Single-formula VsX: a measure derived from interquartile range

Black Gold Extractor · Apr 21, 2020

For offense, the generally accepted metric on HoH is VsX, which uses a “typical” 2nd-place scorer as a baseline for comparison. For the majority of cases, the baseline is the actual 2nd-place scorer, but there are exceptions. (The rules are outlined here. Updated results are here.) The exceptions are what often make VsX somewhat cumbersome (and arguably, somewhat less-rigorous than desired).

Standard VsX rules rely on the implicit assumption that the NHL has been able to generate a typical 2nd-place scorer every season. (For seasons that clearly cannot, such as the WWII years, there are curated benchmarks used instead.) Era “strength” has always been a contentious issue, but as far as I know, there have been few attempts to assess this aspect quantitatively. (It is possible that the reason is because the word “strength” is somewhat inflammatory and inaccurate.) The spread or density of scorers facing similar circumstances may aid in accounting for the talent pool available for NHL in any given era. In theory, a league with access to a larger talent pool should be able to fill in more gaps, resulting in a denser spread of values.

One can account for this by considering the interquartile range (IQR). The IQR is a measure of statistical dispersion, like standard deviation, but it does not assume the shape of the distribution. (Standard deviation assumes a normal/Gaussian distribution.) It relies on quartiles rather than all values, so it is not affected by outliers given a sufficient sample size. Finally, calculating the IQR is child’s play. (It’s not even “pen and paper” easy. It’s literally “do it in your head with simple arithmetic” easy.)

Methodology

Since the interquartile range must contain the middle half of all data points, care must be taken to ensure a proper range of selection given the limited number of first-liners available during the O6 era (18 total). As such, the top 24 scorers in each season should be chosen to maximize sample size, which in this case would be 12 scorers within the IQR. The interquartile range is the 3rd quartile (3Q) minus the 1st quartile (1Q):

IQR = 7th - 18th

In a normal distribution (which, admittedly, this is not), the IQR would span 1.349 standard deviations (SD). Each quartile would be 0.6745 SD from the middle of a normal distribution. In order to estimate a typical 2nd place scorer (which is what VsX endeavours to do), one could add the 3rd quartile to the IQR, which would give us a value that would be approximately 2 SD from the median (containing roughly 95.45% of all values in a normal distribution, which is pretty close to 23/24). An outlier as defined by the IQR method would be 3Q+1.5*IQR, which would be 2.698 SD from the median, but most 2nd place scorers are not on the edge of being outliers.

(Expected 2nd place scorer, “3Q+IQR”) = 7th + 7th - 18th

This estimator relies on only two points, but it can be made slightly more "robust" by using a modifed tri-mean (middle value*2 plus an upper flanking value and a lower flanking value, all divided by 4). After trying several variations, the following gave the best results, with non-whole numbers rounded down:

(Expected 2nd place scorer, “Single-formula VsX”) = (3rd + 11th)/2 + 8th - 18th

The average of the 3rd and 11th place scorers should give us an estimated 7th place scorer, but skewed somewhat higher. Moving the middle of the tri-mean to 8th should account for the skew.

Results

Year	Normal VsX	3Q+IQR	Single-formula VsX	Notes
1924		26	25	pre-consolidation
1925		43	45	pre-consolidation
1926		34	38	pre-consolidation
1927	32	34	33
1928	35	38	37
1929	29	28	28
1930	62	73	69
1931	43	48	48
1932	50	58	52
1933	44	42	44
1934	43	46	46
1935	47	46	47
1936	40	47	46
1937	45	41	43
1938	44	44	46
1939	44	46	44
1940	43	46	46
1941	44	51	48
1942	54	55	51
1943	72	73	77	normal VsX rules: 66
1944	95	89	84	normal VsX rules: 77
1945	78	67	70	normal VsX rules: 62.625
1946	60	59	57	normal VsX rules: 52
1947	63	66	68
1948	60	66	65
1949	54	53	56
1950	69	62	66
1951	66	80	74
1952	69	63	67
1953	61	63	61
1954	61	56	61
1955	74	74	74
1956	71	80	73
1957	77	78	83
1958	71	71	77
1959	83	74	84
1960	80	91	87
1961	90	88	88
1962	84	77	80
1963	81	79	79
1964	78	83	79
1965	83	76	78
1966	78	87	78
1967	70	76	77
1968	84	85	86
1969	107	100	106
1970	86	79	85
1971	90	90	105
1972	109	113	105
1973	104	103	105
1974	91	93	100
1975	121	120	123
1976	119	124	123
1977	105	108	105
1978	109	101	112
1979	116	122	124
1980	119	113	120
1981	135	117	129
1982	147	142	144
1983	124	122	127
1984	121	133	130
1985	135	112	123
1986	141	138	137
1987	108	116	112
1988	131	131	133
1989	139	132	139
1990	129	118	125
1991	115	127	119
1992	116	117	123
1993	148	152	153
1994	120	121	113
1995	70	67	67
1996	120	120	124
1997	109	106	100
1998	91	102	98
1999	107	112	111
2000	94	95	92
2001	96	103	101
2002	90	83	85
2003	104	106	106
2004	87	87	90
2006	106	113	110
2007	114	115	112
2008	106	103	102
2009	110	103	104
2010	109	103	107
2011	99	97	94
2012	97	88	92
2013	57	58	58
2014	87	90	91
2015	86	84	84
2016	89	88	90
2017	89	94	88
2018	102	100	101
2019	110	111	114	normal VsX rules: 116

R-squared	1.000	0.953	0.975

As can be seen, both the “3Q+IQR” and “single-formula VsX” methods produce results that are very similar to VsX. Even the curated “WWII fudge” values for standard VsX are decently (though not entirely) replicated, which serves as a worthwhile sanity check. As expected, going from a two-point estimator (3Q+IQR) to a four-point estimator (single-formula VsX) produces a better fit, going from a 0.953 r-squared value to 0.975.

As a personal preference, I also like that the single-formula VsX benchmarks are somewhat less "jumpy" than the standard VsX benchmarks. It might be enough for single-season benchmarks to be somewhat more reliable than before.

Season	Art Ross	Single-formula VsX bench.	Dominance
1927	37	33	112.1
1928	51	37	137.8
1929	32	28	114.3
1930	73	69	105.8
1931	51	48	106.3
1932	53	52	101.9
1933	50	44	113.6
1934	52	46	113.0
1935	47	47	100.0
1936	45	46	97.8
1937	46	43	107.0
1938	52	46	113.0
1939	47	44	106.8
1940	52	46	113.0
1941	64	48	133.3
1942	56	51	109.8
1943	73	77	94.8
1944	82	84	97.6
1945	80	70	114.3
1946	61	57	107.0
1947	72	68	105.9
1948	61	65	93.8
1949	68	56	121.4
1950	78	66	118.2
1951	86	74	116.2
1952	86	67	128.4
1953	95	61	155.7
1954	81	61	132.8
1955	75	74	101.4
1956	88	73	120.5
1957	89	83	107.2
1958	84	77	109.1
1959	96	84	114.3
1960	81	87	93.1
1961	95	88	108.0
1962	84	80	105.0
1963	86	79	108.9
1964	89	79	112.7
1965	87	78	111.5
1966	97	78	124.4
1967	97	77	126.0
1968	87	86	101.2
1969	126	106	118.9
1970	120	85	141.2
1971	152	105	144.8
1972	133	105	126.7
1973	130	105	123.8
1974	145	100	145.0
1975	135	123	109.8
1976	125	123	101.6
1977	136	105	129.5
1978	132	112	117.9
1979	134	124	108.1
1980	137	120	114.2
1981	164	129	127.1
1982	212	144	147.2
1983	196	127	154.3
1984	205	130	157.7
1985	208	123	169.1
1986	215	137	156.9
1987	183	112	163.4
1988	168	133	126.3
1989	199	139	143.2
1990	142	125	113.6
1991	163	119	137.0
1992	131	123	106.5
1993	160	153	104.6
1994	130	113	115.0
1995	70	67	104.5
1996	161	124	129.8
1997	122	100	122.0
1998	102	98	104.1
1999	127	111	114.4
2000	96	92	104.3
2001	121	101	119.8
2002	96	85	112.9
2003	106	106	100.0
2004	94	90	104.4
2006	125	110	113.6
2007	120	112	107.1
2008	112	102	109.8
2009	113	104	108.7
2010	112	107	104.7
2011	104	94	110.6
2012	109	92	118.5
2013	60	58	103.4
2014	104	91	114.3
2015	87	84	103.6
2016	106	90	117.8
2017	100	88	113.6
2018	108	101	106.9
2019	128	114	112.3

Era "strength"

There does seem to be a trend of improvement in “quality” of the typical 2nd place scorer with the passage of time, which is what proponents of more recent players have trumpeted... but going by the linear fit, the difference is only about 5% over the course of a century.

So, how does this affect our favourite players? Looking at the typical best 7 years:

Player	Normal VsX	3Q+IQR	Single-Formula VsX	Notes
Wayne Gretzky	155.6	157.6	155.1
Phil Esposito	130.4	132.3	125.5
Gordie Howe	125.5	124.7	122.5
Mario Lemieux	119.8	121.4	119.3
Bobby Orr	114.8	116.5	110.5
Jaromir Jagr	114.2	109.9	111.3
Bobby Hull	108.3	105.4	104.1
Stan Mikita	107.8	108.2	107.0
Jean Beliveau	105.7	103.4	104.1
Guy Lafleur	104.5	105.0	102.1
Ted Lindsay	104.4	106.9	102.6
Marcel Dionne	103.3	108.2	103.8
Sidney Crosby	102.4	102.7	102.9
Maurice Richard	102.4	103.8	102.0
Howie Morenz	102.2	98.8	100.0	3Q+IQR and single-formula VsX include pre-consolidation data (96.4 and 98.6 w/o respectively)
Andy Bathgate	101.1	102.8	99.2
Alex Ovechkin	98.4	99.4	99.6
Joe Sakic	97.7	96.5	96.7
Bill Cowley	97.0	95.9	95.9
Charlie Conacher	96.2	89.9	90.7
Bill Cook	96.0	91.1	92.6
Joe Thornton	95.6	95.0	94.7
Frank Boucher	95.1	89.9	90.7
Mike Bossy	94.8	98.4	94.9
Evgeni Malkin	93.7	96.3	96.1
Bryan Trottier	93.7	94.7	91.0
Steve Yzerman	93.2	93.1	92.6
Patrick Kane	92.9	92.5	92.3
Teemu Selanne	92.7	90.2	92.0
Martin St. Louis	92.4	94.0	93.4


R-squared	1.000	0.966	0.981

It's somewhat fitting that using single-formula VsX, Howie Morenz gets a 7-year score of 100.0. The best player of the first half of the 20th century is the benchmark against which all others are measured. (As such, instead of calling it "single-formula VsX", we could consider calling it a "Morenz rating" or "Vs-Morenz" or something like that?)

Summary

Using a single formula,

(Expected 2nd-place scorer) = (3rd + 11th)/2 + 8th - 18th

a benchmark similar to normal VsX can be found without requiring exceptions or conditional rules. In addition, this formula inherently accounts for the density of scorers, thus also accounting for talent pool size. Finally, the resulting benchmarks are less "jumpy" than standard VsX, possibly allowing for comparison of single season results without the need for multi-season averages.

EDIT (July 2, 2023):

Latest revised formula is:

(Expected 2nd-place scorer) = (3rd + 13th)/2 + 8th - 18th

This makes it a proper trimean around the 8th place scorer. Updated benchmarks here.

The top 180 7-year single-formula VsX (updated for 2020-21) scores are here.

The top 120 10-year single-formula VsX (updated for 2020-21) scores are here.

alko · Apr 21, 2020

Sheldon Cooper, is that you?

Black Gold Extractor · Mar 28, 2021

Just another note about league strength over the years. You can make a decent estimate of the VsX baseline by adding the 4th place goal total and 4th place assist total. (VsX baseline from Hockey Outsider's thread here.)

Season	Goals - 4th	Assists - 4th	Est. VsX	VsX Baseline	Ratio
1927	19	13	32	32	1.000
1928	23	12	35	35	1.000
1929	17	11	28	29	0.966
1930	39	30	69	62	1.113
1931	25	23	48	43	1.116
1932	26	25	51	50	1.020
1933	22	25	47	44	1.068
1934	21	21	42	43	0.977
1935	22	27	49	47	1.043
1936	19	23	42	40	1.050
1937	21	25	46	45	1.022
1938	21	25	46	44	1.045
1939	21	28	49	44	1.114
1940	21	26	47	43	1.093
1941	23	25	48	44	1.091
1942	24	30	54	54	1.000
1943	28	42	70	72	0.972
1944	36	42	78	95	0.821
1945	29	36	65	78	0.833
1946	27	27	54	60	0.900
1947	29	34	63	63	1.000
1948	27	31	58	60	0.967
1949	26	28	54	54	1.000
1950	29	34	63	69	0.913
1951	30	39	69	66	1.045
1952	30	39	69	69	1.000
1953	28	38	66	61	1.082
1954	27	33	60	61	0.984
1955	33	42	75	74	1.014
1956	37	41	78	71	1.099
1957	32	45	77	77	1.000
1958	32	44	76	71	1.070
1959	33	46	79	83	0.952
1960	32	43	75	80	0.938
1961	32	48	80	90	0.889
1962	33	44	77	84	0.917
1963	35	46	81	81	1.000
1964	29	47	76	78	0.974
1965	28	42	70	83	0.843
1966	31	46	77	78	0.987
1967	28	44	72	70	1.029
1968	35	47	82	84	0.976
1969	45	58	103	107	0.963
1970	38	50	88	86	1.023
1971	43	62	105	90	1.167
1972	47	56	103	109	0.945
1973	44	61	105	104	1.010
1974	50	61	111	91	1.220
1975	50	74	124	121	1.025
1976	52	69	121	119	1.017
1977	49	66	115	105	1.095
1978	47	68	115	109	1.055
1979	50	71	121	116	1.043
1980	53	66	119	119	1.000
1981	55	73	128	135	0.948
1982	55	83	138	147	0.939
1983	57	67	124	124	1.000
1984	54	73	127	121	1.050
1985	55	77	132	135	0.978
1986	54	81	135	141	0.957
1987	54	64	118	108	1.093
1988	53	77	130	131	0.992
1989	54	83	137	139	0.986
1990	55	78	133	129	1.031
1991	51	73	124	115	1.078
1992	53	79	132	116	1.138
1993	63	91	154	148	1.041
1994	53	77	130	120	1.083
1995	30	41	71	70	1.014
1996	52	86	138	120	1.150
1997	50	63	113	109	1.037
1998	51	62	113	91	1.242
1999	44	60	104	107	0.972
2000	42	53	95	94	1.011
2001	45	65	110	96	1.146
2002	41	50	91	90	1.011
2003	45	57	102	104	0.981
2004	38	54	92	87	1.057
2006	52	69	121	106	1.142
2007	46	71	117	114	1.026
2008	47	61	108	106	1.019
2009	43	66	109	110	0.991
2010	44	67	111	109	1.018
2011	41	57	98	99	0.990
2012	40	59	99	97	1.021
2013	26	37	63	57	1.105
2014	39	58	97	87	1.115
2015	38	56	94	86	1.093
2016	40	57	97	89	1.090
2017	39	56	95	89	1.067
2018	42	65	107	102	1.049
2019	45	68	113	116	0.974
2020	43	60	103	97	1.062

R-squared	-	-	0.95	1.00

[TBODY] [/TBODY]

R-squared value of 0.95 isn't as good as the single-formula VsX in the opening post (r-squared of 0.98), but this is alright for our purposes. The ratios of the values plotted over the years is:

From the slope of the best-fit line, one can observe that the "strength" of the league has improved by roughly 6.4% over a century. This is roughly the same as the 5% over a century that I observed when using the single-formula VsX in the first post. Since this observation arises from two different methods, I'm going to say that it's a real phenomenon (even if it's a minor one).

As such, one can assume that a player getting a VsX score of 80 in the 1960's and another getting a VsX score of 80 in the 2010's aren't quite the same. (I'd say that player 50 years later should get a boost of 2-3%.) This doesn't make a difference for the huge outliers (Gretzky, Esposito, Howe, Lemieux, Orr, Jagr) or even the more typical outliers (Hull, Mikita, Lafleur, etc.), but it might make a difference when comparing players down the list.

