Vs N - new adjusted scoring system

[Hockey Outsider]

Here are the results of a new adjusting scoring system called "VsN".

I'm not saying that this is the best method of adjusted scoring, I'm simply posting the results so that we can discuss them. (In fact, there appear to be obvious flaws, which can be seen below).

The method works as follows. Each year, we calculate a benchmark. This number is equal to the average number of points scored by the highest scorer through the Xth highest scorer in the NHL, where X is the number of teams in the league.

For example, in 1996 there were 26 teams in the NHL. We add up the total number of points scored by the highest scoring player (Mario Lemieux), 2nd highest scoring player (Jaromir Jagr), 3rd highest scoring player (Joe Sakic), all the way down to the 26th highest scoring player (Brian Leetch). This total is divided by 26, and that number is our benchmark. In this case the total number of points is 2,717, so the benchmark is 104.5.

We then adjust each player's actual results to the benchmark. For example, in 1996, Sergei Fedorov scored 107 points. The benchmark was 104.5 points. Thus, his adjusted total is 107/104.5*100 = 102 points (which could be interpreted that he produced slightly more offense than the average #1 forward that year).

Benefits? This method is simple to explain and doesn't involve any convoluted rules. The benchmark should, in theory, represent the actual output of the average #1 forward in any given season, facilitating cross-era comparisons. The benchmark should be minimally swayed by outliers (ie Howe, Gretzky, Lemieux).

Drawbacks? Short of a manual adjustment, the WWII years will always be distorted (most of the league's stars were in the Armed Forces and many of the players who remained took advantage of the low level of competition). The system is brutal during seasons with fewer teams (as seen in the results below).

The benchmarks were taken from BM67's post. They look reasonable, but I haven't recalculated them, so let me know if you see any errors. Link. I took the numbers for 2014 and 2015 from CYM's post. Link.

I'm only doing the analysis starting in 1926-27 (the year that all remaining North American professional hockey leagues were consolidated into the NHL). Perhaps there's a way to manual account for this from 1918 to 1926, but I haven't attempted to do this.

Click to read more...

 

[Hockey Outsider]

VsN results (ten years, unweighted, 1926-2015)

