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# The Standard Deviation Method

01-29-2013, 12:34 PM
#1
jigglysquishy
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Join Date: Jun 2011
Location: Regina, Saskatchewan
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The Standard Deviation Method

Comparing players against eras is hard and adjusted points just don't sit right with me. I thought a new way of doing so is by calculating the standard deviation of a data set and see how far off the Art Ross winner is.

I've compiled a list of the top 101 scorers of every year since 1967-68 and found the mean, standard deviation and how many standard deviations the Art Ross winner is away from the mean. If anyone knows a place to host the Excel file I'll gladly put it up.

A few things of note

The Art Ross winner isn't calculated into the mean (numbers 2-101 are).

I don't have pre 67-68 data for no other reason than I'm lazy.

These numbers don't attempt to take into account teammates or injuries.

But until then I thought I'd throw some graphs up.

Mean of Top 100 Scorers

This doesn't quite follow up nicely to the GPG graph that gets thrown around. I have a comparison later on. The 80s still dominate though.

Standard Deviation of Art Ross Winner Away From Mean

As you can see, the Gretzky years are so much farther ahead of everyone. Its also interesting to note that all the years except for '81 to '89 are within a much smaller frame. If not for Gretzky and Lemieux it looks like Phil Esposito could make a run at the best forward on this list.

Standard Deviation of Top 100 Scorers

I'm not exactly sure how to interpret this data. Is the talent level growing closer as the league gets closer to now?

Best Art Ross Years
I neglected to include years where the number 2 did really well. When I have time I'll make a new list with them.

 Year Player Standard Deviations 1987 Wayne Gretzky 8.131 1983 Wayne Gretzky 7.959 1986 Wayne Gretzky 7.746 1984 Wayne Gretzky 7.514 1982 Wayne Gretzky 7.302 1985 Wayne Gretzky 7.183 1989 Mario Lemieux 6.213 1971 Phil Esposito 5.598 1974 Phil Esposito 5.530 1981 Wayne Gretzky 5.397 1991 Wayne Gretzky 5.203 1988 Mario Lemieux 5.073 1970 Bobby Orr 4.937 1977 Guy Lafleur 4.717 1999 Jaromir Jagr 4.679 1996 Mario Lemieux 4.521 2012 Evgeni Malkin 4.511 1978 Guy Lafleur 4.487 1972 Phil Esposito 4.475 1969 Phil Esposito 4.309 1980 Marcel Dionne 3.982 1997 Mario Lemieux 3.915 1973 Phil Esposito 3.906 2001 Jaromir Jagr 3.874 1993 Mario Lemieux 3.848 1990 Wayne Gretzky 3.832 1975 Bobby Orr 3.797 1979 Bryan Trottier 3.769 2006 Joe Thornton 3.749 2011 Daniel Sedin 3.681 1992 Mario Lemieux 3.665 2009 Evgeni Malkin 3.641 1994 Wayne Gretzky 3.551 2008 Alexander Ovechkin 3.519 2002 Jarome Iginla 3.484 2007 Sidney Crosby 3.464 2010 Henrik Sedin 3.438 1995 Jaromir Jagr 3.414 1998 Jaromir Jagr 3.347 2004 Martin St. Louis 3.203 1976 Guy Lafleur 3.201 2003 Peter Forsberg 3.145 1968 Stan Mikita 3.044 2000 Jaromir Jagr 3.001

Some interesting things to note
Jagr's 2000 year is the worst post expansion Art Ross win. But he missed 19 games.

Malkin's 2011-2012 season was the best season since Jagr was in beast mode. It's also the 6th best non-Lemieux/Gretzky season on the list.

Gretzky is really, REALLY good.

Orr's 1970 season is a higher offensive peak than Jagr.

Crosby and Ovi didn't peak as high as I was expecting.

If Crosby and Malkin's 2011 and 2012 PPG remained constant and they played 82 games their seasons would go down as some of the best ever AND they would have peaked higher than Jagr.

Even if you give Lemieux the biggest benefit of the doubt (his 160 in 60 season) he still only ends up with the 6th best season.

Now, because I know everyone is going to complain about injuries I thought I'd throw this in. Its a little table of some noteworthy injury seasons assuming PPG was constant

 Year Player Actual STD Injury Adjusted STD 1984 Wayne Gretzky 7.514 8.515 1989 Mario Lemieux 6.213 6.720 1992 Mario Lemieux 3.665 5.784 1993 Mario Lemieux 3.848 7.187 1996 Mario Lemieux 4.521 5.985 1999 Jaromir Jagr 4.679 4.820 2000 Jaromir Jagr 3.001 5.558 2011 Sidney Crosby 0.354 6.109 2012 Evgeni Malkin 4.511 5.489

Another benefit of this is allowing cross-year comparisons. Take the Art Ross Deviation and compare it to the mean. Boom. You have an estimate. Some estimates for thought.

 Original Year Player New Year New Year Point Total 1987 Wayne Gretzky 2012 146 2012 Evgeni Malkin 1987 133 1987 Wayne Gretzky 1993 242 1970 Bobby Orr 2012 113

Some notable numbers from non-AR seasons

 Year Player Standard Deviations 1988 Wayne Gretzky 4.030 1989 Wayne Gretzky 4.640 1989 Steve Yzerman 3.980 1991 Brett Hull 3.400 1993 Pat LaFontaine 3.222 1996 Jaromir Jagr 3.894 2001 Joe Sakic 3.653 2006 Jaromir Jagr 3.607

Last edited by jigglysquishy: 01-29-2013 at 03:35 PM.

 01-30-2013, 10:13 AM #2 Czech Your Math Registered User     Join Date: Jan 2006 Location: bohemia Country: Posts: 4,845 vCash: 500 This is interesting work. Thanks for sharing this. There are a couple of other factors which affect the results: 1) As the number of teams increases, the opportunity increases (total ice time and PP time for more players). 2) If there is a substantial change to the total talent pool (e.g. WHA or players from overseas), then it may become substantially easier/more difficult to maintain a similar edge. I'm also not sure whether it's best to exclude the top finisher each season. I think it may be better to include the top finisher, although it becomes less of a factor as the number of players studied increases. The first factor helps players from the period immediately following expansion. 101 players in a 12-16 league is 6+ to 8+ players per team, and with uneven talent distribution, that includes second liners & d-men on weak expansion teams. 101 players in post-WHA NHL is ~3-5 per team, so mainly includes only players with full PP time (first liners and the better second liners). I would like to see and compare the results for, say, the top 2N or 3N players (where N = # teams in league) each year, including the top finisher. Keeping the number of teams proportional to the size of the league prevents opportunity from being a factor. I'm not sure the best way to prevent changes in the talent pool from affecting the results. Perhaps a calculation of the "top 30 Canadian scorers" or something of that sort would be a fairer way (this assumes that the Canadian talent pool is relatively constant, which should be more true post-expansion).

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