The Standard Deviation Method

[jigglysquishy]

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

Click to read more...

 

[Czech Your Math]

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).