1 | Wayne Gretzky | 173.2
2 | Mario Lemieux | 136
3 | Phil Esposito | 127.8
4 | Jaromir Jagr | 127.5
5 | Gordie Howe | 120.1
6 | Marcel Dionne | 114.9
7 | Alex Ovechkin | 114
8 | Joe Sakic | 112.3
9 | Joe Thornton | 109.7
10 | Sidney Crosby | 108.7
11 | Teemu Selanne | 108.4
12 | Stan Mikita | 107.9
13 | Bobby Hull | 107.3
14 | Martin St. Louis | 107
15 | Mike Bossy | 106.8
16 | Guy Lafleur | 106.3
17 | Steve Yzerman | 106.3
18 | Bryan Trottier | 103.4
19 | Adam Oates | 103.2
20 | Jean Beliveau | 103.1
21 | Maurice Richard | 101.4
22 | Mark Messier | 101.1
23 | Ron Francis | 100.6
24 | Mark Recchi | 100.3
25 | Jarome Iginla | 99.6
26 | Brett Hull | 99.6
27 | Paul Coffey | 99.5
28 | Bobby Orr | 99.4
29 | Peter Forsberg | 98.9
30 | Andy Bathgate | 98.5
31 | Henrik Sedin | 98.1
32 | Peter Stastny | 97.9
33 | Jari Kurri | 97.5
34 | Dale Hawerchuk | 96.9
35 | Mats Sundin | 96.9
36 | Luc Robitaille | 96.5
37 | Jean Ratelle | 96.2
38 | Ted Lindsay | 95.7
39 | Ilya Kovalchuk | 95.5
40 | Paul Kariya | 95.4
41 | Pavel Datsyuk | 95.1
42 | Howie Morenz | 95
43 | Pierre Turgeon | 94.7
44 | Frank Boucher | 94.7
45 | Daniel Alfredsson | 94.5
46 | Marian Hossa | 94.1
47 | Bobby Clarke | 94
48 | Daniel Sedin | 93.9
49 | Theoren Fleury | 93.9
50 | Denis Savard | 93.8
51 | Eric Lindros | 93.5
52 | Mike Modano | 93.5
53 | Nels Stewart | 93.1
54 | Darryl Sittler | 92.8
55 | Gilbert Perreault | 92.7
56 | Doug Gilmour | 92.6
57 | Bill Cowley | 92.2
58 | Sergei Fedorov | 91.9
59 | Eric Staal | 91.2
60 | Jeremy Roenick | 91
61 | Frank Mahovlich | 90.4
62 | Bill Cook | 90.2
63 | Dany Heatley | 90.2
64 | John Bucyk | 90.1
65 | Evgeni Malkin | 89.7
66 | Henrik Zetterberg | 89.6
67 | Brendan Shanahan | 89.5
68 | Brad Richards | 89.4
69 | Norm Ullman | 89.4
70 | Keith Tkachuk | 89.2
71 | Rod Gilbert | 89
72 | Patrik Elias | 88.9
73 | Jason Spezza | 88.9
74 | Bernie Nicholls | 88.6
75 | Bernie Federko | 88.5
76 | Ryan Getzlaf | 88.2
77 | Markus Naslund | 88.1
78 | Vincent Lecavalier | 87.9
79 | Toe Blake | 87.8
80 | Syl Apps Sr | 87.8
81 | Pavel Bure | 87.7
82 | Alexander Mogilny | 87.7
83 | John LeClair | 86.5
84 | Alex Delvecchio | 86.5
85 | Doug Weight | 86.3
86 | Marty Barry | 86.3
87 | Alexei Yashin | 86.2
88 | Patrick Marleau | 85.9
89 | Bernie Geoffrion | 85.8
90 | Elmer Lach | 85.8
91 | Charlie Conacher | 85.7
92 | Pat LaFontaine | 85.7
93 | Ray Whitney | 85.4
94 | Vincent Damphousse | 85.3
95 | Michel Goulet | 85.2
96 | Raymond Bourque | 84.2
97 | Busher Jackson | 83.9
98 | Sweeney Schriner | 83.6
99 | Max Bentley | 83.5
100 | Mike Ribeiro | 83.1
101 | Pavol Demitra | 83
102 | Rod Brind'Amour | 83
103 | Alex Kovalev | 83
104 | Syd Howe | 82.9
105 | Ziggy Palffy | 82.8
106 | Brian Leetch | 81.5
107 | Alex Tanguay | 81.4
108 | Tony Amonte | 81.3
109 | Dino Ciccarelli | 81.2
110 | Doug Bentley | 81.1
111 | Ken Hodge | 80.9
112 | Milan Hejduk | 80.9
113 | Henri Richard | 80.7
114 | Lanny McDonald | 80.7
115 | Steve Larmer | 80.5
116 | Peter Bondra | 80.4
117 | Joe Nieuwendyk | 80.3
118 | Milt Schmidt | 80.2
119 | Joe Mullen | 80.1
120 | Aurel Joliat | 80
121 | Bobby Smith | 79.9
122 | Rick Nash | 79.9
123 | Jacques Lemaire | 79.8
124 | Anze Kopitar | 79.7
125 | Rick Middleton | 79.6
126 | Nicklas Lidstrom | 79.5
127 | Denis Potvin | 79.3
128 | Dave Andreychuk | 79.3
129 | Al MacInnis | 78.9
130 | Marian Gaborik | 78.7
131 | Glenn Anderson | 78.6
132 | Mike Gartner | 78.5
133 | Yvan Cournoyer | 78.4
134 | Thomas Vanek | 78.2
135 | Corey Perry | 78.2
136 | Marc Savard | 78.1
137 | Olli Jokinen | 77.2
138 | Sid Abel | 77.2
139 | Brian Propp | 77.1
140 | Dave Taylor | 77.1
141 | Bill Barber | 77.1
142 | Ted Kennedy | 76.8
143 | Scott Gomez | 76.8
144 | Dickie Moore | 76.4
145 | Nicklas Backstrom | 76.2
146 | Shane Doan | 76
147 | Pete Mahovlich | 76
148 | Dennis Maruk | 75.9
149 | Alex Zhamnov | 75.6
150 | Owen Nolan | 75.1
151 | Patrick Kane | 75
152 | Roy Conacher | 74.9
153 | Lorne Carr | 74.8
154 | Bryan Hextall | 74.8
155 | Miroslav Satan | 74.7
156 | Jason Pominville | 74.3
157 | Bill Mosienko | 74.2
158 | Phil Housley | 74.1
159 | Hooley Smith | 73.9
160 | Dave Keon | 73.8
161 | Cooney Weiland | 73.4
162 | Steve Sullivan | 73.4
163 | Bun Cook | 73.3
164 | Phil Watson | 73.3
165 | Bobby Rousseau | 73
166 | Todd Bertuzzi | 72.9
167 | Brian Bellows | 72.8
168 | Clint Smith | 72.8
169 | Paul Thompson | 72.8
170 | Tom Lysiak | 72.8
171 | Rick MacLeish | 72.8
172 | Zach Parise | 72.8
173 | Red Kelly | 72.7
174 | Craig Janney | 72.5
175 | Petr Sykora | 72.4
176 | Steve Shutt | 72.3
177 | Dit Clapper | 72.3
178 | Rick Martin | 72.1
179 | Robert Lang | 72.1
180 | Ryan Smyth | 72
181 | Pat Verbeek | 71.8
182 | Jason Arnott | 71.7
183 | Johnny Gottselig | 71.7
184 | Vyacheslav Kozlov | 71.4
185 | Andrew Brunette | 71.2
186 | Garry Unger | 71.2
187 | Martin Straka | 71.1
188 | Cory Stillman | 70.9
189 | Kirk Muller | 70.8
190 | Lynn Patrick | 70.8
191 | Petr Nedved | 70.7
192 | Butch Goring | 70.7
193 | Pierre Larouche | 70.6
194 | Cecil Dillon | 70.4
195 | Sergei Gonchar | 70.3
196 | Larry Murphy | 70.3
197 | Phil Kessel | 70.2
198 | Bill Guerin | 70.2
199 | Pit Martin | 70.2
200 | Cliff Ronning | 70.2
201 | Neal Broten | 70
202 | Patrice Bergeron | 70
203 | Herbie Lewis | 70
204 | Bert Olmstead | 69.9
205 | Phil Goyette | 69.8
206 | Woody Dumart | 69.6
207 | Chris Drury | 69.6
208 | Rick Tocchet | 69.4
209 | Saku Koivu | 69.3
210 | Peter McNab | 69.2
211 | Steve Thomas | 68.9
212 | Rene Robert | 68.9
213 | Kevin Stevens | 68.8
214 | Don McKenney | 68.8
215 | Mike Ridley | 68.8
216 | Wilf Paiement | 68.7
217 | Andrew Cassels | 68.6
218 | Robert Reichel | 68.6
219 | Jozef Stumpel | 68.5
220 | Steven Stamkos | 68.4
221 | Gary Roberts | 68.3
222 | Ivan Boldirev | 68.3
223 | Jonathan Toews | 68.2
224 | Tomas Sandstrom | 68.2
225 | Dave Gagner | 67.8
226 | Sergei Zubov | 67.7
227 | Brian Rolston | 67.7
228 | Herb Cain | 67.6
229 | Vaclav Prospal | 67.5
230 | Jean Pronovost | 67.4
231 | Michael Nylander | 67.4
232 | Jeff Carter | 67.3
233 | Greg Adams | 67.3
234 | Bill Thoms | 67.2
235 | Wayne Cashman | 67.1
236 | Daymond Langkow | 67.1
237 | Geoff Courtnall | 67
238 | Glen Murray | 66.9
239 | Alexander Semin | 66.8
240 | Chris Kunitz | 66.7
241 | Vic Hadfield | 66.7
242 | Ray Ferraro | 66.7
243 | Ebbie Goodfellow | 66.5
244 | Patrick Sharp | 66.4
245 | John Ogrodnick | 66.4
246 | Dean Prentice | 66.2
247 | Brad Park | 66.1
248 | John MacLean | 66.1
249 | Simon Gagne | 66
250 | Ken Linseman | 66