Black Gold Extractor · Mar 29, 2021

Eliminating the gaps: Paul Kariya Edition

So, what happened in 1996-97? Apparently, Paul Kariya had the gall to score his 99th point of the season, or something like that.

Rk	Player	PTS
1	Mario Lemieux*	122
2	Teemu Selanne*	109
3	Paul Kariya*	99
4	Wayne Gretzky*	97
5	John LeClair	97
6	Jaromir Jagr	95
7	Mats Sundin*	94
8	Ron Francis*	90
9	Ziggy Palffy	90
10	Brendan Shanahan*	88
11	Peter Forsberg*	86
12	Keith Tkachuk	86
13	Pierre Turgeon	85
14	Steve Yzerman*	85
15	Mark Messier*	84
16	Mike Modano*	83
17	Doug Gilmour*	82
18	Brett Hull*	82
19	Adam Oates*	82
20	Doug Weight	82

[TBODY] [/TBODY]

Based on VsX rules, the 2nd-place scorer here gets the nod as the baseline (Selanne with 109 points). Selanne looks like he might be an outlier according to the rules, but not so! 99/109 = 0.908, which is above the cutoff of 0.9. Kariya's VsX for 1996-97 is thus 90.8.

But what if Kariya had only scored 98 points? (Let's call this version "Kariya-1".) Then the VsX baseline goes to "Kariya-1" because 98/109 = 0.899 < 0.9. "Kariya-1" has a VsX of 100.0 for 1996-97.

In summary,

Kariya with 99 points:

VsX baseline = 109
Kariya VsX = 90.8

Kariya with 98 points ("Kariya-1"):

VsX baseline = 98
"Kariya-1" VsX = 100.0

Single-formula VsX method

So, as stated in the opening post,
(Expected 2nd-place scorer) = (3rd + 11th)/2 + 8th - 18th

For Kariya scoring 99 points:
(Expected 2nd-place scorer) = (99 + 86)/2 + 90 - 82 = 100.5

For "Kariya-1" scoring 98 points:
(Expected 2nd-place scorer) = (98 + 86)/2 + 90 - 82 = 100.0

In summary,

Kariya with 99 points:

Single-formula VsX baseline = 100.5
Kariya single-formula VsX = 98.5

Kariya with 98 points ("Kariya-1"):

Single-formula VsX baseline = 100.0
"Kariya-1" single-formula VsX = 98.0

Q.E.D.

To quote Hockey Outsider, "I'll end this post the way Sturminator ended his - Comments, criticisms, fact-checking and personal attacks are all welcome."

TheDevilMadeMe · Mar 29, 2021

Tagging @Sturminator in this thread too.

I will say one thing - I don't think VsX was ever intended to be precise enough to apply when comparing individual seasons - there's a reason we speak of 7-year and 10-year average scores. At some point, there is a tradeoff between simplicity and accuracy.

TheDevilMadeMe · Apr 8, 2021

I'm just going to put this here because I just did another comparison using VsX in the top 200 project.

I think your method is likely a slight improvement on VsX in terms of accuracy.

However, I look at your comparison table in post #1, and the differences between the two calculations are generally quite small - pretty close to what I would consider the "margin of error" of a VsX number.

Given that the differences aren't that big, I think that's just why VsX has stuck around so long - it's relatively simple to calculate and envision what it's doing. And it gets results that appear "good enough"

Black Gold Extractor · May 8, 2021

Here is a "tweaked" version of the formula:

(Expected 2nd place scorer) = (3rd + 13th)/2 + 8th - 18th

Revised benchmarks:

Season	Normal VsX	SF VsX	Notes
1925		41.5	Pre-consolidation, 6 teams
1926		37.5	Pre-consolidation, 7 teams
1927	32	32.5
1928	35	35.0
1929	29	28.0
1930	62	67.5
1931	43	46.0
1932	50	52.5
1933	44	43.0
1934	43	45.5
1935	47	47.0
1936	40	45.0
1937	45	42.5
1938	44	45.0
1939	44	44.5
1940	43	44.0
1941	44	47.0
1942	54	51.0
1943	72	75.5
1944	95	83.0
1945	78	69.0
1946	60	57.0
1947	63	68.0
1948	60	64.5
1949	54	55.5
1950	69	65.0
1951	66	71.5
1952	69	66.5
1953	61	60.0
1954	61	59.5
1955	74	73.0
1956	71	72.5
1957	77	82.0
1958	71	75.0
1959	83	83.0
1960	80	82.5
1961	90	87.0
1962	84	79.5
1963	81	79.0
1964	78	78.5
1965	83	76.5
1966	78	78.0
1967	70	76.0
1968	84	84.5
1969	107	106.0
1970	86	84.5
1971	90	103.5
1972	109	103.0
1973	104	105.5
1974	91	99.5
1975	121	122.0
1976	119	121.5
1977	105	105.0
1978	109	111.0
1979	116	123.0
1980	119	120.0
1981	135	126.0
1982	147	143.0
1983	124	123.5
1984	121	128.5
1985	135	122.0
1986	141	136.0
1987	108	110.5
1988	131	129.5
1989	139	138.5
1990	129	125.0
1991	115	119.0
1992	116	122.0
1993	148	151.0
1994	120	113.5
1995	70	66.0
1996	120	121.5
1997	109	100.0
1998	91	97.0
1999	107	110.0
2000	94	92.0
2001	96	99.5
2002	90	85.0
2003	104	104.0
2004	87	88.0
2006	106	109.0
2007	114	111.0
2008	106	101.5
2009	110	102.5
2010	109	106.5
2011	99	94.0
2012	97	92.0
2013	57	58.0
2014	87	90.0
2015	86	84.5
2016	89	89.5
2017	89	88.0
2018	102	100.5
2019	116	113.0
2020	97	102.0
2021	69	72.5
2022	115	120.0
2023	113	120.0

Average	87.8	87.8
R-squared	1.000	0.976

In essence, the expected 2nd place scorer is defined as "just under" 2 standard deviations from the median of the top 24 scorers.

Comparing the top 35 scorers in 7-year (normal) VsX, using years 1926-27 through 2022-23:

Player	Normal VsX	SF VsX (July 2, 2023)	Difference
Wayne Gretzky	155.6	156.8	+1.2
Phil Esposito	130.4	126.4	-4.0
Gordie Howe	125.5	124.3	-1.2
Mario Lemieux	119.8	120.7	+0.9
Connor McDavid	116.1	113.4	-2.7
Bobby Orr	114.8	111.3	-3.5
Jaromir Jagr	114.2	112.6	-1.6
Bobby Hull	108.3	105.4	-2.9
Stan Mikita	107.8	108.0	+0.2
Jean Beliveau	105.7	105.0	-0.7
Guy Lafleur	104.5	102.9	-1.6
Ted Lindsay	104.4	104.3	-0.1
Marcel Dionne	103.3	104.6	+1.3
Sidney Crosby	102.4	103.4	+1.0
Maurice Richard	102.4	103.4	+1.0
Howie Morenz	102.2	101.0	-1.2
Andy Bathgate	101.1	100.2	-0.9
Leon Draisaitl	98.5	96.0	-2.5
Alex Ovechkin	98.4	100.0	+1.6
Joe Sakic	97.7	97.8	+0.1
Bill Cowley	97	97.6	+0.6
Patrick Kane	96.2	95.4	-0.8
Charlie Conacher	96.2	92.2	-4.0
Bill Cook	96	93.9	-2.1
Joe Thornton	95.6	95.6	-0.0
Frank Boucher	95.1	92.6	-2.5
Mike Bossy	94.8	96.2	+1.4
Evgeni Malkin	93.7	96.5	+2.8
Bryan Trottier	93.7	91.9	-1.8
Steve Yzerman	93.2	92.9	-0.3
Teemu Selanne	92.7	92.7	-0.0
Martin St. Louis	92.4	94.0	+1.6
Syl Apps Sr	92.4	90.7	-1.7
Nikita Kucherov	91.4	91.1	-0.3
Steven Stamkos	91.4	92.9	+1.5

Average	103.6	103.0	-0.6
R-squared	1.000	0.983

Black Gold Extractor · May 8, 2021

The top 180 7-year single-formula VsX scores (from 1924-25 to 2022-23):

