have been about the 2 or 3 years after expansion. But for me, I've been more focused on a wider spectrum of time that involves more variables.

 

[Averick*]

I like your approach. The data suggests to me that the standard deviation in GF is much more influential than that of GA, in terms of the difficulty for top players to score.

My previous basic attempts at regression may provide some food for thought:

Adjusting Adjusted Points for Top Players Using Regression

The factors that seem most important, at least in the period studied (post-O6 expansion):

- disparity, esp. in team GF
- the effect of the presence of non-Canadians in the top tier
- expansion (number of teams & fraction of teams in their first 1-2 seasons)
- power play opportunities

I've said numerous times that the expansion era wasn't exacly fair when it came to redistributing talent. You've correctly identified that the expansion teams scored less. That could simply mean they had less offensively skilled talent. Which might also explain why they might try to play a more defensive game as a function of choice.

When I started this thread, I did so thinking there were bigger fluctuations from year to year in the 80s than in the 60s. This kind of statistical volatility makes it problematic when putting emphasis on the expansion era of the 1960s. To wit, in 1986, the average goals per game was 8.0 per game. In 1987, it was 7.4 goals per game. This is a disparity of .6 goals per game in a non expansion year.

 

[Hardyvan123]

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 was thinking along the same lines, like excluding expansion teams numbers for a period of 2-3 years until they become more "normal" but the problem with this is that it all becomes very subjective the more variables one tries to account for and how does one weigh a 6 team expansion to a 6 team league with little in the way of new talent streams to adding 2 teams in a 28 team league with a larger player pool than an only Canadian one?

it all begins to get a bit fuzzy then.