I'll repeat what I put in the first post. I am NOT saying that this is a definitive ranking. I'm simply posting data with the hopes that the system can be adjusted and refined. In fact, it appears obvious to me that there are serious problems with this approach.

First impression: this system is brutally unforgiving to players from the Original Six era (and earlier). A score of 100 represents an average #1 forward. During the Original Six era, with so much talent and so few teams, it's very difficult to consistently be a top three scorer (especially with Howe having one of those spots most years).

Examples of outputs that appear to be false: Crosby and Ovechkin are ranked ahead of Hull and Mikita. Iginla is barely behind Maurice Richard. Henrik Sedin is virtually tied with Andy Bathgate.

Any thoughts on how this can be improved? (More importantly, is this worth saving, or do we go back to the drawing board?)

 

[Czech Your Math]

Here are the results of a new adjusting scoring system called "VsN".

I'm not saying that this is the best method of adjusted scoring, I'm simply posting the results so that we can discuss them. (In fact, there appear to be obvious flaws, which can be seen below).

The method works as follows. Each year, we calculate a benchmark. This number is equal to the average number of points scored by the highest scorer through the Xth highest scorer in the NHL, where X is the number of teams in the league.

For example, in 1996 there were 26 teams in the NHL. We add up the total number of points scored by the highest scoring player (Mario Lemieux), 2nd highest scoring player (Jaromir Jagr), 3rd highest scoring player (Joe Sakic), all the way down to the 26th highest scoring player (Brian Leetch). This total is divided by 26, and that number is our benchmark. In this case the total number of points is 2,717, so the benchmark is 104.5.

We then adjust each player's actual results to the benchmark. For example, in 1996, Sergei Fedorov scored 107 points. The benchmark was 104.5 points. Thus, his adjusted total is 107/104.5*100 = 102 points (which could be interpreted that he produced slightly more offense than the average #1 forward that year).

Benefits? This method is simple to explain and doesn't involve any convoluted rules. The benchmark should, in theory, represent the actual output of the average #1 forward in any given season, facilitating cross-era comparisons. The benchmark should be minimally swayed by outliers (ie Howe, Gretzky, Lemieux).