Name	1	2	3	4	5	6	7	8	9	10	5-yr	7-yr	10-yr	Career
Wayne Gretzky	170.5	165.6	159.5	158.7	158.1	148.3	137.0	130.2	121.3	115.1	162.5	156.8	146.4	2351.5
Phil Esposito	146.9	145.7	129.1	123.2	118.9	117.2	104.1	99.4	80.3	76.2	132.8	126.4	114.1	1572.7
Gordie Howe	158.3	136.1	129.3	120.3	109.0	108.9	108.5	104.6	102.7	99.3	130.6	124.3	117.7	2428.6
Mario Lemieux	143.7	132.5	129.7	122.0	107.4	106.0	103.7	98.4	96.8	87.5	127.1	120.7	112.8	1423.3
Connor McDavid	144.8	127.5	113.6	107.5	102.7	102.5	95.1	53.6			119.2	113.4		847.3
Jaromír Jágr	122.6	121.6	115.5	112.8	106.1	105.2	104.3	95.0	92.9	87.2	115.7	112.6	106.3	1926.6
Bobby Orr	142.0	134.3	122.6	113.6	110.7	95.7	60.4	53.9	36.7	21.9	124.6	111.3	89.2	909.9
Stan Mikita	127.6	113.7	113.4	103.0	101.8	100.0	96.9	96.2	91.5	80.4	111.9	108.0	102.4	1597.2
Bobby Hull	124.4	110.8	105.7	105.3	100.9	98.2	92.8	92.8	90.3	88.8	109.4	105.4	101.0	1369.1
Jean Beliveau	121.4	109.6	103.4	102.4	100.0	99.4	98.7	89.7	84.8	80.5	107.4	105.0	99.0	1503.5
Marcel Dionne	116.2	114.2	107.1	105.7	103.3	99.2	86.6	85.3	81.8	78.4	109.3	104.6	97.8	1484.6
Ted Lindsay	120.0	118.3	104.2	103.8	103.7	97.3	82.5	80.6	69.9	69.0	110.0	104.3	94.9	1246.3
Maurice Richard	112.6	105.8	104.4	101.7	101.4	100.0	97.9	92.3	86.0	82.2	105.2	103.4	98.4	1407.6
Sidney Crosby	115.6	108.1	102.3	101.1	100.5	99.4	96.6	95.0	93.6	88.6	105.5	103.4	100.1	1549.7
Howie Morenz	145.7	110.9	98.5	96.4	94.0	93.3	83.7	78.5	72.3	69.3	109.1	103.2	94.3	1082.6
Guy Lafleur	129.5	118.9	104.9	104.2	102.9	97.5	62.1	61.5	58.7	56.3	112.1	102.9	89.7	1146.1
Andy Bathgate	106.0	105.7	104.0	102.5	98.1	93.9	91.0	89.7	88.5	69.8	103.3	100.2	94.9	1214.8
Alex Ovechkin	110.3	107.3	102.3	97.2	96.6	95.9	90.4	87.8	86.6	82.9	102.8	100.0	95.7	1525.6
Joe Sakic	118.6	98.9	98.8	93.9	92.9	91.6	90.1	88.0	87.3	81.6	100.6	97.8	94.2	1539.8
Bill Cowley	136.2	95.4	94.4	94.2	90.9	86.7	85.5	80.0	55.9	52.9	102.2	97.6	87.2	986.4
Evgeni Malkin	118.5	110.2	104.4	97.5	82.8	81.8	80.0	76.6	72.5	72.3	102.7	96.5	89.7	1264.3
Mike Bossy	102.8	102.4	95.9	95.5	94.4	91.8	90.4	82.0	76.7	67.9	98.2	96.2	90.0	899.9
Leon Draisaitl	115.9	107.8	106.7	92.9	91.7	87.5	69.7	57.0	10.7		103.0	96.0		739.7
Joe Thornton	114.7	102.7	97.1	94.6	91.6	84.4	83.9	83.7	83.6	83.0	100.1	95.6	91.9	1604.8
Patrick Kane	118.4	101.1	97.3	94.8	91.0	82.6	82.4	77.7	76.7	76.7	100.6	95.4	89.9	1308.6
Martin St. Louis	106.8	105.3	103.4	91.9	88.3	81.8	80.4	78.0	76.7	67.3	99.1	94.0	88.0	1100.2
Bill Cook	116.3	113.8	91.3	89.5	87.4	82.1	76.6	68.6	57.1	37.8	99.7	93.9	82.1	832.4
Steven Stamkos	105.4	98.3	96.8	89.2	88.3	86.7	85.6	85.2	71.5	70.0	95.6	92.9	87.7	1100.7
Steve Yzerman	111.9	101.6	90.8	90.7	85.9	85.0	84.4	81.4	78.8	78.2	96.2	92.9	88.9	1534.0
Nels Stewart	112.0	103.6	97.1	85.7	84.8	83.7	83.0	82.4	81.5	80.0	96.6	92.8	89.4	1193.9
Syl Apps	111.1	105.9	93.6	89.9	85.4	82.2	81.5	80.6	80.4	72.1	97.2	92.8	88.3	1375.5
Teemu Selänne	109.0	97.3	92.4	88.9	88.7	87.4	85.1	84.7	82.6	72.7	95.2	92.7	88.9	1433.6
Frank Boucher	100.0	96.7	95.7	92.9	91.9	86.2	84.8	81.4	68.6	64.4	95.4	92.6	86.3	928.7
Charlie Conacher	121.3	114.3	93.5	91.4	84.4	76.7	63.6	49.4	46.8	43.0	101.0	92.2	78.5	838.9
Bryan Trottier	110.8	108.9	90.2	86.7	86.4	81.7	78.7	78.2	72.1	70.6	96.6	91.9	86.4	1156.8
Nikita Kucherov	113.3	99.5	96.6	94.2	83.3	76.9	73.7	57.5	20.0		97.4	91.1		715.0
Syl Apps	111.1	105.9	93.6	89.9	82.2	80.4	72.1	70.2	68.2	53.0	96.5	90.7	82.6	826.5
Bernie Geoffrion	109.2	102.7	90.8	86.1	85.5	81.2	79.5	74.2	66.7	65.0	94.9	90.7	84.1	1090.9
Peter Stastny	100.4	97.2	92.6	89.7	86.5	85.7	82.0	69.7	61.4	58.4	93.3	90.6	82.4	968.4
Peter Forsberg	101.9	95.5	93.8	89.4	88.2	86.0	75.8	68.8	62.5	55.4	93.8	90.1	81.7	880.7
Sweeney Schriner	108.2	101.1	100.0	85.1	84.4	80.9	70.6	59.1	53.6	47.7	95.8	90.0	79.1	825.8
Doug Bentley	118.9	96.7	92.8	88.4	81.5	80.9	70.2	59.6	51.0	44.8	95.7	89.9	78.5	855.5
Paul Coffey	101.5	99.2	98.1	87.9	82.4	81.6	78.2	77.7	67.8	62.2	93.8	89.8	83.7	1273.5
Jarome Iginla	112.9	96.6	91.5	86.8	84.7	83.0	72.8	71.4	69.8	68.5	94.5	89.8	83.8	1365.8
Elmer Lach	115.9	97.7	94.6	86.7	82.5	76.8	73.8	68.3	62.9	52.3	95.5	89.7	81.2	944.4
Adam Oates	98.7	96.6	94.0	91.8	82.4	82.0	81.6	81.1	80.3	78.4	92.7	89.6	86.7	1287.9
Jean Ratelle	105.8	92.3	89.5	89.1	87.6	86.4	75.7	74.6	73.6	69.6	92.9	89.5	84.4	1238.6
Jari Kurri	110.7	97.7	96.3	87.9	84.2	74.4	74.1	73.6	67.8	60.1	95.4	89.3	82.7	1132.0
Mark Messier	103.2	96.8	87.7	85.8	85.7	84.0	81.5	80.3	78.6	74.0	91.9	89.3	85.8	1630.6
Ron Francis	97.9	90.6	90.0	89.7	89.4	84.2	81.9	80.8	79.3	73.1	91.5	89.1	85.7	1601.9
Bobby Clarke	98.6	97.9	95.1	87.4	85.7	80.2	78.6	68.8	60.9	59.3	93.0	89.1	81.3	1066.9
Claude Giroux	101.5	101.1	95.6	86.4	82.8	80.9	75.2	74.9	65.9	65.8	93.5	89.1	83.0	1065.9
Frank Mahovlich	96.6	93.2	92.4	89.3	88.2	82.8	80.4	73.6	71.8	70.5	91.9	89.0	83.9	1253.1
Norm Ullman	108.5	92.3	92.1	85.2	82.1	80.5	80.5	72.6	71.0	70.9	92.0	88.7	83.6	1418.2
Nicklas Backstrom	97.7	94.8	92.3	87.8	85.9	82.8	78.2	73.1	70.6	69.1	91.7	88.5	83.2	1092.4
Busher Jackson	102.3	101.0	94.1	93.6	83.5	75.6	67.4	60.7	55.3	48.9	94.9	88.2	78.2	961.6
Toe Blake	105.6	97.1	88.2	87.7	86.4	78.1	73.5	73.3	71.1	68.1	93.0	88.1	82.9	924.9
Mark Recchi	98.9	95.0	94.3	85.2	81.5	80.0	79.5	77.4	76.3	75.3	91.0	87.8	84.3	1451.7
Brett Hull	110.1	90.4	89.3	85.5	82.0	79.4	77.3	75.8	74.2	74.1	91.5	87.7	83.8	1275.1
Marty Barry	103.5	92.1	88.9	86.0	85.7	85.1	72.4	67.4	64.4	48.9	91.3	87.7	79.5	829.2
Max Bentley	107.0	105.9	92.7	86.7	83.7	73.9	63.1	61.7	58.8	53.8	95.2	87.6	78.7	861.8
Henrik Sedin	105.2	100.0	88.0	86.4	80.0	77.6	74.9	73.0	68.8	61.5	91.9	87.4	81.5	1134.1
Eric Lindros	106.1	94.7	85.9	85.5	84.5	79.0	73.2	64.1	51.0	49.7	91.3	87.0	77.4	853.5
Denis Savard	101.2	98.0	86.1	85.3	83.2	81.4	73.2	64.0	59.5	59.2	90.7	86.9	79.1	1076.0
Aurele Joliat	111.4	101.2	88.4	79.1	76.1	75.3	74.3	69.3	61.7	60.7	91.2	86.5	79.8	980.3
Alex Delvecchio	98.3	88.5	87.6	86.8	82.8	81.0	80.5	78.7	78.3	72.4	88.8	86.5	83.5	1574.7
Sid Abel	106.2	97.3	96.1	85.3	79.7	70.6	68.2	68.1	55.6	15.0	92.9	86.2	74.2	765.5
Dale Hawerchuk	106.6	93.4	90.5	80.3	79.4	77.2	75.8	74.8	73.7	72.0	90.0	86.2	82.4	1129.8
John Bucyk	112.1	88.2	83.5	81.7	81.7	80.6	75.5	75.4	73.1	72.3	89.4	86.2	82.4	1497.1
Gordie Drillon	115.6	93.6	93.2	80.4	77.6	76.4	66.2				92.1	86.1		603.0
Roy Conacher	122.5	86.2	83.1	83.0	79.4	76.0	72.5	69.9	68.2	6.0	90.8	86.1	74.7	752.1
Ilya Kovalchuk	98.9	90.2	89.9	88.8	85.7	79.8	68.5	64.4	63.8	60.0	90.7	86.0	79.0	899.0
Pavel Bure	102.2	94.3	92.8	92.5	81.2	72.8	65.2	55.0	49.2	28.8	92.6	85.8	73.4	759.1
Nathan MacKinnon	96.5	92.5	91.2	89.7	87.6	73.3	70.0	60.2	58.1	45.0	91.5	85.8	76.4	764.1
Paul Kariya	99.0	93.5	91.8	88.9	78.0	77.9	68.5	67.3	67.1	64.0	90.2	85.4	79.6	982.9
Ryan Getzlaf	96.7	88.8	84.5	83.0	82.8	80.9	80.8	70.4	64.8	62.0	87.1	85.3	79.5	1081.2
Milt Schmidt	118.2	91.2	85.3	80.9	75.2	71.9	68.6	63.1	60.0	57.7	90.1	84.5	77.2	1017.1
Darryl Sittler	105.4	85.7	84.4	82.3	80.8	76.2	73.0	70.7	67.2	65.6	87.7	84.0	79.1	959.9
Pavel Datsyuk	95.6	94.6	84.5	79.8	78.4	77.3	76.9	72.8	65.7	62.8	86.6	83.9	78.8	974.5
Dickie Moore	115.7	112.0	79.3	77.6	70.7	67.6	63.3	51.6	49.6	49.3	91.1	83.7	73.7	775.7
Gilbert Perreault	93.0	90.5	88.3	83.4	80.2	78.7	71.8	70.0	69.6	69.1	87.1	83.7	79.5	1131.9
John Tavares	101.8	88.0	83.6	81.0	78.2	77.9	75.0	73.3	71.3	69.0	86.5	83.6	79.9	1038.6
Brad Marchand	96.6	95.2	88.5	85.3	84.6	68.2	66.7	62.1	59.8	58.9	90.0	83.6	76.6	915.8
Henri Richard	106.7	92.4	88.5	78.2	78.2	72.4	68.0	67.5	65.9	62.9	88.8	83.5	78.1	1237.6
Phil Kessel	91.5	89.7	89.1	88.9	79.5	72.6	72.2	68.1	65.9	59.3	87.8	83.4	77.7	1060.2
Mike Modano	90.6	88.0	84.4	83.0	81.9	81.7	73.6	70.6	66.7	63.1	85.6	83.3	78.4	1297.8
Rod Gilbert	94.2	91.1	81.5	79.7	79.6	79.5	77.4	72.6	71.4	70.8	85.2	83.3	79.8	1060.7
Syd Howe	100.0	93.6	84.1	83.1	76.8	72.8	72.3	68.6	66.7	63.5	87.5	83.3	78.2	1007.1
Doug Gilmour	97.8	95.0	84.1	82.0	79.3	72.8	71.3	68.1	66.4	61.4	87.7	83.2	77.8	1235.3
Luc Robitaille	88.4	87.7	85.7	82.8	80.8	80.4	76.5	76.0	75.8	70.8	85.1	83.2	80.5	1250.4
Daniel Alfredsson	94.5	90.9	87.7	83.5	78.4	75.0	72.2	71.0	70.4	66.7	87.0	83.2	79.0	1177.3
Artemi Panarin	93.1	86.0	84.1	81.6	80.0	80.0	77.0	76.7			85.0	83.1		658.5
Daniel Sedin	110.6	89.9	80.0	79.8	75.7	72.9	72.8	69.0	68.2	65.1	87.2	83.1	78.4	1104.0
Dany Heatley	94.6	94.5	85.6	80.8	78.8	77.0	70.2	68.1	57.6	36.2	86.9	83.1	74.3	802.9
Mats Sundin	94.1	94.0	85.2	79.3	76.8	76.3	75.5	75.5	74.9	74.4	85.9	83.0	80.6	1294.0
Marián Hossa	93.2	90.1	84.4	83.7	77.6	76.9	75.4	72.2	69.3	66.7	85.8	83.0	78.9	1193.6
Jamie Benn	103.0	99.4	87.8	78.6	78.4	68.5	65.0	59.6	56.9	48.3	89.4	83.0	74.5	907.4
Markus Näslund	105.9	100.0	95.5	75.4	72.5	70.7	60.0	54.2	54.1	45.3	89.8	82.8	73.3	870.0
Pierre Turgeon	87.4	85.0	84.8	82.8	82.4	79.0	77.9	71.7	71.2	70.1	84.5	82.8	79.2	1203.5
John LeClair	97.0	89.7	83.7	81.8	81.8	79.8	62.5	60.0	46.8	37.9	86.8	82.3	72.1	816.9
Bryan Hextall	109.8	100.0	90.9	80.9	78.1	65.1	51.2	46.7	46.4	44.1	92.0	82.3	71.3	902.6
Bernie Nicholls	108.3	89.6	82.0	77.3	73.9	73.3	71.3	61.3	60.2	49.4	86.2	82.2	74.7	1005.6
Sergei Fedorov	105.7	88.1	80.0	79.8	75.8	73.9	70.5	69.3	67.4	66.4	85.9	82.0	77.7	1123.0
Eric Staal	91.7	91.4	80.9	80.8	76.1	75.6	73.9	73.2	67.8	65.7	84.2	81.5	77.7	1117.0
Tyler Seguin	93.3	91.1	81.8	81.6	77.6	72.8	70.8	55.2	49.0	41.7	85.1	81.3	71.5	781.9
Paul Thompson	97.8	88.9	83.0	82.4	79.1	76.7	60.7	41.9	33.7	30.8	86.2	81.2	67.5	757.0
Jeremy Roenick	94.3	84.8	84.4	79.0	78.8	76.4	70.9	69.0	65.5	57.7	84.3	81.2	76.1	1133.9
Theoren Fleury	87.9	87.4	84.5	80.4	79.0	74.9	74.4	74.1	69.6	67.0	83.8	81.2	77.9	1014.3
Brendan Shanahan	89.9	88.2	88.0	84.8	76.4	74.3	65.4	64.2	62.3	62.1	85.5	81.0	75.6	1267.9
Henrik Zetterberg	90.6	85.1	82.8	78.1	78.0	77.3	75.0	71.2	65.7	61.3	82.9	81.0	76.5	1021.2
Johnny Gaudreau	95.8	87.6	87.2	83.6	75.7	69.3	67.6	61.7	56.9	1.1	86.0	81.0	68.6	686.5
Patrik Elias	96.5	92.0	84.8	78.3	76.1	71.8	66.0	62.2	62.1	58.9	85.5	80.8	74.9	1081.6
Anze Kopitar	91.5	82.7	82.6	77.8	77.7	76.1	75.9	75.7	72.4	69.0	82.5	80.6	78.1	1129.5
Ziggy Pálffy	90.0	89.7	89.4	81.7	71.7	71.6	69.4	46.6	45.5	38.5	84.5	80.5	69.4	720.0
Keith Tkachuk	88.2	86.0	80.7	80.7	79.4	77.3	71.4	68.0	61.8	57.1	83.0	80.5	75.1	1053.7
Erik Karlsson	91.6	84.8	84.2	82.2	80.7	78.1	61.7	47.9	39.8	39.2	84.7	80.5	69.0	798.2
Blake Wheeler	90.5	87.2	84.1	80.5	76.7	72.2	70.7	69.6	63.7	63.4	83.8	80.3	75.9	980.8
Michel Goulet	94.9	86.9	85.0	81.9	77.9	76.5	58.7	56.3	54.6	51.6	85.3	80.3	72.4	911.2
Jason Spezza	91.3	90.6	82.6	78.4	73.4	73.3	71.2	70.4	62.5	60.6	83.3	80.1	75.4	1030.0
Ken Hodge	105.5	101.4	84.9	76.8	66.3	63.9	59.0	54.4	54.1	50.2	87.0	79.7	71.7	868.4
Brad Richards	89.8	85.4	83.5	81.9	72.9	71.7	71.2	63.1	62.3	61.1	82.7	79.5	74.3	1055.5
Clint Smith	92.1	87.7	86.7	82.2	78.3	68.6	54.5	53.2	43.7	38.2	85.4	78.6	68.5	687.7
Bernie Federko	84.4	83.3	82.5	78.3	77.2	75.0	68.7	68.0	65.2	64.3	81.2	78.5	74.7	899.9
Bill Mosienko	84.3	84.2	79.7	78.3	76.5	75.7	70.8	61.7	57.1	50.3	80.6	78.5	71.9	824.4
Alexei Yashin	88.4	88.2	85.5	75.0	74.2	69.6	66.7	62.5	60.6	45.0	82.3	78.2	71.6	786.5
Doug Weight	90.5	85.6	82.0	78.3	73.9	72.2	65.2	64.4	60.6	57.6	82.0	78.2	73.0	1012.9
Alexander Mogilny	88.1	84.1	83.4	76.0	73.0	71.2	69.6	68.9	67.1	53.8	80.9	77.9	73.5	961.6
Vincent Lecavalier	97.3	90.6	75.0	75.0	72.8	68.8	65.7	65.4	57.4	55.2	82.2	77.9	72.3	981.7
Joe Pavelski	87.8	87.2	82.8	77.3	70.3	70.2	67.5	66.3	65.7	64.2	81.1	77.6	73.9	1049.8
Lynn Patrick	107.8	93.6	80.8	75.6	65.2	63.6	56.5	55.6	46.8	24.6	84.6	77.6	67.0	670.0
Ted Kennedy	88.2	85.3	78.3	78.2	71.3	71.2	70.3	67.7	63.9	61.7	80.3	77.5	73.6	832.0
Mitch Marner	92.4	83.2	82.5	80.8	69.3	68.7	65.7				81.7	77.5		542.6
Jacques Lemaire	90.0	87.4	78.6	75.4	71.4	71.0	67.3	59.4	54.1	49.7	80.6	77.3	70.5	792.0
Lorne Carr	89.2	83.1	80.0	79.5	70.2	69.6	68.1	64.7	56.8	51.1	80.4	77.1	71.2	776.8
Phil Watson	102.0	83.1	81.8	76.6	71.1	65.9	59.0	55.6	51.2	45.6	82.9	77.1	69.2	750.4
Pat LaFontaine	98.0	84.0	76.2	74.9	71.4	71.0	63.9	63.5	63.3	44.3	80.9	77.1	71.1	829.2
Hooley Smith	95.3	84.4	83.8	81.3	67.9	66.7	57.8	57.4	56.5	54.3	82.6	76.8	70.6	978.9
Corey Perry	104.3	91.1	71.4	70.2	69.3	65.2	65.1	62.1	60.2	53.2	81.2	76.7	71.2	936.0
Alex Kovalev	95.5	89.4	82.8	74.0	71.7	63.4	59.6	54.6	51.1	49.3	82.7	76.6	69.2	1023.2
Jonathan Huberdeau	95.8	84.1	81.4	76.5	68.7	65.9	63.9	53.4	45.8	31.1	81.3	76.6	66.7	696.3
Auston Matthews	91.0	88.3	78.4	78.4	70.8	64.6	62.7				81.4	76.3		534.3
Mike Ribeiro	84.5	81.8	76.1	75.5	73.9	73.4	68.5	55.9	53.2	52.2	78.3	76.2	69.5	859.5
Cecil Dillon	86.7	85.7	72.9	72.4	72.3	72.1	71.1	60.7	38.6	21.7	78.0	76.2	65.4	654.3
Bert Olmstead	96.6	87.4	79.5	75.4	75.0	59.8	58.5	57.3	52.6	49.4	82.8	76.0	69.1	833.3
Cooney Weiland	108.1	82.6	80.9	70.3	64.3	62.8	62.2	51.4	51.1	36.0	81.2	75.9	67.0	705.0
Vincent Damphousse	81.0	80.2	77.4	76.1	75.2	73.0	68.2	64.2	61.3	60.8	78.0	75.9	71.7	1101.8
Red Kelly	82.4	80.5	76.7	75.9	75.5	70.7	69.0	61.6	61.6	61.5	78.2	75.8	71.5	1128.2
Bun Cook	86.0	80.0	76.9	76.1	72.5	72.3	64.8	64.3	62.2	21.2	78.3	75.5	67.6	696.4
Bobby Rousseau	100.0	82.9	76.9	71.3	68.6	66.0	61.4	56.6	55.3	51.3	80.0	75.3	69.0	809.9
Yvan Cournoyer	82.1	80.6	74.9	74.6	73.4	71.0	70.5	60.7	56.0	52.6	77.1	75.3	69.6	864.7
Ray Bourque	86.0	80.2	79.0	74.7	70.5	67.5	67.2	66.4	65.2	62.5	78.1	75.0	71.9	1345.1
Pavol Demitra	91.8	89.4	81.5	80.9	65.9	57.7	56.9	53.6	53.2	51.7	81.9	74.9	68.3	772.2
Ray Whitney	83.7	77.2	75.1	74.8	73.1	71.8	67.0	60.6	60.1	58.2	76.8	74.7	70.2	1093.0
Jonathan Toews	82.8	80.9	78.1	75.6	71.7	67.3	65.9	64.8	63.8	62.0	77.8	74.6	71.3	933.2
Patrick Marleau	78.9	77.9	77.8	77.7	70.3	69.6	69.3	67.5	64.8	54.8	76.5	74.5	70.8	1249.9
Marc Savard	89.0	86.5	85.9	76.8	65.3	59.1	57.6	48.1	40.9	38.8	80.7	74.3	64.8	695.8
Brian Leetch	83.6	79.4	78.0	73.9	70.0	69.6	64.7	62.1	58.0	51.5	77.0	74.2	69.1	958.0
Jakub Voracek	95.9	84.6	79.3	69.3	68.9	61.5	59.3	58.4	54.9	53.3	79.6	74.1	68.5	869.9
Milan Hejduk	94.2	85.2	79.4	78.3	63.1	59.6	57.6	53.2	53.2	51.8	80.0	73.9	67.5	819.6
Lanny McDonald	85.7	79.4	78.4	76.5	69.1	64.3	62.5	57.3	52.2	51.4	77.8	73.7	67.7	827.6
Rick Middleton	81.7	81.7	77.7	76.7	69.9	65.7	62.3	61.5	54.1	41.2	77.6	73.7	67.3	802.4
Herbie Lewis	91.5	82.2	79.1	75.3	68.9	68.1	50.0	45.7	44.4	36.2	79.4	73.6	64.1	677.3
Alex Tanguay	89.8	77.4	73.4	73.0	71.6	65.1	64.4	57.1	56.5	55.4	77.0	73.5	68.4	909.5
Tony Amonte	91.3	77.6	77.0	75.3	68.2	64.3	60.2	56.6	53.0	51.9	77.9	73.4	67.5	877.3
Phil Goyette	92.3	82.8	80.3	76.9	61.3	60.1	58.9	53.8	52.1	42.8	78.7	73.2	66.1	803.4
Denis Potvin	84.7	82.1	80.7	76.2	66.1	62.3	60.3	55.7	54.3	53.4	78.0	73.2	67.6	873.5
Mark Scheifele	93.2	86.9	74.3	71.6	68.2	59.7	58.3	58.0	56.7	37.8	78.8	73.2	66.5	665.7
Kent Nilsson	104.0	84.2	81.1	77.5	62.3	57.0	44.1	38.5	1.5		81.8	72.9		550.2
Glenn Anderson	84.2	77.0	75.0	73.4	68.0	66.4	66.1	57.6	46.7	46.2	75.5	72.9	66.1	879.0
Dave Keon	76.7	76.4	73.4	73.4	70.9	69.2	69.2	68.4	65.4	57.5	74.2	72.8	70.1	1059.6
Taylor Hall	92.5	88.9	86.2	72.6	60.2	57.6	51.0	50.8	45.5	45.0	80.1	72.7	65.0	770.0
Zach Parise	91.7	77.0	75.0	73.4	65.5	64.0	62.2	59.2	55.9	54.0	76.5	72.7	67.8	912.7
Bobby Bauer	97.7	83.0	79.4	73.3	69.7	68.6	36.8	3.0	2.4		80.6	72.7		513.9
Peter Bondra	82.4	81.4	80.4	77.0	65.8	65.2	56.3	55.7	53.8	50.0	77.4	72.6	66.8	865.0
Johnny Gottselig	87.6	78.7	71.1	70.6	69.6	65.9	64.4	55.2	52.3	51.2	75.5	72.6	66.7	781.2
Steve Larmer	84.9	76.0	72.9	72.0	70.5	68.7	62.8	60.7	58.4	55.9	75.3	72.5	68.3	826.7
Don McKenney	83.6	77.3	74.7	73.2	72.2	69.2	57.5	56.3	52.2	46.9	76.2	72.5	66.3	731.3
Aleksander Barkov	85.0	80.0	77.6	73.3	65.9	65.0	60.8	59.1	42.6	26.7	76.4	72.5	63.6	636.0
Rick MacLeish	94.8	92.4	77.4	64.8	63.1	58.7	55.0	47.2	37.0	32.9	78.5	72.3	62.3	660.8
Rick Martin	86.4	77.9	71.8	70.8	69.2	65.8	61.9	56.8	43.1	18.3	75.2	72.0	62.2	624.8