Drawbacks? Short of a manual adjustment, the WWII years will always be distorted (most of the league's stars were in the Armed Forces and many of the players who remained took advantage of the low level of competition). The system is brutal during seasons with fewer teams (as seen in the results below).

The benchmarks were taken from BM67's post. They look reasonable, but I haven't recalculated them, so let me know if you see any errors. Link. I took the numbers for 2014 and 2015 from CYM's post. Link.

I'm only doing the analysis starting in 1926-27 (the year that all remaining North American professional hockey leagues were consolidated into the NHL). Perhaps there's a way to manual account for this from 1918 to 1926, but I haven't attempted to do this.

I have two adjustments that I would suggest.

One is for the WWII years ('43 thru '46). This WWII adjustment is objective and I believe it's based on sound methodology. Basically, it's using the surrounding seasons ('40 thru '42 and '47 thru '49) as "control" seasons and then comparing the actual 1N for those seasons to what the 1N would be if players missing in each of the war years were also missing in each control year.

Another adjustment I would suggest is for the post-expansion ('68 to present) period. Repeated expansions at differing intervals and the differing nature of those expansions causes the league to contain teams which don't have players of the quality to compete for spots in the top ~1N scorers. The best remedy I can think of at the moment is to reduce the "1N" number for those seasons to a more realistic number. One solution would be to count the number of teams represented in the top 1N scorers, then make that number the new "N" used for calculating the benchmark.

I will expound on each of these ideas in separate posts to follow.

 

[Czech Your Math]

As far as the WWII years, this is what I came up with for VsN:

It appears that '43 to '46 are the four seasons affected.
Determine which top players missed each of the war seasons due to WWII.
Use the 1-3 seasons before & after the '43-'46 period as a sort of control to calculate an adjustment factor.
When calculating for any of the seasons during the war years, deduct those players who were missing during that season, and use the difference to calculate an adjustment factor.

I know this sounds confusing, so here is an example:

The season for which we are calculating an adjustment is 1944-45.
One of the control seasons used for the calculation will be 1941-42.
Normally we would just take the top N (in this case, 7) players and average their point totals:

1. Bryan Hextall*-NYR 56
2. Lynn Patrick*-NYR 54
3. Don Grosso-DET 53
4. Phil Watson-NYR 52
5. Sid Abel*-DET 49
6. Toe Blake*-MTL 45
Bill Thoms-CBH 45

This would give us an average of 354 / 7 = 50.57 points

Since we are calculating for '45, we deduct any players from the list who missed the '45 season due to WWII, until we reach 7 remaining players. The players deducted are bolded in the following list. The remaining players which will be used in the new calculation are underlined:

1. Bryan Hextall*-NYR 56
2. Lynn Patrick*-NYR 54
3. Don Grosso-DET 53
4. Phil Watson-NYR 52
5. Sid Abel*-DET 49
6. Toe Blake*-MTL 45
Bill Thoms-CBH 45
8. Gordie Drillon*-TOR 41
Syl Apps*-TOR 41
Tom Anderson-BRO 41
11. Billy Taylor-TOR 38
Eddie Wares-DET 38
13. Roy Conacher*-BOS 37
Mel Hill-BRO 37
15. Sweeney Schriner*-TOR 36

So using only players that were available during the '45 season (if not for WWII), the 1N score in '42 would have been: 309/7 = 44.14

The adjustment factor is simply the actual 1N divided by the "would have been" 1N: 50.57 / 44.14 = 1.146

I also calculated a similar score for the '45 season, using the '47 season (the first season after the war period) as control. In this case the adjustment factor was: 62.17 / 55.50 = 1.150

So if one was using only the first seasons before and after the war period, then the adjustment factor would be: (1.146 + 1.150) / 2 = 1.148

So the "adjusted" 1N for the '45 season would then be the actual 1N for '45 multiplied by the calculated adjustment factor:

1. Elmer Lach*-MTL 80
2. Maurice Richard*-MTL 73
3. Toe Blake*-MTL 67
4. Bill Cowley*-BOS 65
5. Ted Kennedy*-TOR 54
Bill Mosienko*-CBH 54

1N = 393 / 6 = 65.5
Adjustment factor = 1.148
Adjusted 1N = 65.5 * 1.148 = 75.19

I did this rather quickly for each of the 4 war seasons, using 1-3 control seasons both before and after the war period ('42 & '47 = one season; '40-42 & '47-49 = three seasons). These were the calculated adjustment factors:

YEAR 1Year 2Years 3Years
-------------------------
1943 1.013 1.008 1.026
1944 1.106 1.080 1.098
1945 1.148 1.110 1.124
1946 1.035 1.025 1.037

I would suggest using the 3 Year numbers, which yield new benchmarks as follows:

'43: Instead of 66.00, use 67.70
'44: Instead of 75.00, use 82.34
'45: Instead of 65.50, use 73.61
'46: Instead of 51.50, use 53.41

 

[Czech Your Math]

For the post-expansion ('68 to present) seasons, I found an alternative that better reflects how many teams are a factor in the top 1N scorers.

Count the number of teams represented in the top 1N scorers.
Use that number as the "N" for that year.

For example, if there were 21 teams in the NHL that season, and there were 12 teams represented in the top 21 scorers, then use an average of the top 12 scorers as the VsN # for that season. When players in the top 1N play for two teams, each of those teams is counted as 0.5.

When multiple players are tied for the (original) Nth spot, each of those players' teams receives credit using the formula (# spots tied) / (# players tied for those spots). If there are 21 teams and 5 players are tied for 20th, then each of those players is weighted (20th + 21st = 2 spots) / (5 players) = 2/5 = 0.4 (note: each team not previously represented is only weighted once).

I would keep the original method for pre-expansion seasons, at least for now.

Here are the new benchmarks I calculated for post-expansion seasons:

2015 76.46
2014 79.39
2013 51.59
2012 81.50
2011 84.43
2010 91.17
2009 90.26
2008 88.33
2007 98.12
2006 97.94
2004 78.88
2003 89.14
2002 78.19
2001 93.87
2000 80.79
1999 90.18
1998 81.02
1997 92.47
1996 114.13
1995 56.94
1994 103.95
1993 126.48
1992 107.31
1991 114.67
1990 111.79
1989 124.49
1988 118.83
1987 102.06
1986 125.04
1985 121.25
1984 122.56
1983 119.20
1982 127.75
1981 114.62
1980 107.75
1979 116.25
1978 100.24
1977 98.75
1976 111.06
1975 114.22
1974 96.70
1973 101.25
1972 109.67
1971 124.44
1970 89.00
1969 100.23
1968 82.82

 

[Hockey Outsider]

Here are the revised numbers using CYM's two adjustments (one for WWII, one for post-expansion years):