Black Gold Extractor · May 8, 2021

The top 180 10-year single-formula VsX scores (from 1924-25 to 2022-23).

Name	1	2	3	4	5	6	7	8	9	10	5-yr	7-yr	10-yr	Career
Wayne Gretzky	170.5	165.6	159.5	158.7	158.1	148.3	137.0	130.2	121.3	115.1	162.5	156.8	146.4	2351.5
Gordie Howe	158.3	136.1	129.3	120.3	109.0	108.9	108.5	104.6	102.7	99.3	130.6	124.3	117.7	2428.6
Phil Esposito	146.9	145.7	129.1	123.2	118.9	117.2	104.1	99.4	80.3	76.2	132.8	126.4	114.1	1572.7
Mario Lemieux	143.7	132.5	129.7	122.0	107.4	106.0	103.7	98.4	96.8	87.5	127.1	120.7	112.8	1423.3
Jaromír Jágr	122.6	121.6	115.5	112.8	106.1	105.2	104.3	95.0	92.9	87.2	115.7	112.6	106.3	1926.6
Stan Mikita	127.6	113.7	113.4	103.0	101.8	100.0	96.9	96.2	91.5	80.4	111.9	108.0	102.4	1597.2
Bobby Hull	124.4	110.8	105.7	105.3	100.9	98.2	92.8	92.8	90.3	88.8	109.4	105.4	101.0	1369.1
Sidney Crosby	115.6	108.1	102.3	101.1	100.5	99.4	96.6	95.0	93.6	88.6	105.5	103.4	100.1	1549.7
Jean Beliveau	121.4	109.6	103.4	102.4	100.0	99.4	98.7	89.7	84.8	80.5	107.4	105.0	99.0	1503.5
Maurice Richard	112.6	105.8	104.4	101.7	101.4	100.0	97.9	92.3	86.0	82.2	105.2	103.4	98.4	1407.6
Marcel Dionne	116.2	114.2	107.1	105.7	103.3	99.2	86.6	85.3	81.8	78.4	109.3	104.6	97.8	1484.6
Alex Ovechkin	110.3	107.3	102.3	97.2	96.6	95.9	90.4	87.8	86.6	82.9	102.8	100.0	95.7	1525.6
Andy Bathgate	106.0	105.7	104.0	102.5	98.1	93.9	91.0	89.7	88.5	69.8	103.3	100.2	94.9	1214.8
Ted Lindsay	120.0	118.3	104.2	103.8	103.7	97.3	82.5	80.6	69.9	69.0	110.0	104.3	94.9	1246.3
Howie Morenz	145.7	110.9	98.5	96.4	94.0	93.3	83.7	78.5	72.3	69.3	109.1	103.2	94.3	1082.6
Joe Sakic	118.6	98.9	98.8	93.9	92.9	91.6	90.1	88.0	87.3	81.6	100.6	97.8	94.2	1539.8
Joe Thornton	114.7	102.7	97.1	94.6	91.6	84.4	83.9	83.7	83.6	83.0	100.1	95.6	91.9	1604.8
Mike Bossy	102.8	102.4	95.9	95.5	94.4	91.8	90.4	82.0	76.7	67.9	98.2	96.2	90.0	899.9
Patrick Kane	118.4	101.1	97.3	94.8	91.0	82.6	82.4	77.7	76.7	76.7	100.6	95.4	89.9	1308.6
Evgeni Malkin	118.5	110.2	104.4	97.5	82.8	81.8	80.0	76.6	72.5	72.3	102.7	96.5	89.7	1264.3
Guy Lafleur	129.5	118.9	104.9	104.2	102.9	97.5	62.1	61.5	58.7	56.3	112.1	102.9	89.7	1146.1
Nels Stewart	112.0	103.6	97.1	85.7	84.8	83.7	83.0	82.4	81.5	80.0	96.6	92.8	89.4	1193.9
Bobby Orr	142.0	134.3	122.6	113.6	110.7	95.7	60.4	53.9	36.7	21.9	124.6	111.3	89.2	909.9
Teemu Selänne	109.0	97.3	92.4	88.9	88.7	87.4	85.1	84.7	82.6	72.7	95.2	92.7	88.9	1433.6
Steve Yzerman	111.9	101.6	90.8	90.7	85.9	85.0	84.4	81.4	78.8	78.2	96.2	92.9	88.9	1534.0
Syl Apps	111.1	105.9	93.6	89.9	85.4	82.2	81.5	80.6	80.4	72.1	97.2	92.8	88.3	1375.5
Martin St. Louis	106.8	105.3	103.4	91.9	88.3	81.8	80.4	78.0	76.7	67.3	99.1	94.0	88.0	1100.2
Steven Stamkos	105.4	98.3	96.8	89.2	88.3	86.7	85.6	85.2	71.5	70.0	95.6	92.9	87.7	1100.7
Bill Cowley	136.2	95.4	94.4	94.2	90.9	86.7	85.5	80.0	55.9	52.9	102.2	97.6	87.2	986.4
Adam Oates	98.7	96.6	94.0	91.8	82.4	82.0	81.6	81.1	80.3	78.4	92.7	89.6	86.7	1287.9
Bryan Trottier	110.8	108.9	90.2	86.7	86.4	81.7	78.7	78.2	72.1	70.6	96.6	91.9	86.4	1156.8
Frank Boucher	100.0	96.7	95.7	92.9	91.9	86.2	84.8	81.4	68.6	64.4	95.4	92.6	86.3	928.7
Mark Messier	103.2	96.8	87.7	85.8	85.7	84.0	81.5	80.3	78.6	74.0	91.9	89.3	85.8	1630.6
Ron Francis	97.9	90.6	90.0	89.7	89.4	84.2	81.9	80.8	79.3	73.1	91.5	89.1	85.7	1601.9
Jean Ratelle	105.8	92.3	89.5	89.1	87.6	86.4	75.7	74.6	73.6	69.6	92.9	89.5	84.4	1238.6
Mark Recchi	98.9	95.0	94.3	85.2	81.5	80.0	79.5	77.4	76.3	75.3	91.0	87.8	84.3	1451.7
Bernie Geoffrion	109.2	102.7	90.8	86.1	85.5	81.2	79.5	74.2	66.7	65.0	94.9	90.7	84.1	1090.9
Frank Mahovlich	96.6	93.2	92.4	89.3	88.2	82.8	80.4	73.6	71.8	70.5	91.9	89.0	83.9	1253.1
Brett Hull	110.1	90.4	89.3	85.5	82.0	79.4	77.3	75.8	74.2	74.1	91.5	87.7	83.8	1275.1
Jarome Iginla	112.9	96.6	91.5	86.8	84.7	83.0	72.8	71.4	69.8	68.5	94.5	89.8	83.8	1365.8
Paul Coffey	101.5	99.2	98.1	87.9	82.4	81.6	78.2	77.7	67.8	62.2	93.8	89.8	83.7	1273.5
Norm Ullman	108.5	92.3	92.1	85.2	82.1	80.5	80.5	72.6	71.0	70.9	92.0	88.7	83.6	1418.2
Alex Delvecchio	98.3	88.5	87.6	86.8	82.8	81.0	80.5	78.7	78.3	72.4	88.8	86.5	83.5	1574.7
Nicklas Backstrom	97.7	94.8	92.3	87.8	85.9	82.8	78.2	73.1	70.6	69.1	91.7	88.5	83.2	1092.4
Claude Giroux	101.5	101.1	95.6	86.4	82.8	80.9	75.2	74.9	65.9	65.8	93.5	89.1	83.0	1065.9
Toe Blake	105.6	97.1	88.2	87.7	86.4	78.1	73.5	73.3	71.1	68.1	93.0	88.1	82.9	924.9
Jari Kurri	110.7	97.7	96.3	87.9	84.2	74.4	74.1	73.6	67.8	60.1	95.4	89.3	82.7	1132.0
Syl Apps	111.1	105.9	93.6	89.9	82.2	80.4	72.1	70.2	68.2	53.0	96.5	90.7	82.6	826.5
John Bucyk	112.1	88.2	83.5	81.7	81.7	80.6	75.5	75.4	73.1	72.3	89.4	86.2	82.4	1497.1
Dale Hawerchuk	106.6	93.4	90.5	80.3	79.4	77.2	75.8	74.8	73.7	72.0	90.0	86.2	82.4	1129.8
Peter Stastny	100.4	97.2	92.6	89.7	86.5	85.7	82.0	69.7	61.4	58.4	93.3	90.6	82.4	968.4
Bill Cook	116.3	113.8	91.3	89.5	87.4	82.1	76.6	68.6	57.1	37.8	99.7	93.9	82.1	832.4
Peter Forsberg	101.9	95.5	93.8	89.4	88.2	86.0	75.8	68.8	62.5	55.4	93.8	90.1	81.7	880.7
Henrik Sedin	105.2	100.0	88.0	86.4	80.0	77.6	74.9	73.0	68.8	61.5	91.9	87.4	81.5	1134.1
Bobby Clarke	98.6	97.9	95.1	87.4	85.7	80.2	78.6	68.8	60.9	59.3	93.0	89.1	81.3	1066.9
Elmer Lach	115.9	97.7	94.6	86.7	82.5	76.8	73.8	68.3	62.9	52.3	95.5	89.7	81.2	944.4
Mats Sundin	94.1	94.0	85.2	79.3	76.8	76.3	75.5	75.5	74.9	74.4	85.9	83.0	80.6	1294.0
Luc Robitaille	88.4	87.7	85.7	82.8	80.8	80.4	76.5	76.0	75.8	70.8	85.1	83.2	80.5	1250.4
John Tavares	101.8	88.0	83.6	81.0	78.2	77.9	75.0	73.3	71.3	69.0	86.5	83.6	79.9	1038.6
Rod Gilbert	94.2	91.1	81.5	79.7	79.6	79.5	77.4	72.6	71.4	70.8	85.2	83.3	79.8	1060.7
Aurele Joliat	111.4	101.2	88.4	79.1	76.1	75.3	74.3	69.3	61.7	60.7	91.2	86.5	79.8	980.3
Paul Kariya	99.0	93.5	91.8	88.9	78.0	77.9	68.5	67.3	67.1	64.0	90.2	85.4	79.6	982.9
Gilbert Perreault	93.0	90.5	88.3	83.4	80.2	78.7	71.8	70.0	69.6	69.1	87.1	83.7	79.5	1131.9
Marty Barry	103.5	92.1	88.9	86.0	85.7	85.1	72.4	67.4	64.4	48.9	91.3	87.7	79.5	829.2
Ryan Getzlaf	96.7	88.8	84.5	83.0	82.8	80.9	80.8	70.4	64.8	62.0	87.1	85.3	79.5	1081.2
Pierre Turgeon	87.4	85.0	84.8	82.8	82.4	79.0	77.9	71.7	71.2	70.1	84.5	82.8	79.2	1203.5
Darryl Sittler	105.4	85.7	84.4	82.3	80.8	76.2	73.0	70.7	67.2	65.6	87.7	84.0	79.1	959.9
Denis Savard	101.2	98.0	86.1	85.3	83.2	81.4	73.2	64.0	59.5	59.2	90.7	86.9	79.1	1076.0
Sweeney Schriner	108.2	101.1	100.0	85.1	84.4	80.9	70.6	59.1	53.6	47.7	95.8	90.0	79.1	825.8
Daniel Alfredsson	94.5	90.9	87.7	83.5	78.4	75.0	72.2	71.0	70.4	66.7	87.0	83.2	79.0	1177.3
Ilya Kovalchuk	98.9	90.2	89.9	88.8	85.7	79.8	68.5	64.4	63.8	60.0	90.7	86.0	79.0	899.0
Marián Hossa	93.2	90.1	84.4	83.7	77.6	76.9	75.4	72.2	69.3	66.7	85.8	83.0	78.9	1193.6
Pavel Datsyuk	95.6	94.6	84.5	79.8	78.4	77.3	76.9	72.8	65.7	62.8	86.6	83.9	78.8	974.5
Max Bentley	107.0	105.9	92.7	86.7	83.7	73.9	63.1	61.7	58.8	53.8	95.2	87.6	78.7	861.8
Doug Bentley	118.9	96.7	92.8	88.4	81.5	80.9	70.2	59.6	51.0	44.8	95.7	89.9	78.5	855.5
Charlie Conacher	121.3	114.3	93.5	91.4	84.4	76.7	63.6	49.4	46.8	43.0	101.0	92.2	78.5	838.9
Daniel Sedin	110.6	89.9	80.0	79.8	75.7	72.9	72.8	69.0	68.2	65.1	87.2	83.1	78.4	1104.0
Mike Modano	90.6	88.0	84.4	83.0	81.9	81.7	73.6	70.6	66.7	63.1	85.6	83.3	78.4	1297.8
Busher Jackson	102.3	101.0	94.1	93.6	83.5	75.6	67.4	60.7	55.3	48.9	94.9	88.2	78.2	961.6
Syd Howe	100.0	93.6	84.1	83.1	76.8	72.8	72.3	68.6	66.7	63.5	87.5	83.3	78.2	1007.1
Anze Kopitar	91.5	82.7	82.6	77.8	77.7	76.1	75.9	75.7	72.4	69.0	82.5	80.6	78.1	1129.5
Henri Richard	106.7	92.4	88.5	78.2	78.2	72.4	68.0	67.5	65.9	62.9	88.8	83.5	78.1	1237.6
Theoren Fleury	87.9	87.4	84.5	80.4	79.0	74.9	74.4	74.1	69.6	67.0	83.8	81.2	77.9	1014.3
Doug Gilmour	97.8	95.0	84.1	82.0	79.3	72.8	71.3	68.1	66.4	61.4	87.7	83.2	77.8	1235.3
Eric Staal	91.7	91.4	80.9	80.8	76.1	75.6	73.9	73.2	67.8	65.7	84.2	81.5	77.7	1117.0
Sergei Fedorov	105.7	88.1	80.0	79.8	75.8	73.9	70.5	69.3	67.4	66.4	85.9	82.0	77.7	1123.0
Phil Kessel	91.5	89.7	89.1	88.9	79.5	72.6	72.2	68.1	65.9	59.3	87.8	83.4	77.7	1060.2
Eric Lindros	106.1	94.7	85.9	85.5	84.5	79.0	73.2	64.1	51.0	49.7	91.3	87.0	77.4	853.5
Milt Schmidt	118.2	91.2	85.3	80.9	75.2	71.9	68.6	63.1	60.0	57.7	90.1	84.5	77.2	1017.1