1 | Wayne Gretzky | 156.8
2 | Mario Lemieux | 125.3
3 | Jaromir Jagr | 119.5
4 | Gordie Howe | 118.4
5 | Phil Esposito | 113.6
6 | Alex Ovechkin | 106.5
7 | Joe Sakic | 104.6
8 | Marcel Dionne | 104.5
9 | Stan Mikita | 104.1
10 | Joe Thornton | 102.8
11 | Jean Beliveau | 102
12 | Bobby Hull | 101.6
13 | Sidney Crosby | 101.5
14 | Teemu Selanne | 101.4
15 | Martin St. Louis | 99.9
16 | Maurice Richard | 99.8
17 | Steve Yzerman | 98.5
18 | Andy Bathgate | 97.8
19 | Mike Bossy | 96.7
20 | Adam Oates | 96.7
21 | Guy Lafleur | 96.2
22 | Ted Lindsay | 95.7
23 | Ron Francis | 95.1
24 | Howie Morenz | 95
25 | Frank Boucher | 94.7
26 | Mark Recchi | 94.1
27 | Bryan Trottier | 93.8
28 | Jarome Iginla | 93.7
29 | Mark Messier | 93.6
30 | Brett Hull | 93.1
31 | Nels Stewart | 93.1
32 | Peter Forsberg | 92.5
33 | Mats Sundin | 91.6
34 | Henrik Sedin | 91.5
35 | Paul Coffey | 90.3
36 | Bill Cook | 90.2
37 | Bill Cowley | 90
38 | Luc Robitaille | 89.4
39 | Ilya Kovalchuk | 89.4
40 | Paul Kariya | 89.3
41 | Jari Kurri | 89
42 | Pavel Datsyuk | 89
43 | Pierre Turgeon | 89
44 | Peter Stastny | 88.8
45 | Daniel Alfredsson | 88.6
46 | Dale Hawerchuk | 88.4
47 | Marian Hossa | 88.2
48 | Eric Lindros | 87.8
49 | Bobby Orr | 87.8
50 | Mike Modano | 87.8
51 | Daniel Sedin | 87.7
52 | Theoren Fleury | 87.6
53 | Syl Apps Sr | 87.4
54 | Jean Ratelle | 87
55 | Doug Gilmour | 86.3
56 | Marty Barry | 86.3
57 | Sergei Fedorov | 86
58 | Bernie Geoffrion | 85.8
59 | Charlie Conacher | 85.7
60 | Toe Blake | 85.4
61 | Bobby Clarke | 85.3
62 | Jeremy Roenick | 85.2
63 | Eric Staal | 85.2
64 | Norm Ullman | 85.2
65 | Denis Savard | 85.1
66 | Frank Mahovlich | 85
67 | Darryl Sittler | 84.9
68 | Brendan Shanahan | 84.2
69 | Dany Heatley | 84.2
70 | Evgeni Malkin | 84
71 | Keith Tkachuk | 83.9
72 | Busher Jackson | 83.9
73 | Gilbert Perreault | 83.9
74 | Alex Delvecchio | 83.8
75 | Henrik Zetterberg | 83.7
76 | Brad Richards | 83.5
77 | Patrik Elias | 83.5
78 | Jason Spezza | 83.3
79 | Elmer Lach | 83
80 | Max Bentley | 82.8
81 | Pavel Bure | 82.8
82 | Sweeney Schriner | 82.8
83 | Markus Naslund | 82.7
84 | Ryan Getzlaf | 82.4
85 | Vincent Lecavalier | 82.2
86 | Rod Gilbert | 82.2
87 | Alexander Mogilny | 81.6
88 | John LeClair | 81.6
89 | Doug Weight | 81.3
90 | John Bucyk | 81.2
91 | Syd Howe | 81.1
92 | Bernie Nicholls | 80.9
93 | Alexei Yashin | 80.8
94 | Henri Richard | 80.7
95 | Vincent Damphousse | 80.5
96 | Ray Whitney | 80.3
97 | Bernie Federko | 80.1
98 | Patrick Marleau | 80.1
99 | Aurel Joliat | 80
100 | Milt Schmidt | 80
101 | Doug Bentley | 79.7
102 | Pat LaFontaine | 79.2
103 | Pavol Demitra | 78.2
104 | Alex Kovalev | 78.1
105 | Ziggy Palffy | 77.9
106 | Raymond Bourque | 77.8
107 | Mike Ribeiro | 77.8
108 | Rod Brind'Amour | 77.7
109 | Michel Goulet | 77.4
110 | Sid Abel | 77
111 | Tony Amonte | 76.6
112 | Dickie Moore | 76.4
113 | Alex Tanguay | 76.3
114 | Brian Leetch | 75.9
115 | Milan Hejduk | 75.8
116 | Peter Bondra | 75.4
117 | Ted Kennedy | 75.3
118 | Dino Ciccarelli | 74.9
119 | Roy Conacher | 74.9
120 | Rick Nash | 74.7
121 | Nicklas Lidstrom | 74.7
122 | Joe Nieuwendyk | 74.6
123 | Anze Kopitar | 74.4
124 | Hooley Smith | 73.9
125 | Joe Mullen | 73.7
126 | Dave Andreychuk | 73.6
127 | Marian Gaborik | 73.6
128 | Cooney Weiland | 73.4
129 | Bun Cook | 73.3
130 | Steve Larmer | 73.3
131 | Lanny McDonald | 73.2
132 | Marc Savard | 73.2
133 | Thomas Vanek | 73.1
134 | Al MacInnis | 73
135 | Corey Perry | 72.9
136 | Lorne Carr | 72.9
137 | Paul Thompson | 72.8
138 | Red Kelly | 72.7
139 | Bryan Hextall | 72.4
140 | Phil Watson | 72.3
141 | Rick Middleton | 72.3
142 | Dit Clapper | 72.3
143 | Mike Gartner | 72.3
144 | Bobby Smith | 72.2
145 | Olli Jokinen | 72.1
146 | Bill Mosienko | 72.1
147 | Scott Gomez | 72.1
148 | Denis Potvin | 71.9
149 | Jacques Lemaire | 71.9
150 | Ken Hodge | 71.8
151 | Johnny Gottselig | 71.7
152 | Shane Doan | 71.3
153 | Glenn Anderson | 71.3
154 | Nicklas Backstrom | 71.2
155 | Alex Zhamnov | 71.2
156 | Clint Smith | 70.6
157 | Owen Nolan | 70.6
158 | Bill Barber | 70.5
159 | Lynn Patrick | 70.4
160 | Cecil Dillon | 70.4
161 | Miroslav Satan | 70.3
162 | Patrick Kane | 70
163 | Herbie Lewis | 70
164 | Bert Olmstead | 69.9
165 | Dave Taylor | 69.9
166 | Yvan Cournoyer | 69.8
167 | Dave Keon | 69.8
168 | Brian Propp | 69.7
169 | Jason Pominville | 69.5
170 | Bobby Rousseau | 69.4
171 | Woody Dumart | 69.4
172 | Don McKenney | 68.8
173 | Steve Sullivan | 68.8
174 | Phil Housley | 68.7
175 | Dennis Maruk | 68.7
176 | Todd Bertuzzi | 68.3
177 | Zach Parise | 68.1
178 | Pete Mahovlich | 67.9
179 | Petr Sykora | 67.9
180 | Robert Lang | 67.7
181 | Ryan Smyth | 67.5
182 | Jason Arnott | 67.4
183 | Craig Janney | 67.3
184 | Pat Verbeek | 67
185 | Bill Thoms | 67
186 | Rick MacLeish | 66.9
187 | Vyacheslav Kozlov | 66.8
188 | Andrew Brunette | 66.8
189 | Brian Bellows | 66.7
190 | Cory Stillman | 66.5
191 | Ebbie Goodfellow | 66.5
192 | Martin Straka | 66.4
193 | Tom Lysiak | 66.2
194 | Petr Nedved | 66.2
195 | Sergei Gonchar | 66
196 | Steve Shutt | 66
197 | Cliff Ronning | 65.9
198 | Phil Goyette | 65.8
199 | Larry Murphy | 65.8
200 | Bill Guerin | 65.7
201 | Rick Martin | 65.7
202 | Phil Kessel | 65.6
203 | Herb Cain | 65.6
204 | Patrice Bergeron | 65.4
205 | Kirk Muller | 65.3
206 | Chris Drury | 65.3
207 | Larry Aurie | 65
208 | Saku Koivu | 64.9
209 | Dean Prentice | 64.8
210 | Jozef Stumpel | 64.7
211 | Pierre Larouche | 64.7
212 | Andrew Cassels | 64.5
213 | Robert Reichel | 64.5
214 | Eddie Wiseman | 64.5
215 | Butch Goring | 64.5
216 | Gary Roberts | 64.3
217 | Steve Thomas | 64.2
218 | Kevin Stevens | 64.1
219 | Rick Tocchet | 64
220 | Neal Broten | 63.8
221 | Jonathan Toews | 63.7
222 | Steven Stamkos | 63.7
223 | Mike Ridley | 63.7
224 | Pit Martin | 63.6
225 | Jimmy Ward | 63.5
226 | Garry Unger | 63.5
227 | Vaclav Prospal | 63.4
228 | Sergei Zubov | 63.3
229 | Brian Rolston | 63.3
230 | Michael Nylander | 63.3
231 | Glen Murray | 63.1
232 | Rene Robert | 63.1
233 | Daymond Langkow | 63
234 | Kenny Wharram | 63
235 | Peter McNab | 63
236 | Dave Gagner | 63
237 | Tomas Sandstrom | 62.9
238 | Jeff Carter | 62.8
239 | Gordie Drillon | 62.8
240 | Wilf Paiement | 62.6
241 | Tod Sloan | 62.6
242 | Chris Kunitz | 62.4
243 | Alexander Semin | 62.3
244 | Geoff Courtnall | 62.2
245 | Greg Adams | 62.1
246 | Patrick Sharp | 62.1
247 | Ivan Boldirev | 62.1
248 | Buddy O'Connor | 62
249 | Ray Ferraro | 61.9
250 | Johnny Gagnon | 61.8