Brad Marchand	96.6	95.2	88.5	85.3	84.6	68.2	66.7	62.1	59.8	58.9	90.0	83.6	76.6	915.8
Henrik Zetterberg	90.6	85.1	82.8	78.1	78.0	77.3	75.0	71.2	65.7	61.3	82.9	81.0	76.5	1021.2
Nathan MacKinnon	96.5	92.5	91.2	89.7	87.6	73.3	70.0	60.2	58.1	45.0	91.5	85.8	76.4	764.1
Jeremy Roenick	94.3	84.8	84.4	79.0	78.8	76.4	70.9	69.0	65.5	57.7	84.3	81.2	76.1	1133.9
Blake Wheeler	90.5	87.2	84.1	80.5	76.7	72.2	70.7	69.6	63.7	63.4	83.8	80.3	75.9	980.8
Brendan Shanahan	89.9	88.2	88.0	84.8	76.4	74.3	65.4	64.2	62.3	62.1	85.5	81.0	75.6	1267.9
Jason Spezza	91.3	90.6	82.6	78.4	73.4	73.3	71.2	70.4	62.5	60.6	83.3	80.1	75.4	1030.0
Keith Tkachuk	88.2	86.0	80.7	80.7	79.4	77.3	71.4	68.0	61.8	57.1	83.0	80.5	75.1	1053.7
Patrik Elias	96.5	92.0	84.8	78.3	76.1	71.8	66.0	62.2	62.1	58.9	85.5	80.8	74.9	1081.6
Bernie Federko	84.4	83.3	82.5	78.3	77.2	75.0	68.7	68.0	65.2	64.3	81.2	78.5	74.7	899.9
Roy Conacher	122.5	86.2	83.1	83.0	79.4	76.0	72.5	69.9	68.2	6.0	90.8	86.1	74.7	752.1
Bernie Nicholls	108.3	89.6	82.0	77.3	73.9	73.3	71.3	61.3	60.2	49.4	86.2	82.2	74.7	1005.6
Jamie Benn	103.0	99.4	87.8	78.6	78.4	68.5	65.0	59.6	56.9	48.3	89.4	83.0	74.5	907.4
Dany Heatley	94.6	94.5	85.6	80.8	78.8	77.0	70.2	68.1	57.6	36.2	86.9	83.1	74.3	802.9
Brad Richards	89.8	85.4	83.5	81.9	72.9	71.7	71.2	63.1	62.3	61.1	82.7	79.5	74.3	1055.5
Sid Abel	106.2	97.3	96.1	85.3	79.7	70.6	68.2	68.1	55.6	15.0	92.9	86.2	74.2	765.5
Joe Pavelski	87.8	87.2	82.8	77.3	70.3	70.2	67.5	66.3	65.7	64.2	81.1	77.6	73.9	1049.8
Dickie Moore	115.7	112.0	79.3	77.6	70.7	67.6	63.3	51.6	49.6	49.3	91.1	83.7	73.7	775.7
Ted Kennedy	88.2	85.3	78.3	78.2	71.3	71.2	70.3	67.7	63.9	61.7	80.3	77.5	73.6	832.0
Alexander Mogilny	88.1	84.1	83.4	76.0	73.0	71.2	69.6	68.9	67.1	53.8	80.9	77.9	73.5	961.6
Pavel Bure	102.2	94.3	92.8	92.5	81.2	72.8	65.2	55.0	49.2	28.8	92.6	85.8	73.4	759.1
Markus Näslund	105.9	100.0	95.5	75.4	72.5	70.7	60.0	54.2	54.1	45.3	89.8	82.8	73.3	870.0
Doug Weight	90.5	85.6	82.0	78.3	73.9	72.2	65.2	64.4	60.6	57.6	82.0	78.2	73.0	1012.9
Michel Goulet	94.9	86.9	85.0	81.9	77.9	76.5	58.7	56.3	54.6	51.6	85.3	80.3	72.4	911.2
Vincent Lecavalier	97.3	90.6	75.0	75.0	72.8	68.8	65.7	65.4	57.4	55.2	82.2	77.9	72.3	981.7
John LeClair	97.0	89.7	83.7	81.8	81.8	79.8	62.5	60.0	46.8	37.9	86.8	82.3	72.1	816.9
Ray Bourque	86.0	80.2	79.0	74.7	70.5	67.5	67.2	66.4	65.2	62.5	78.1	75.0	71.9	1345.1
Bill Mosienko	84.3	84.2	79.7	78.3	76.5	75.7	70.8	61.7	57.1	50.3	80.6	78.5	71.9	824.4
Vincent Damphousse	81.0	80.2	77.4	76.1	75.2	73.0	68.2	64.2	61.3	60.8	78.0	75.9	71.7	1101.8
Ken Hodge	105.5	101.4	84.9	76.8	66.3	63.9	59.0	54.4	54.1	50.2	87.0	79.7	71.7	868.4
Alexei Yashin	88.4	88.2	85.5	75.0	74.2	69.6	66.7	62.5	60.6	45.0	82.3	78.2	71.6	786.5
Red Kelly	82.4	80.5	76.7	75.9	75.5	70.7	69.0	61.6	61.6	61.5	78.2	75.8	71.5	1128.2
Tyler Seguin	93.3	91.1	81.8	81.6	77.6	72.8	70.8	55.2	49.0	41.7	85.1	81.3	71.5	781.9
Bryan Hextall	109.8	100.0	90.9	80.9	78.1	65.1	51.2	46.7	46.4	44.1	92.0	82.3	71.3	902.6
Jonathan Toews	82.8	80.9	78.1	75.6	71.7	67.3	65.9	64.8	63.8	62.0	77.8	74.6	71.3	933.2
Lorne Carr	89.2	83.1	80.0	79.5	70.2	69.6	68.1	64.7	56.8	51.1	80.4	77.1	71.2	776.8
Corey Perry	104.3	91.1	71.4	70.2	69.3	65.2	65.1	62.1	60.2	53.2	81.2	76.7	71.2	936.0
Pat LaFontaine	98.0	84.0	76.2	74.9	71.4	71.0	63.9	63.5	63.3	44.3	80.9	77.1	71.1	829.2
Patrick Marleau	78.9	77.9	77.8	77.7	70.3	69.6	69.3	67.5	64.8	54.8	76.5	74.5	70.8	1249.9
Hooley Smith	95.3	84.4	83.8	81.3	67.9	66.7	57.8	57.4	56.5	54.3	82.6	76.8	70.6	978.9
Jacques Lemaire	90.0	87.4	78.6	75.4	71.4	71.0	67.3	59.4	54.1	49.7	80.6	77.3	70.5	792.0
Ray Whitney	83.7	77.2	75.1	74.8	73.1	71.8	67.0	60.6	60.1	58.2	76.8	74.7	70.2	1093.0
Dave Keon	76.7	76.4	73.4	73.4	70.9	69.2	69.2	68.4	65.4	57.5	74.2	72.8	70.1	1059.6
Yvan Cournoyer	82.1	80.6	74.9	74.6	73.4	71.0	70.5	60.7	56.0	52.6	77.1	75.3	69.6	864.7
Mike Ribeiro	84.5	81.8	76.1	75.5	73.9	73.4	68.5	55.9	53.2	52.2	78.3	76.2	69.5	859.5
Ziggy Pálffy	90.0	89.7	89.4	81.7	71.7	71.6	69.4	46.6	45.5	38.5	84.5	80.5	69.4	720.0
Phil Watson	102.0	83.1	81.8	76.6	71.1	65.9	59.0	55.6	51.2	45.6	82.9	77.1	69.2	750.4
Alex Kovalev	95.5	89.4	82.8	74.0	71.7	63.4	59.6	54.6	51.1	49.3	82.7	76.6	69.2	1023.2
Bert Olmstead	96.6	87.4	79.5	75.4	75.0	59.8	58.5	57.3	52.6	49.4	82.8	76.0	69.1	833.3
Brian Leetch	83.6	79.4	78.0	73.9	70.0	69.6	64.7	62.1	58.0	51.5	77.0	74.2	69.1	958.0
Bobby Rousseau	100.0	82.9	76.9	71.3	68.6	66.0	61.4	56.6	55.3	51.3	80.0	75.3	69.0	809.9
Erik Karlsson	91.6	84.8	84.2	82.2	80.7	78.1	61.7	47.9	39.8	39.2	84.7	80.5	69.0	798.2
Johnny Gaudreau	95.8	87.6	87.2	83.6	75.7	69.3	67.6	61.7	56.9	1.1	86.0	81.0	68.6	686.5
Clint Smith	92.1	87.7	86.7	82.2	78.3	68.6	54.5	53.2	43.7	38.2	85.4	78.6	68.5	687.7
Jakub Voracek	95.9	84.6	79.3	69.3	68.9	61.5	59.3	58.4	54.9	53.3	79.6	74.1	68.5	869.9
Rod Brind'Amour	85.5	76.3	73.9	71.6	67.3	64.7	64.2	63.1	59.1	59.0	74.9	71.9	68.5	1108.4
Alex Tanguay	89.8	77.4	73.4	73.0	71.6	65.1	64.4	57.1	56.5	55.4	77.0	73.5	68.4	909.5
Steve Larmer	84.9	76.0	72.9	72.0	70.5	68.7	62.8	60.7	58.4	55.9	75.3	72.5	68.3	826.7
Pavol Demitra	91.8	89.4	81.5	80.9	65.9	57.7	56.9	53.6	53.2	51.7	81.9	74.9	68.3	772.2
Zach Parise	91.7	77.0	75.0	73.4	65.5	64.0	62.2	59.2	55.9	54.0	76.5	72.7	67.8	912.7
Lanny McDonald	85.7	79.4	78.4	76.5	69.1	64.3	62.5	57.3	52.2	51.4	77.8	73.7	67.7	827.6
Bun Cook	86.0	80.0	76.9	76.1	72.5	72.3	64.8	64.3	62.2	21.2	78.3	75.5	67.6	696.4
Denis Potvin	84.7	82.1	80.7	76.2	66.1	62.3	60.3	55.7	54.3	53.4	78.0	73.2	67.6	873.5
Milan Hejduk	94.2	85.2	79.4	78.3	63.1	59.6	57.6	53.2	53.2	51.8	80.0	73.9	67.5	819.6
Tony Amonte	91.3	77.6	77.0	75.3	68.2	64.3	60.2	56.6	53.0	51.9	77.9	73.4	67.5	877.3
Joe Mullen	79.4	78.7	75.4	71.3	66.2	66.1	64.9	61.7	56.1	55.2	74.2	71.7	67.5	867.8
Paul Thompson	97.8	88.9	83.0	82.4	79.1	76.7	60.7	41.9	33.7	30.8	86.2	81.2	67.5	757.0
Dino Ciccarelli	93.2	74.1	66.4	65.4	65.2	64.2	63.2	62.3	60.7	60.0	72.9	70.3	67.5	992.3
Rick Middleton	81.7	81.7	77.7	76.7	69.9	65.7	62.3	61.5	54.1	41.2	77.6	73.7	67.3	802.4
Mike Gartner	83.6	74.6	68.8	66.4	66.1	66.1	63.0	62.5	61.5	58.0	71.9	69.8	67.1	1092.3
Lynn Patrick	107.8	93.6	80.8	75.6	65.2	63.6	56.5	55.6	46.8	24.6	84.6	77.6	67.0	670.0
Cooney Weiland	108.1	82.6	80.9	70.3	64.3	62.8	62.2	51.4	51.1	36.0	81.2	75.9	67.0	705.0
Patrice Bergeron	76.0	69.9	69.6	68.9	67.0	66.2	65.1	63.1	62.7	60.6	70.3	68.9	66.9	1079.9
Peter Bondra	82.4	81.4	80.4	77.0	65.8	65.2	56.3	55.7	53.8	50.0	77.4	72.6	66.8	865.0
Joe Nieuwendyk	76.0	75.8	71.4	71.1	71.0	68.2	66.1	59.2	56.8	52.3	73.1	71.4	66.8	1035.1
Dit Clapper	90.4	80.9	74.3	65.2	65.1	63.6	58.8	58.4	55.6	55.3	75.2	71.2	66.8	945.0
Jonathan Huberdeau	95.8	84.1	81.4	76.5	68.7	65.9	63.9	53.4	45.8	31.1	81.3	76.6	66.7	696.3
Johnny Gottselig	87.6	78.7	71.1	70.6	69.6	65.9	64.4	55.2	52.3	51.2	75.5	72.6	66.7	781.2
Mark Scheifele	93.2	86.9	74.3	71.6	68.2	59.7	58.3	58.0	56.7	37.8	78.8	73.2	66.5	665.7
Dave Andreychuk	87.2	74.6	66.1	65.6	65.6	64.0	62.3	61.0	60.2	58.0	71.8	69.3	66.4	1171.9
Bobby Smith	79.7	73.8	71.8	69.2	67.9	63.2	62.3	60.2	59.9	56.0	72.5	69.7	66.4	815.1
Nicklas Lidström	79.3	73.4	71.4	69.4	69.0	66.0	60.8	59.6	57.6	57.0	72.5	69.9	66.3	1117.5
Thomas Vanek	77.7	75.7	75.6	70.7	66.3	63.1	62.4	61.5	55.7	54.5	73.2	70.2	66.3	834.7
Don McKenney	83.6	77.3	74.7	73.2	72.2	69.2	57.5	56.3	52.2	46.9	76.2	72.5	66.3	731.3
Woody Dumart	97.7	76.5	72.3	65.2	60.0	60.0	59.6	57.4	57.3	56.9	74.3	70.2	66.3	777.8
Rick Nash	81.7	77.1	72.4	70.2	68.0	64.8	64.1	62.9	51.4	49.5	73.9	71.2	66.2	860.1
Phil Goyette	92.3	82.8	80.3	76.9	61.3	60.1	58.9	53.8	52.1	42.8	78.7	73.2	66.1	803.4
Glenn Anderson	84.2	77.0	75.0	73.4	68.0	66.4	66.1	57.6	46.7	46.2	75.5	72.9	66.1	879.0
Al MacInnis	86.6	72.2	72.0	68.8	65.4	64.1	63.1	56.4	54.3	54.1	73.0	70.3	65.7	1119.3
Pete Mahovlich	95.9	86.4	73.4	65.0	62.2	59.0	58.9	55.9	55.0	43.1	76.6	71.6	65.5	701.1
Cecil Dillon	86.7	85.7	72.9	72.4	72.3	72.1	71.1	60.7	38.6	21.7	78.0	76.2	65.4	654.3

Midnight Judges · May 9, 2021

I do not know why the results aren't raising major red flags for the OP.

What you are doing is taking arbitrary aspects of data (the timing of great seasons, and injuries by great players) and attributing a tremendous amount of meaning to them.

There is no rational basis to suggest the baseline for '01-02 ought to be a whopping 19% lower than '02-03. League-wide scoring changed by roughly 3%. Power play opportunities also increased by 7%. I don't see how that gets to a 19% difference in the baseline.

What actually happened here is Peter Forsberg was out, Jagr had a down season, and Joe Sakic peaked a year before. There was no league-wide environmental condition that caused this. It's simply a normal fluctuation in a small data sample.

Same goes for 14-15 to 15-16. Scoring actually went down but this system has the baseline going up by 7%. Powerplay opportunities were less than 2% apart in those seasons which suggests these two seasons - in reality - are actually quite comparable. Crosby had a nice point total in 2014, and Kane had a great season in 16, but neither had high points in 15. But there was no significant change to the scoring environment that suggests Kane couldn't have had his best season a year earlier, or Crosby could not have racked up his 35 secondary assists in 2015 instead of 2014. This is simply the randomness of what happened, and anyone basing data on such a small group of occurrences ought to understand that this is unnecessarily volatile data.

There are numerous other examples of this in the data. This entire methodology is massively flawed. The math is neat but the logic is a disaster. VsX is not sufficiently indicative of the scoring environment.

Black Gold Extractor · May 9, 2021

Midnight Judges said:
I do not know why the results aren't raising major red flags for the OP.

What you are doing is taking arbitrary aspects of data (the timing of great seasons, and injuries by great players) and attributing a tremendous amount of meaning to them.

There is no rational basis to suggest the baseline for '01-02 ought to be a whopping 19% lower than '02-03. League-wide scoring changed by roughly 3%. Power play opportunities also increased by 7%. I don't see how that gets to a 19% difference in the baseline.

What actually happened here is Peter Forsberg was out, Jagr had a down season, and Joe Sakic peaked a year before. There was no league-wide environmental condition that caused this. It's simply a normal fluctuation in a small data sample.

Oh, there are definitely a some faulty years. 2001-02 is unusually low. 2002-03 is unusually high. Both forms of VsX assume that it "evens out" with enough seasons. (Hence, VsX is usually given as 7-year and 10-year values.)

Same goes for 14-15 to 15-16. Scoring actually went down but this system has the baseline going up by 7%. Powerplay opportunities were less than 2% apart in those seasons which suggests these two seasons - in reality - are actually quite comparable. Crosby had a nice point total in 2014, and Kane had a great season in 16, but neither had high points in 15. But there was no significant change to the scoring environment that suggests Kane couldn't have had his best season a year earlier, or Crosby could not have racked up his 35 secondary assists in 2015 instead of 2014. This is simply the randomness of what happened, and anyone basing data on such a small group of occurrences ought to understand that this is unnecessarily volatile data.

There are numerous other examples of this in the data. This entire methodology is massively flawed. The math is neat but the logic is a disaster. VsX is not sufficiently indicative of the scoring environment.

Yeah, the small sample size is what's causing the most problems. The IQR (as well as 1st and 3rd quartiles) should be robust for a sufficiently large sample. The "top 24" is adequate for many seasons, but as you point out, there are the problem ones. In a 30+ team environment, a "top 120" should yield better results. (For most statistics to really work well, one would probably need 1000 samples... which is more than even a 31-team NHL can offer.) The issue is from the small 6-team environment and me trying to avoid n-count variance.

In any case, I'm going to see if using points-per-game (with some minimum games played standard) will yield better results.

FWIW, I appreciate you taking time to look over the results and offering criticism. (Scientific method!) From the WHA merger onward, I'm actually fairly certain that if one adjusted for EV, PP, and SH situations separately, it would yield the best results. (A unified North American professional league that expanded hand-in-hand with incorporating more and more overseas talent.) It's the older eras that pose a challenge.

Black Gold Extractor · May 15, 2021

Barring something unthinkable happening (such as Flames or Canucks players surging into the top 18 in scoring in the three remaining regular season games), the single-formula VsX points benchmark for 2020-21 is:

(69 + 58)/2 + 65 - (57 + 52)/2 = 74

The tables for 7-year and 10-year single-formula VsX scores have been updated.

Also, that Connor McDavid guy isn't doing too badly so far, at least when looking at 5-year single-formula VsX.

Player	1st	2nd	3rd	4th	5th	5-yr
Wayne Gretzky	169.1	164.9	158.9	156.8	155.8	161.1
Phil Esposito	147.6	143.6	126.7	121.5	120.0	131.9
Gordie Howe	158.3	135.0	126.5	119.4	108.5	129.6
Mario Lemieux	144.2	132.0	129.2	122.0	107.4	127.0
Bobby Orr	141.2	135.0	120.8	112.5	111.4	124.2
Jaromir Jagr	122.1	121.0	114.4	112.8	106.1	115.3
Connor McDavid	141.9	113.6	104.9	100.9	97.0	111.7
Guy Lafleur	128.3	117.9	105.7	103.3	101.6	111.4
Stan Mikita	127.6	111.5	108.5	101.2	101.2	110.0
Ted Lindsay	118.3	118.2	103.7	103.3	101.5	109.0
Marcel Dionne	115.1	113.2	106.6	105.5	102.4	108.6
Bobby Hull	124.4	106.1	105.3	105.0	101.9	108.5
Howie Morenz	141.7	108.5	96.4	94.2	94.1	107.0
Jean Beliveau	118.9	109.6	102.4	101.1	98.7	106.2
Sidney Crosby	114.3	108.1	101.9	101.1	100.0	105.1
Maurice Richard	111.7	104.4	104.3	101.7	100.0	104.4
Alex Ovechkin	108.7	106.8	101.9	97.2	96.6	102.2
Andy Bathgate	106.0	105.0	102.6	101.3	93.9	101.8
Bill Cowley	136.2	96.0	93.3	92.9	88.9	101.4
Evgeni Malkin	117.2	109.7	102.9	95.1	81.8	101.4
Charlie Conacher	121.3	113.0	92.3	91.5	84.4	100.5
Joe Sakic	118.0	98.4	96.7	93.9	91.9	99.8
Patrick Kane	117.8	101.1	95.7	94.8	89.2	99.7
Joe Thornton	114.7	102.7	96.2	93.2	91.1	99.6
Martin St. Louis	104.4	104.2	103.4	91.9	87.9	98.4
Mike Bossy	103.5	103.3	95.1	94.4	93.0	97.9
Bill Cook	108.8	108.7	90.4	89.4	89.4	97.3
Bryan Trottier	109.8	109.8	90.8	86.0	86.0	96.5
Steve Yzerman	112.3	100.8	91.3	90.0	85.9	96.1
Syl Apps Sr	111.1	104.7	93.6	88.9	80.4	95.7
Sweeney Schriner	107.0	100.0	100.0	85.1	84.4	95.3
Frank Boucher	97.2	95.7	95.7	93.9	92.9	95.1
Teemu Selanne	109.0	96.4	92.4	88.7	88.5	95.0

[TBODY] [/TBODY]

McDavid's 2020-21 score of 141.9 is bigger than anything put up by anyone who's not a member of the Big Four and Phil Esposito. How long this will last, who knows? For now, I'll just enjoy the ride.

EDIT (July 3, 2021): Updated to reflect revised benchmarks.

Vilica · May 16, 2021

I keep meaning to respond to you, whether here or in my other thread, because I think we're both trying to accomplish the same objective - making VsX more accurate. Where we differ, I believe, is how to assess that accuracy. We both agree with Midnight Judges' criticism about how individual scoring seasons are more volatile than we would hope, but while you keep trying to expand the number of individual seasons in each year to provide a better sample, I'm just using all the years.

What lies at the heart of most VsX criticism, I think, is that a 100 in year a is not necessarily equal to a 100 in year b. I didn't try and set a particular season as my 100 benchmark, but the 4 seasons closest to 100 in my sample are Marcel Dionne's 80-81, Jarome Iginla's 07-08, Corey Perry's 10-11 and Mark Messier's 89-90. That may be setting the bar too high, but those are the four closest seasons to 100. So if your season is higher than 100, it was better than those years (with some fudging for error bars). Another way to look at it would be to take the 103 seasons of top 20 results, or 2060 total player-seasons, and count up the total number of seasons higher than 100, which is 155 [I think], and find out that seasons higher than 100 are in the top 7.5% of the sample. I don't know if that's where you'd set the cutoff for the elite of the elite, but that's where it ends up (also choosing 20 was quite arbitrary, if I had just chosen 10, the sample would be 1030 player-seasons, and the cutoff would be top 15%).

I took your table where you compared your VsX to default VsX, and added my Average VsX to the third column - the point total each year that would be the equivalent of 100. I could and probably will paste it eventually, but it would just be another huge table in a thread full of huge tables, so I thought I'd just stick to paragraphs here. For most years, we are the same directionally, but I wasn't able to discern much of a pattern between who would have the bigger difference. There are even years where we disagree whether to be higher or lower than VsX. For this year, your single-formula VsX of 74 is quite near mine, though I have to wait for the last 3 Calgary/Vancouver games before I can finalize the number.

Since Average VsX is based on league average, all the games need to be played to get the total for the North division. Total league average is 161, with the Pacific at 162, the East at 164, the Central at 159 and done, and the North at 161 with the pending games. It should end up around 164, which leads to a McDavid Average VsX of somewhere between 145-147, as the derived VsX ends up being right around 72. Interestingly, if we assume the same number of Calgary/Vancouver goals in both scenarios, their last 3 games is likely to increase league average to 162, while in the smaller sample of the North division, bump it all the way to 164.

Finally, looking at McDavid's 5 year VsX does show that in this modern era, the number of teams does fill out the point totals to get a more accurate VsX benchmark. Depending on what the consensus for VsX is, his 5 year under that system will be between 113-115. Under your system, it is 111.8. Under my system, it's 113.2. The error bars are big enough that I'd say 111.8 and 113.2 are functionally identical. But yea, whether this year is a 141 (by your formula), or a 145 (by mine), or in the 150s (by normal VsX), it's a freakish year.

Hockey Outsider · May 16, 2021

I've been meaning to respond to this but haven't had time. I'd like to review the posts that are proposing changes to the approach, but I want to do it when I have free time to really digest them.

Conceptually, I'm all for improving VsX. I'm completely fine if someone else is able to fine-tune it, and/or take care of the record-keeping going forward.

Czech Your Math · May 16, 2021

I commend those that developed the VsX metric, as well as the OP, for creating alternatives to the cruder approaches of the past.

Let's remember, we started with simple raw data (points or points per scheduled game), then used adjusted points (based on league-wide GPG).
That was a big leap forward, since it adjusted for scoring levels that fluctuated quite dramatically over time.
However, it was later realized that league averages don't capture comparative advantages/disadvantages for top line players in different seasons, so alternatives have been sought.

While there may not be a "perfect" solution, the main flaw I see in VsX as well as OP's method (as much as I understand it at least, after a cursory reading), is the reliance on arbitrary data points, rather than including as much data as is reasonable. IMO, we should only be excluding data for a legitimate reason, since the more data points we include, the less arbitrary the metric is.

One thing that I think we need to recognize is that it's probably always going to be highly problematic comparing scoring in say, the O6 to the modern era. The O6 had the unique problem that opportunity was very limited. There were probably players that had the potential for high scoring finishes that were not on the first line or maybe not yet even in the NHL at all in some cases. Another problem is expansion, as players on expansion teams don't tend to finish high in scoring for at least for the first season or two. Also, expansions aren't equal: Vegas or WHA teams that merged, aren't the same as the expansions of the late 60s & 70s. The O6 also, by its very nature, presented a small sample size (18 first liners each season). Rather than strive, at least initially, for a one size fits all metric (one metric used for all seasons), it might be better to look at eras (big chunks of seasons). I see three main eras:

O6 Era(until expansions of late 60s): Sample size and limited opportunity were always a problem. Lower population and WWII lead to questions about the talent pool at least until the mid-late 50s.
Expansion/Transitor Era: Expansion imbalances pose a major issue, as does the WHA siphoning talent. Generally, I think one could almost ignore the expansion teams for benchmark purposes in the late 60s and early 70s to lump in those seasons with the O6... and pretty much lump in the late 70s with the 80s. The mid-70s are still rather tricky though.
Modern Era: The 80s had a much smaller talent pool than the last~30 years, but mass integration of European/Russian talent also coincided with a gradual expansion from 21 teams in '90-91 to 30 teams in '00-01. If our metric is based on proportionality to opportunity (number of teams), this mitigates much of the concern with integrating the 80s with the last ~30 years. It is a bit tricky though, because the talent was probably proportionately closer to the 30 team level achieved in '00-01, but the opportunity was actually proportional to the number of teams (and perhaps a bit less, because the players on the expansion teams generally accounted for fewer top finishes).

I'm going to focus on methodology that I believe would be most appropriate in the more modern era (late 70s or 80s to present).
First, there are two basic approaches we need to decide between:

A) Fixed amounts such as the top X scorers or scorer Y thru scorer Y+Z (e.g,. top 20 scorers or scorers 11-30): The main rationales for this method are that the talent pool supposedly remains relatively constant across the era and that opportunity (i.e., playing on first or even second line) isn't that important. I think the mass influx of European/Russian talent beginning in the 90s invalidates the first rationale (at least for the pre-90s periods), and it seems common sense that increased ice time and an almost monopoly on power play time for first/second liners invalidates the second rationale. This leads us to...
B) Variable amounts proportional to the number of teams (e.g. top N scorers or scorers N+1 thru 2N): This could be modified slightly upon further study and agreement, mainly of the effects of expansion, but seems the most logical starting point, based on the reasoning given previously in the section A.

Now that we have settled that (in my mind at least), I previously stated we should not use arbitrary standards/benchmarks and should only exclude data points for good reasons. What are some good reasons to exclude data points:

1) Sample size: While second liners still tend to get a lot of ice time and power play time, and in some circumstances may get just as much ice/PP time as first liners on their (or other) teams, there are also many circumstances in which this is probably not the case. Since second line opportunity is often less than first line opportunity, we should limit the last scorer in our metric to at least the 3Nth scorer (where N is the number of teams, so in a 30 team league it would be the 90th scorer). Also, while opportunity is far more balanced than in the O6 era, there likely still are cases where a second liner on one team is talented/productive enough to be a first liner on another team. For that reason, it seems best to further limit the scope of our metric to around the 2Nth scorer (60th scorer in 30 team league). I think you could even go as far as the 1.5Nth (45th) or even 1Nth scorer (30th scorer in 30 team league). Going much below the 1Nth scorer though would seem to unnecessarily sacrifice sample size (especially in light of possible further reductions in sample size as later illustrated) with very little (if any) gain in quality of the sample size.

2) Excluding outliers. How many true outliers are there in a given season? Typically, not more than a handful IMO. The exact number isn't exactly determinable, but that's okay, what's important is that we don't arbitrarily determine that from season to season, but instead use the same formula, proportional to opportunity, for each season. If we were using a fixed amount of scorers, it would make sense to use a fixed number of outliers (e.g., always exclude the top 5 scorers). Since I believe it far more logical to use a sample size proportional to opportunity (number of teams), then the number of outliers should be as well. So, for example, we could exclude the top 0.1N (top 3 in 30 team league) or top 0.2N (top 6) scorers.

So I've given what I believe to be the most logical methodology to develop an individual scoring benchmark, at least for the modern era, that accomplishes the following:

A) Is not arbitrary (i.e., does not fluctuate substantially due to one or two players retiring, entering the league, getting injured, having career years or having off years).
B) Has a relatively large sample size, but not so large that it includes a significant number of players with less than maximum opportunity, nor of vastly inferior quality.
C) Very probably excludes most/all of the true outliers that can skew the results, without excluding such a large number of top players that we sacrifice the quality of our sample.