 

[steve141]

I really like the simplicity of it.

Would a seven year sample be more fair to older players?

 

[supsens]

How big of a swing is injuries in these benchmarks? I am not strong on stats but i notice the year you posted as your topic Lemieux was NO.1 in points but he also only played 70 games vs most peoples 82, Messier played 74 and Oats 70.
messier PPG that year would have moved him up to 10th and Oats would have been in 12th.
Isn't using only the top 12 like CYM suggests a large handicap for some years? Seems like it is an unfair adjustment, you can't take an average of X for some guys and Z for others, 95-96 had two sets of players from the same team that both play the same position so they did not feed of each other too much.

 

[TheDevilMadeMe]

I really like the simplicity of it.

Would a seven year sample be more fair to older players?

Probably. When we originally came up with VsX, there was an assumption that 7 years was an "average" historical prime, while 10 years was an average prime post-expansion. So 7 years is the preferred metric for any "all-time" ranking.

That said, my biggest question to HO - how many players reach certain benchmarks (50%, 60%, 70%, 80%, 90%) in the years immediately before and immediately after expansion. That would determine if VsN is historically useful at all, IMO. My first thought was that I wasn't surprised it was brutal towards pre-expansion players, since there is no reason to assume that the average of the top 12 players in 1968 is going to be of similar quality to the average of the top 6 players in 1967.

 

[Sturminator]

Sadly, although this system has the benefit of simplicity very much on its side, it seems to be systematically brutal to pre-expansion players.

 

[Hockey Outsider]

That said, my biggest question to HO - how many players reach certain benchmarks (50%, 60%, 70%, 80%, 90%) in the years immediately before and immediately after expansion. That would determine if VsN is historically useful at all, IMO. My first thought was that I wasn't surprised it was brutal towards pre-expansion players, since there is no reason to assume that the average of the top 12 players in 1968 is going to be of similar quality to the average of the top 6 players in 1967.

Season | >70 | >80 | >90 | >100 | >110 | >120
1965 | 12 | 7 | 5 | 3 | 2 | 0
1966 | 14 | 7 | 6 | 1 | 1 | 1
1967 | 13 | 9 | 3 | 2 | 1 | 1
1968 | 19 | 12 | 6 | 2 | 0 | 0
1969 | 16 | 9 | 5 | 3 | 1 | 1
1970 | 21 | 9 | 3 | 2 | 2 | 1

At a first glance, although there are significant increases in "good" seasons (>70 and >80) right after expansion, there isn`t a big change in "great" seasons (>100).