Since '01-02 & '02-03 were brought up ITT, here's five consecutive seasons ('00-01 to '05-06) that include those two, using variations on the above methodology:

Top 1N = Top 30 scorers
Top 2N = Top 60
2nd N = 31st-60th
Med2N= 16st-45th
Top 1N - Top 0.1N = 4th-30th
Top 1N - Top 0.2N = 7th-30th
Top 2N - Top 0.1N = 4th-60th
Top 2N - Top 0.2N = 7th-60th

	1N	2N	2ndN	Med2N	1N-0.1N	1N-0.2N	2N-0.1N	2N-0.2N
00-01	86.4	78.1	69.8	76.3	83.6	82.2	76.3	75.3
01-02	74.9	68.8	62.7	67.6	73.2	72.4	67.7	67.0
02-03	82.6	72.9	63.2	70.3	80.2	78.3	71.2	69.9
03-04	74.7	65.7	56.7	63.8	73.0	71.9	64.4	63.4
05-06	91.6	81.6	71.7	79.1	88.6	86.9	79.7	78.4

[TBODY] [/TBODY]

If you set the average for each column to 100, here are the results:

	1N	2N	2ndN	Med2N	1N-0.1N	1N-0.2N	2N-0.1N	2N-0.2N
00-01	105.4	106.4	107.7	106.8	104.9	105.0	106.2	106.3
01-02	91.3	93.7	96.8	94.7	91.8	92.5	94.1	94.6
02-03	100.7	99.3	97.5	98.4	100.6	99.9	99.1	98.7
03-04	91.0	89.4	87.4	89.3	91.6	91.8	89.6	89.6
05-06	111.6	111.2	110.6	110.8	111.1	110.9	110.9	110.8

[TBODY] [/TBODY]

As you can see, there's much more fluctuation between seasons (although to be fair, I picked these seasons because there was a good amount of fluctuation between them), than there is fluctuation between the different metrics within each season. IOW, within reason, almost any of the variations of the metrics using this methodology will yield substantially similar results for benchmarks to compare various (groups of) seasons. For '01-02, the lowest benchmarks (compared to the other seasons) are for the three metrics using 1N, meaning that the top 30 scorers underperformed relative to the 31st-60th scorers in comparison to the other seasons.

From my point of view, this methodology makes the most sense, at least for the more modern era. When comparing Crosby vs. Ovechkin for example, we're already comparing outliers at least to some degree. What we want is a fairly large sample size that tells us how other first liners (not other outliers like Malkin & Kane that can skew the reults and not 2nd/3rd liners) produced during each season. From there, it's only a matter of agreeing upon the best choice for the individual components of the metric: Base sample size (1N, 2N, 1.5N, 2ndN, etc.) and outlier size (0.1N, 0.2N, 0.15N, 0.25N, 0.3N, etc.), to determine the formula, which as demonstrated won't change the results all that much, especially when comparing multiple seasons for each player.

As previously noted, expansion creates complications, but fortunately from the 80s to present, it's primarily the 90s where we may have to consider its effects. One approach might be to adjust for how players on expansion teams actually produce and (based on our sample size), adjust the metric based on that. For example, NHL expands from 21 to 22 teams. If we're using a sample size of 1N, if a player from the expansion team finishes in the top 22 scorers, then N=22 for that season and going forward (at least until further expansion may further increase N) otherwise N=21 until that happens. If we're using a sample size of 2N, then if at least 2 players from the expansion team finish in top 44 scorers, then N=22 for that season and going forward (with the same caveat re: further expansion). If only one player from the expansion team finishes in top 44, then N=21.5 for that season and going forward, etc. Another consideration, when there are multiple expansion teams, is whether to consider the expansion teams individually or as a whole for these purposes. We could also ignore expansion in the modern era completely and consider expansion teams as any other team, especially since it mainly coincided with a substantial influx of new talent from overseas. I don't think it would have a major impact on the metric, no matter how it's decided to adjust the equation, if at all.

Black Gold Extractor · May 16, 2021

Vilica said:
I keep meaning to respond to you, whether here or in my other thread, because I think we're both trying to accomplish the same objective - making VsX more accurate. Where we differ, I believe, is how to assess that accuracy. We both agree with Midnight Judges' criticism about how individual scoring seasons are more volatile than we would hope, but while you keep trying to expand the number of individual seasons in each year to provide a better sample, I'm just using all the years.

Thank you for responding! You've taken on quite the task, as it looks quite intensive. However, your method should be less vulnerable to the volatility that Midnight Judges mentioned.

Fundamentally, I suppose that I was trying to elucidate the meaning of a "typical 2nd place scorer" as defined by VsX from a statistical point of view. Seeing that it was roughly one IQR away from the 3rd quartile of the top 24 scorers allowed me to expand it into the current five-point estimator (turning the 3rd quartile into a trimean of sorts, turning the 1st quartile into an average of two points). By accounting for the dispersion of scorers, I can tell that Mike Bossy in 1981-82 is better than a typical 2nd place scorer or that no one in 1942-43 and 1943-44 managed to even match a "typical 2nd place scorer".

Correct me if I'm wrong, but I think that you're fundamentally using a probabilistic approach to the problem. Looking at 1980-81 to 1985-86 (a relatively similar and stable scoring environment across those six seasons), you can see that after adjusting for league averages, no one outside of Gretzky scores as much as Bossy in 1981-82, so according to probability, Bossy in 1981-82 must score higher than 100?

What lies at the heart of most VsX criticism, I think, is that a 100 in year a is not necessarily equal to a 100 in year b. I didn't try and set a particular season as my 100 benchmark, but the 4 seasons closest to 100 in my sample are Marcel Dionne's 80-81, Jarome Iginla's 07-08, Corey Perry's 10-11 and Mark Messier's 89-90. That may be setting the bar too high, but those are the four closest seasons to 100. So if your season is higher than 100, it was better than those years (with some fudging for error bars). Another way to look at it would be to take the 103 seasons of top 20 results, or 2060 total player-seasons, and count up the total number of seasons higher than 100, which is 155 [I think], and find out that seasons higher than 100 are in the top 7.5% of the sample. I don't know if that's where you'd set the cutoff for the elite of the elite, but that's where it ends up (also choosing 20 was quite arbitrary, if I had just chosen 10, the sample would be 1030 player-seasons, and the cutoff would be top 15%).

I think that's a reasonable number of "elite of elite" seasons. Most of the time, there's one elite of elite guy. Occasionally, there's two. Sometimes, it's frigging 1988-89. Others, it's 2014-15.

Then, there are the sneakily slightly-above-100 seasons. As aforementioned, Bossy in 1981-82. But also, say, Ovechkin in 2008-09 and 2009-10 scores a bit higher than 100 each of those years despite being the benchmark in normal VsX.

On the other hand, there's just something appealing to normal VsX's approach. It just makes sense intuitively if you're not overly concerned at calculating exact numbers. I can just look at a scoring table and say "holy crap, Gordie Howe's 95 points is more than 1.5 times more than Richard's 61" and realize that it's an all-time great season.

I took your table where you compared your VsX to default VsX, and added my Average VsX to the third column - the point total each year that would be the equivalent of 100. I could and probably will paste it eventually, but it would just be another huge table in a thread full of huge tables, so I thought I'd just stick to paragraphs here. For most years, we are the same directionally, but I wasn't able to discern much of a pattern between who would have the bigger difference. There are even years where we disagree whether to be higher or lower than VsX. For this year, your single-formula VsX of 74 is quite near mine, though I have to wait for the last 3 Calgary/Vancouver games before I can finalize the number.

Since Average VsX is based on league average, all the games need to be played to get the total for the North division. Total league average is 161, with the Pacific at 162, the East at 164, the Central at 159 and done, and the North at 161 with the pending games. It should end up around 164, which leads to a McDavid Average VsX of somewhere between 145-147, as the derived VsX ends up being right around 72. Interestingly, if we assume the same number of Calgary/Vancouver goals in both scenarios, their last 3 games is likely to increase league average to 162, while in the smaller sample of the North division, bump it all the way to 164.

Finally, looking at McDavid's 5 year VsX does show that in this modern era, the number of teams does fill out the point totals to get a more accurate VsX benchmark. Depending on what the consensus for VsX is, his 5 year under that system will be between 113-115. Under your system, it is 111.8. Under my system, it's 113.2. The error bars are big enough that I'd say 111.8 and 113.2 are functionally identical. But yea, whether this year is a 141 (by your formula), or a 145 (by mine), or in the 150s (by normal VsX), it's a freakish year.

I'm glad that our methods actually agree for the most part. As I always say, if you come to similar results from different methods, that's a good sign. But I definitely hope I'm not jumping the gun.

Hockey Outsider said:
I've been meaning to respond to this but haven't had time. I'd like to review the posts that are proposing changes to the approach, but I want to do it when I have free time to really digest them.

I would love to hear your input!

Black Gold Extractor · May 17, 2021

Czech Your Math said:
While there may not be a "perfect" solution, the main flaw I see in VsX as well as OP's method (as much as I understand it at least, after a cursory reading), is the reliance on arbitrary data points, rather than including as much data as is reasonable. IMO, we should only be excluding data for a legitimate reason, since the more data points we include, the less arbitrary the metric is.

One thing that I think we need to recognize is that it's probably always going to be highly problematic comparing scoring in say, the O6 to the modern era. The O6 had the unique problem that opportunity was very limited. There were probably players that had the potential for high scoring finishes that were not on the first line or maybe not yet even in the NHL at all in some cases. Another problem is expansion, as players on expansion teams don't tend to finish high in scoring for at least for the first season or two. Also, expansions aren't equal: Vegas or WHA teams that merged, aren't the same as the expansions of the late 60s & 70s. The O6 also, by its very nature, presented a small sample size (18 first liners each season). Rather than strive, at least initially, for a one size fits all metric (one metric used for all seasons), it might be better to look at eras (big chunks of seasons).

Firstly, thank you for responding!

As you correctly inferred, I was trying to maintain a relatively simple approach that could be used across all eras. Additionally, I managed to basically replace normal VsX's cumbersome and piecemeal rules for atypical seasons. (Plus, I solved the Paul Kariya conundrum!) What you are saying is absolutely true, though: the more data we can reasonably include, the better the metric will perform.

Since '01-02 & '02-03 were brought up ITT, here's five consecutive seasons ('00-01 to '05-06) that include those two, using variations on the above methodology:

Top 1N = Top 30 scorers
Top 2N = Top 60
2nd N = 31st-60th
Med2N= 16st-45th
Top 1N - Top 0.1N = 4th-30th
Top 1N - Top 0.2N = 7th-30th
Top 2N - Top 0.1N = 4th-60th
Top 2N - Top 0.2N = 7th-60th

1N 2N 2ndN Med2N 1N-0.1N 1N-0.2N 2N-0.1N 2N-0.2N
00-01 86.4 78.1 69.8 76.3 83.6 82.2 76.3 75.3
01-02 74.9 68.8 62.7 67.6 73.2 72.4 67.7 67.0
02-03 82.6 72.9 63.2 70.3 80.2 78.3 71.2 69.9
03-04 74.7 65.7 56.7 63.8 73.0 71.9 64.4 63.4
05-06 91.6 81.6 71.7 79.1 88.6 86.9 79.7 78.4
[TBODY] [/TBODY]
If you set the average for each column to 100, here are the results:

1N 2N 2ndN Med2N 1N-0.1N 1N-0.2N 2N-0.1N 2N-0.2N
00-01 105.4 106.4 107.7 106.8 104.9 105.0 106.2 106.3
01-02 91.3 93.7 96.8 94.7 91.8 92.5 94.1 94.6
02-03 100.7 99.3 97.5 98.4 100.6 99.9 99.1 98.7
03-04 91.0 89.4 87.4 89.3 91.6 91.8 89.6 89.6
05-06 111.6 111.2 110.6 110.8 111.1 110.9 110.9 110.8
[TBODY] [/TBODY]
As you can see, there's much more fluctuation between seasons (although to be fair, I picked these seasons because there was a good amount of fluctuation between them), than there is fluctuation between the different metrics within each season. IOW, within reason, almost any of the variations of the metrics using this methodology will yield substantially similar results for benchmarks to compare various (groups of) seasons. For '01-02, the lowest benchmarks (compared to the other seasons) are for the three metrics using 1N, meaning that the top 30 scorers underperformed relative to the 31st-60th scorers in comparison to the other seasons.

From my point of view, this methodology makes the most sense, at least for the more modern era. When comparing Crosby vs. Ovechkin for example, we're already comparing outliers at least to some degree. What we want is a fairly large sample size that tells us how other first liners (not other outliers like Malkin & Kane that can skew the reults and not 2nd/3rd liners) produced during each season. From there, it's only a matter of agreeing upon the best choice for the individual components of the metric: Base sample size (1N, 2N, 1.5N, 2ndN, etc.) and outlier size (0.1N, 0.2N, 0.15N, 0.25N, 0.3N, etc.), to determine the formula, which as demonstrated won't change the results all that much, especially when comparing multiple seasons for each player.

I absolutely love those results. However, from post-WHA merger onward, we can basically adjust points by strength or simply by comparing to median points for "first-line forwards" (for example) without losing too much in the process. The challenge has always been to move back before the 1967 expansion.

As previously noted, expansion creates complications, but fortunately from the 80s to present, it's primarily the 90s where we may have to consider its effects. One approach might be to adjust for how players on expansion teams actually produce and (based on our sample size), adjust the metric based on that. For example, NHL expands from 21 to 22 teams. If we're using a sample size of 1N, if a player from the expansion team finishes in the top 22 scorers, then N=22 for that season and going forward (at least until further expansion may further increase N) otherwise N=21 until that happens. If we're using a sample size of 2N, then if at least 2 players from the expansion team finish in top 44 scorers, then N=22 for that season and going forward (with the same caveat re: further expansion). If only one player from the expansion team finishes in top 44, then N=21.5 for that season and going forward, etc. Another consideration, when there are multiple expansion teams, is whether to consider the expansion teams individually or as a whole for these purposes. We could also ignore expansion in the modern era completely and consider expansion teams as any other team, especially since it mainly coincided with a substantial influx of new talent from overseas. I don't think it would have a major impact on the metric, no matter how it's decided to adjust the equation, if at all.

I wonder if this would work for regular adjustment by league goals. Each time an expansion team outscores a "family member", it automatically joins the family. For example, in 1969-70, both the Blues and North Stars finally join the O6 to make it 8 clubs that are used for league comparison.

Anyways, I have something to sleep on. Good night!

Czech Your Math · May 17, 2021

Black Gold Extractor said:
Firstly, thank you for responding!

Thanks for responding to my response.

As you correctly inferred, I was trying to maintain a relatively simple approach that could be used across all eras. Additionally, I managed to basically replace normal VsX's cumbersome and piecemeal rules for atypical seasons. (Plus, I solved the Paul Kariya conundrum!) What you are saying is absolutely true, though: the more data we can reasonably include, the better the metric will perform.

Personally, I don't think any method can even pretend to be trying to accurately compare O6 to modern era, unless it in some way tries to account for the difference in talent pool due to the influx of non-Canadian talent beginning primarily in the early 90s. I don't think sacrificing accuracy for relative simplicity really solves that, no matter how much we turn a blind eye to the actual issue.

Congratulations on "solving" the Kariya conundrum, except I don't see how it ultimately solves it at all. When a metric potentially relies on single data points (like 3rd, 7th, 11th 18th, etc.), there is much more potential for fluctuation than when using a large sample, where any fluctuations are smoothed out by a relatively large denominator (whether it be two dozen or 50+). For example, Jagr scored 95 points in 63 games in that '97 season. What if he played 82 games? Then we would expect he would have scored 123-124 points, instead of 95. In any case, likely more than Selanne's 109, which would push Selanne's 109 into third place, instead of Kariya's 99. It seems that wouldn't affect your "3Q+IQR" metric (in this case), but it would increase your "single-formula VsX" by 5 points or ~5%. Another way of looking at it is that one would expect Jagr to need 9 or 10 games to score at least 14 more points in that season, which would make 109 points the 3rd place number. A single player playing 9 or 10 more games shouldn't cause a properly developed metric's benchmark to increase by ~5% for that season IMO.

In my previous post, I gave 8 examples of metrics that could be used (although the first two didn't exclude any outliers). Here is what happens to those same 8 metrics, if you change Jagr's points from 95 to 124 (the most dramatic increase we could expect). Note: Original is 95, Revised is 124:

1996-97	1N	2N	2ndN	Med2N	1N-0.1N	1N-0.2N	2N-0.1N	2N-0.2N
Original	99.5	86.4	73.2	83.7	98.2	98.3	85.0	84.4
Revised	100.7	86.9	73.2	83.7	98.5	98.4	85.2	85.4
Change	1.12	0.56	0.0	0.0	0.34	0.08	0.16	0.03
% Change	1.1%	0.6%	0.0%	0.0%	0.3%	0.1%	0.2%	0.0%

[TBODY] [/TBODY]

Even the first two metrics, which don't exclude any outliers, only change by 0.6-1.1%. Of the other six metrics, two don't change at all, and four change no more than 0.3%.
So it would take multiple changes such of similar magnitude as the example provided, all in the same direction, to approach 5%... even in the metrics that do not exlude any outliers.

1997 is a good example of a season when things could have been substantially different for the elite scorers:
* Several top 30 scorers missed significant time due to injuries: Sakic (74 Pts/65 GP), Lindros (79/52), Forsberg (86/65), Jagr (95/63), Kariya (99/69), etc.; what if they played 82 games? what if they missed most of the season?
* What if Selanne blew out his knee in the first game? What if Lemieux, Gretzky or Messier retired before the season?

The point is that two or three of these events happening shouldn't have a significant effect on the metric, but when a metric relies on arbitrary finishes as part of its basis, they can.

I absolutely love those results. However, from post-WHA merger onward, we can basically adjust points by strength or simply by comparing to median points for "first-line forwards" (for example) without losing too much in the process. The challenge has always been to move back before the 1967 expansion.

I just took a quick glance at the two threads you linked. Can you put in simpler terms what your measuring?

In any case, we can at least agree that there are methodologies that yield accurate benchmarks for post-WHA era.

I also agree that the challenge is to compare that post-WHA merger era to the preceding era(s). I think any attempt to do so must consider (in its methodology) that without the fall of the Berlin wall and increased representation of Americans in the NHL, the last ~30 seasons would look much different. Sure, we would still have some Euros in the NHL, players like Selanne & Forsberg in the 90s/00s instead of players like Kurri & Stastny in the 80s, but the scoring benchmarks would be significantly lower over the past ~30 seasons, so it seems unfair to penalize players in this modern period for playing in a much deeper talent pool.

I'm not sure what the answer is in comparing the modern era to the O6. Ideally, it would minimize subjectivity. One idea is something along the following lines:

* Use a version of VsX and/or one of the methodologies that you presented that uses only Canadian players in determining the benchmarks and gives results that are agreed upon as acceptable (although I wonder how may would agree upon results that likely diminish the averages of most/all of the O6 players which played in a Canadian-only era).
* Find non-arbitrary methodologies for each of the O6 and modern eras that closely mirrors those results.

The bottom line is that if we can't agree that modern era players have distorted benchmarks due to the much deeper worldwide talent pool, and perhaps due to much wider available opportunities (number of teams) as well, then we'll never agree on the correct benchmarks to compare players across eras.

I wonder if this would work for regular adjustment by league goals. Each time an expansion team outscores a "family member", it automatically joins the family. For example, in 1969-70, both the Blues and North Stars finally join the O6 to make it 8 clubs that are used for league comparison.

Anyways, I have something to sleep on. Good night!

I like that idea! We need further examination of the expansion teams on various fronts: How many, if any existing teams, do expansion teams outscore and how many seasons does it take them to do so? How long does it take expansion players to finish in the top X players and so on. We seem to agree that once expansion team(s)/player(s) do(es) so to an acceptable degree, then they become part of the family and are treated the same as any other team going forward. It's just a matter of what those thresholds are for team and/or player, and whether they should be treated as a full team (entirely ignoring expansion effects), a fractional team, or a non-existent ("zero") team for benchmark purposes until they reach such a threshold.

Black Gold Extractor · May 17, 2021

Czech Your Math said:
Thanks for responding to my response.

I'm always glad to get feedback! When it's just me staring at my own work, especially after a long time, it becomes easy to become my own echo chamber.

Personally, I don't think any method can even pretend to be trying to accurately compare O6 to modern era, unless it in some way tries to account for the difference in talent pool due to the influx of non-Canadian talent beginning primarily in the early 90s. I don't think sacrificing accuracy for relative simplicity really solves that, no matter how much we turn a blind eye to the actual issue.

My hope was that by incorporating the dispersion that it would do a decent job of estimating the density of talent, so to speak. To use 1967-68 and 2014-15 to demonstrate:

Rk	Player	PTS	Rk	Player	PTS	Rk	Player	PTS
1	Stan Mikita*	87	1	Jamie Benn	87	1	Jamie Benn	87
2	Phil Esposito*	84	2	John Tavares	86	3	Sidney Crosby	84
3	Gordie Howe*	82	3	Sidney Crosby	84	5	Jakub Voracek	81
4	Jean Ratelle*	78	4	Alex Ovechkin	81	7	Tyler Seguin	77
5	Rod Gilbert*	77	5	Jakub Voracek	81	9	Daniel Sedin	76
6	Bobby Hull*	75	6	Nicklas Backstrom	78	11	Claude Giroux	73
7	Norm Ullman*	72	7	Tyler Seguin	77	13	Vladimir Tarasenko	73
8	Alex Delvecchio*	70	8	Jiri Hudler	76	15	Steven Stamkos	72
9	John Bucyk*	69	9	Daniel Sedin	76	17	Ryan Getzlaf	70
10	Kenny Wharram	69	10	Nick Foligno	73	19	Joe Pavelski	70
11	Jean Beliveau*	68	11	Claude Giroux	73	21	Logan Couture	67
12	John McKenzie	66	12	Henrik Sedin	73	23	Erik Karlsson	66
13	Phil Goyette	65	13	Vladimir Tarasenko	73	25	Henrik Zetterberg	66
14	Bobby Rousseau	65	14	Tyler Johnson	72	27	Nikita Kucherov	65
15	Fred Stanfield	64	15	Steven Stamkos	72	29	Johnny Gaudreau	64
16	Yvan Cournoyer*	60	16	Ryan Johansen	71	31	Anze Kopitar	64
17	Andy Bathgate*	59	17	Ryan Getzlaf	70	33	Mark Stone	64
18	Mike Walton	59	18	Evgeni Malkin	70	35	Jordan Eberle	63
			19	Joe Pavelski	70
			20	Rick Nash	69
			21	Logan Couture	67
			22	Max Pacioretty	67
			23	Erik Karlsson	66
			24	Jonathan Toews	66
			25	Henrik Zetterberg	66
			26	Pavel Datsyuk	65
			27	Nikita Kucherov	65
			28	Joe Thornton	65
			29	Johnny Gaudreau	64
			30	Patrick Kane	64
			31	Anze Kopitar	64
			32	Alex Steen	64
			33	Mark Stone	64
			34	Kyle Turris	64
			35	Jordan Eberle	63
			36	Filip Forsberg	63

	Normal VsX	84		Normal VsX	86		Normal VsX	84
	3Q+IQR	85		3Q+IQR	84		3Q+IQR	83
	Single-Formula VsX	86		Single-Formula VsX	84		Single-Formula VsX	83

[TBODY] [/TBODY]

Normal VsX yields a harsher benchmark for 2014-15 than for 1967-68. However, if we look closely, we can see that the density of scorers in 2014-15 is higher than in 1967-68. What if we removed every even-number-ranked scorer in 2014-15? All of a sudden, it looks quite a lot like 1967-68. (It's almost as though the NHL found some means to double its talent pool sometime between 1967-68 and 2014-15...) And suddenly, the normal VsX yields an identical result for the decimated 2014-15 leaderboard as 1967-68.

On the other hand, the 3Q+IQR and single-formula VsX methods both yield harsher benchmarks for 1967-68 due to the greater dispersion of scorers in the sample of top 18 scorers here. To use 3Q+IQR to demonstrate the point (with the dispersion in bold):

1967-68: 72 + (72 - 59) = 72 + 13 = 85
2014-15: 77 + (77 - 70) = 77 + 7 = 84
2014-15 (decimated): 73 + (73-63) = 73 + 10 = 83

Of course, this is a carefully selected example, but I think it demonstrates the concept well.

Congratulations on "solving" the Kariya conundrum, except I don't see how it ultimately solves it at all. When a metric potentially relies on single data points (like 3rd, 7th, 11th 18th, etc.), there is much more potential for fluctuation than when using a large sample, where any fluctuations are smoothed out by a relatively large denominator (whether it be two dozen or 50+). For example, Jagr scored 95 points in 63 games in that '97 season. What if he played 82 games? Then we would expect he would have scored 123-124 points, instead of 95. In any case, likely more than Selanne's 109, which would push Selanne's 109 into third place, instead of Kariya's 99. It seems that wouldn't affect your "3Q+IQR" metric (in this case), but it would increase your "single-formula VsX" by 5 points or ~5%. Another way of looking at it is that one would expect Jagr to need 9 or 10 games to score at least 14 more points in that season, which would make 109 points the 3rd place number. A single player playing 9 or 10 more games shouldn't cause a properly developed metric's benchmark to increase by ~5% for that season IMO.

Whoa, pitting both prime Jagr and prime Kariya against me? That would make any defender wet their pants in fear.

In all seriousness, you've shown me that by using a trimean for the single-formula VsX instead of just the 3rd quartile in the 3Q+IQR method, I've actually made it the method less robust (which is contrary to what I intended)... but even the less-stable-than-intended single-formula VsX is more robust than normal VsX.

In my previous post, I gave 8 examples of metrics that could be used (although the first two didn't exclude any outliers). Here is what happens to those same 8 metrics, if you change Jagr's points from 95 to 124 (the most dramatic increase we could expect). Note: Original is 95, Revised is 124:

1996-97 1N 2N 2ndN Med2N 1N-0.1N 1N-0.2N 2N-0.1N 2N-0.2N
Original 99.5 86.4 73.2 83.7 98.2 98.3 85.0 84.4
Revised 100.7 86.9 73.2 83.7 98.5 98.4 85.2 85.4
Change 1.12 0.56 0.0 0.0 0.34 0.08 0.16 0.03
% Change 1.1% 0.6% 0.0% 0.0% 0.3% 0.1% 0.2% 0.0%
[TBODY] [/TBODY]
Even the first two metrics, which don't exclude any outliers, only change by 0.6-1.1%. Of the other six metrics, two don't change at all, and four change no more than 0.3%.
So it would take multiple changes such of similar magnitude as the example provided, all in the same direction, to approach 5%... even in the metrics that do not exlude any outliers.

1997 is a good example of a season when things could have been substantially different for the elite scorers:
* Several top 30 scorers missed significant time due to injuries: Sakic (74 Pts/65 GP), Lindros (79/52), Forsberg (86/65), Jagr (95/63), Kariya (99/69), etc.; what if they played 82 games? what if they missed most of the season?
* What if Selanne blew out his knee in the first game? What if Lemieux, Gretzky or Messier retired before the season?

The point is that two or three of these events happening shouldn't have a significant effect on the metric, but when a metric relies on arbitrary finishes as part of its basis, they can.

I think we can both agree that bigger samples will yield better results precisely because one or two (or five) weird occurrences should not have a measurable impact on the metric.

I just took a quick glance at the two threads you linked. Can you put in simpler terms what your measuring?

For the post-expansion breakdown of even strength, powerplay, and shorthanded scoring, it's exactly what it says on the tin. Instead of adjusting to a league-wide average of total goals scored per game, we adjust even strength, powerplay, and shorthanded goals separately, and then further adjust for assists awarded per goal in each situation.

For the median PTS for different lines, I just listed the median for each expected "line". For a median 1st line forward in a 30-team league, for example, that would be the average of the 45th and 46th scorer. For a median 2nd line forward, that would be the average of the 135th and 136th scorer, and so on.

In any case, we can at least agree that there are methodologies that yield accurate benchmarks for post-WHA era.

I also agree that the challenge is to compare that post-WHA merger era to the preceding era(s). I think any attempt to do so must consider (in its methodology) that without the fall of the Berlin wall and increased representation of Americans in the NHL, the last ~30 seasons would look much different. Sure, we would still have some Euros in the NHL, players like Selanne & Forsberg in the 90s/00s instead of players like Kurri & Stastny in the 80s, but the scoring benchmarks would be significantly lower over the past ~30 seasons, so it seems unfair to penalize players in this modern period for playing in a much deeper talent pool.

I'm not sure what the answer is in comparing the modern era to the O6. Ideally, it would minimize subjectivity. One idea is something along the following lines:

* Use a version of VsX and/or one of the methodologies that you presented that uses only Canadian players in determining the benchmarks and gives results that are agreed upon as acceptable (although I wonder how may would agree upon results that likely diminish the averages of most/all of the O6 players which played in a Canadian-only era).
* Find non-arbitrary methodologies for each of the O6 and modern eras that closely mirrors those results.

The bottom line is that if we can't agree that modern era players have distorted benchmarks due to the much deeper worldwide talent pool, and perhaps due to much wider available opportunities (number of teams) as well, then we'll never agree on the correct benchmarks to compare players across eras.

I did note a near-linear trend (at least post-consolidation) of a "strengthening" of the "typical 2nd-place scorer" over the years (between 5% and 6% per 100 years). Maybe the solution is just to look at normal VsX and just apply a "how many years apart did this take place" factor. (For example, looking at someone in the 1960's versus the 2010's would yield a 3% bonus for the more modern player.)

I like that idea! We need further examination of the expansion teams on various fronts: How many, if any existing teams, do expansion teams outscore and how many seasons does it take them to do so? How long does it take expansion players to finish in the top X players and so on. We seem to agree that once expansion team(s)/player(s) do(es) so to an acceptable degree, then they become part of the family and are treated the same as any other team going forward. It's just a matter of what those thresholds are for team and/or player, and whether they should be treated as a full team (entirely ignoring expansion effects), a fractional team, or a non-existent ("zero") team for benchmark purposes until they reach such a threshold.

I suspect that we can both agree that the 2018 Stanley Cup runners-up should be exempt from this analysis.

Looking back briefly at the 1998-99 Predators, they managed to outscore LA, Montreal, and Tampa in their inaugural season. I'm not sure what it means that they managed to outscore a few bottom-feeders. Cliff Ronning led them with 53 points...

Yup, this looks like a massive undertaking.

In the meantime, I'll look at the 3Q+IQR method applied to points-per-game (minimum half a season played?) and see what that turns out.

Vilica · May 22, 2021

You're forgetting one thing in your comparison between 67-68 and 14-15. Mikita and them played 74 games, while Benn and his played 82. There should be a gap in their seasonal VsX just due to that. Beyond that, the 67-68 season is higher scoring than 14-15. League average in 67-68 was 206 goals for, while in 14-15, league average was 218. Converted to per game, that's 2.78/g versus 2.66/g. That's the reason why the VsX matches up, the increase in games is matched by a decrease in scoring.

Converted to 82 games, a league average of 206 is just over 228, and there are a few years post-lockout in the 220s - 07-08, 09-10, 10-11 and 16-17 (223, 227, 224, 223). There's a huge variation in VsX numbers for those years despite the similar scoring level - 106, 109, 99, 89 - but if you average those 4, its basically the same as the derived number (average of 100.75, derived VsX somewhere between 97-100 [Two things - a one goal increase/decrease in league average changes expected VsX by around 0.5 points, so 223 is 97.8 while 227 is 99.5 Second, you can see the effect of missed games on the low 89 VsX in 16-17. Both Crosby and Kucherov missed 7-8 games, and if you assume their PPG for a full season, they're right around 95-97, not that huge drop.]).

Now, going back to 67-68, you take Mikita's PPG, scale it to 80 or 82 games, and his point total is between 97 and 99, and Esposito/Howe would be in the low 90s in the same manner. There are a few other older seasons in the 220s - 40-41, 48-49, 49-50, 50-51, 56-57, 57-58, 63-64, and generally speaking the 1st/2nd place finishers in those years lead to an 82 game VsX equivalent in the mid-high 90s, with the 49-50 season being the only real outlier.

Single-formula VsX: a measure derived from interquartile range

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