Still, the biggest problem is that the benchmark can easily be skewed by outliers. Not a problem today when there are 30 teams, but it's a big problem during the Original Six era and right after expansion. In 1951, Gordie Howe raised the benchmark to such an extent that he was the only >100. Bobby Hull did the same in 1966, as did Bill Cowley in 1941.

Another example. In 1971, Orr and Esposito raised the benchmark so high that there are only five >70 seasons, four of those being Bruins.

I like the simplicity and intuitive appeal of the system, but unless someone can think of a way to correct these issues - I can't - then I recommend we reject this method.

 

[Czech Your Math]

Isn't using only the top 12 like CYM suggests a large handicap for some years? Seems like it is an unfair adjustment, you can't take an average of X for some guys and Z for others, 95-96 had two sets of players from the same team that both play the same position so they did not feed of each other too much.

It's a way to approximate how many teams had an effect on the scoring race. The rule would be some variation of "an average of the # Z players who were represented in the top N scorers, where N is the number of NHL teams, with Z having a minimum value of (?)."

Since that method seems to not quite go far enough in increasing the post-expansion benchmarks, I don't really see it as a handicap on the post-expansion players. However, I do understand your concern that the rule should be consistent from era to era. Mainly, I wanted to get an idea of how the numbers looked, to see if further refinement would be worthwhile or it should be scrapped entirely.

After reviewing the numbers HO provided, I do see the need for further improvement in the system, but am not yet sure the best way to do that without making it much more complicated.

 

[Czech Your Math]

Still, the biggest problem is that the benchmark can easily be skewed by outliers. Not a problem today when there are 30 teams, but it's a big problem during the Original Six era and right after expansion. In 1951, Gordie Howe raised the benchmark to such an extent that he was the only >100. Bobby Hull did the same in 1966, as did Bill Cowley in 1941.

Another example. In 1971, Orr and Esposito raised the benchmark so high that there are only five >70 seasons, four of those being Bruins.

I like the simplicity and intuitive appeal of the system, but unless someone can think of a way to correct these issues - I can't - then I recommend we reject this method.

I'm not sure it should be discarded, but understand the need for further refinement.

No matter what system is used, it is going to seem unfair to certain players or certain eras, and overly generous to others. If anything, I believe a system like VsN is probably less skewed by outliers, because it takes an average of several players. It's not so dependent on whether one or two players have career seasons or miss much of the season with injuries.

Seasons like 1971 (and 1974) are going to be problematic, no matter what the system. VsX gives Bucyk a score of 129 and Hodge 117. It becomes a matter of whether one wants to adjust the Bruins' numbers down to more realistic levels or to give the rest of the league unrealistically low numbers. In 1989, the only player besides Gretzky, Lemieux and their teammates to hit 80 was Yzerman. So there are always going to be tricky seasons where some players are going to have numbers that seem much too high or much too low. When several seasons are used, those variations have a much better chance of balancing out, or at least not having such a dramatic effect as in 1 or 2 seasons.

 

[TheDevilMadeMe]

The drastic increase in number of players hitting the 70th and 80th percentiles after expansion tell me that this method isn't going to work.

 

[Hardyvan123]

The drastic increase in number of players hitting the 70th and 80th percentiles after expansion tell me that this method isn't going to work.

Sometimes the destination isn't as important as the journey.

The reality is that the state of the NHL has changed dramatically over time and trying to find the best way to fairly compare player A form one period to player B in another period is never to be perfect.

the fact that we are having these discussions and raise the concerns of different eras and circumstances is far more important than any conclusions one method or another brings IMO.

that being said it's also important not to have preconceived notions of "fairness" or "equality" being represented equally over time as changes have happened and probably will continue to happen to make these comparisons or metrics good guesses at best.

 

[Triffy]

HO, have you tried how the results change if you replace mean with median? Median is much less sensitive to outliers.

 

[TheDevilMadeMe]

Worth looking at, I guess, but the median is just going to be an even more direct function of the number of teams. Compare to the mean of the 3rd/4th best scorers in 1967, then the mean of the 6th/7th best scorers in 1968.

 

[MXD]

I can think of doing something like "past 115% per given year, count a point out of two only for the purposes of setting the benchmark".

But then you'll end up with situations like, Hodge's input looking way more important than it was in reality versus Orr.

Not to mention -- it wouldn't alleviate that system's biggest flaw (brutal treatment of every pre-expansion player except Gordie Howe and MAYBE Frank Boucher, in that he's very close to Howie Morenz, though that might be a function of the 10 season period as opposed to the system itself, plus non-inclusion of pre-consolidation years).

115 was a completely random number by the way.

 

[jigglysquishy]

Why don't we just use the same adjustments for 73-74 or any other outlier year with the same formula from VsX? Or was the VsX criticism from these formulas?

I don't know if you can account for a year like 73-74 while being consistent with every year.

Edit: I believe 72-73 is the crazy Bruins year