"VsEst" - An attempt to account for league depth by estimating the highest non-outlier scorer

[Black Gold Extractor]

I suspect that the biggest contention between people who do historical rankings of players is whether league depth can be accounted for, as well as how it should be done. (See this thread page for a glimpse of that.)

VsX assumes that the league can reliably generate a typical 2nd-place scorer (or typical highest non-outlier scorer to be more accurate) in every era and that this is a good benchmark to use to compare other players. Personally, I think that averaged over several seasons that this is a good assumption. However, can we test this?

RATIONALE

First, let's consider a completely fictional list of numbers:

50, 43, 39, 38, 37, 36, 35, 34, 33, 32, ...

The VsX benchmark for this list would be 43. This is a little bit of an outlier, but 39/43 = 0.907 >= 0.9, so it stays put. The VsX score for the outlier would be 116.

Now, let's say that our sample size is halved.

50, 39, 37, 35, 33, ...

The VsX benchmark for this list would be 39. The VsX score for the outlier would be 128. That's a pretty big difference. But wait, I'm kind of cheating, aren't I? Let's halve the sample size another way:

50, 43, 38, 36, 34, ...

The VsX benchmark for this list would be 38. This is because 38/43 = 0.884 < 0.9, so instead of the 2nd place scorer we use the 3rd. The VsX score for the outlier would be 132 (as opposed to 116 for the full sample).

Yeah, I'm still kind of cheating. What if the 2nd number was 42 instead of 43?

50, 42, 39, 38, 37, 36, 35, 34, 33, 32, ... benchmark 42, VsX 119
50, 39, 37, 35, 33, ... benchmark 39, VsX 128
50, 42, 38, 36, 34, ... benchmark 42, VsX 119

While the above are heavily constructed examples showing the worst possible outcomes, it does raise the possibility that the loss of "resolution" due to a smaller talent pool could benefit the outlier's VsX score. The rest of the field is basically the same with regard to the outlier, but the outlier can get some fairly different scores.

What if we wanted to find some value X, Y, Z for these lists, then:

X, a, 39, 38, 37, 36, 35, 34, 33, 32, ...
Y, b, 37, 35, 33, ...
Z, c, 38, 36, 34, ...

It's not too hard given the above lists. We would find that X = 41, Y = 41, and Z = 42. (If you're wondering, a = 40, b = 39, and c = 40.) As such, given the outlier of 50, the VsX = VsY = 50/41 = 122, and VsZ = 50/42 = 119. That's a much smaller variation, and it doesn't matter if the second number is 43, 42, or 49.

So that's basically it. We estimate the highest non-outlier using a decent sample size and then we compare the real numbers to the estimate, hence VsEst. (Bonus: it sounds like "VsX" if you say it really quickly, too!)

SPECIFICS

It's a bit tough to find a balance between a large sample size and equal opportunity for the sample being analyzed. Using the top 12 scorers basically guarantees a first-line-caliber player in the O6 era and provides an okay sample size. (If we're really pushing it, the top 12 is basically the starters for the 4-team era pre-consolidation, i.e. 1919-20 onward.)

I make two estimates for all years: one using a sample from 2-12*, and one using a sample from 5-12. Then I average the estimates to give a final VsEst benchmark.

The estimate for each sample is made using OpenOffice Calc/Microsoft Excel by adding the slope and intercept of each sample.

*Edited on March 31, 2018.

BENCHMARK COMPARISON

I'm going to compare the VsEst benchmark with the actual VsX benchmarks and what I'm going to call VsX*. VsX* is going to be VsX without the wartime fudges, Bathgate rule, and Orr rules applied. Additionally, the averaging for benchmarks is contracted by one on each end, e.g. the VsX* benchmark for 1988-89 is the average of 168, 155, 150, 115, 113, and 110, giving 135 instead of the original 139.

Yr.	VsX	VsX*	VsEst
2016-17	89	89	92	*
2015-16	89	89	86
2014-15	86	86	85
2013-14	87	87	85
2012-13	57	57	58
2011-12	97	97	90
2010-11	99	99	99
2009-10	109	109	105
2008-09	110	110	102
2007-08	106	106	104
2006-07	114	114	109
2005-06	106	106	113	*
2003-04	87	87	86
2002-03	104	104	105
2001-02	90	90	84
2000-01	96	96	103	*
1999-00	94	94	92
1998-99	107	107	106
1997-98	91	91	95	*
1996-97	109	109	104
1995-96	120	120	128	*
1994-95	70	70	66
1993-94	120	120	117
1992-93	148	148	147
1991-92	123	123	117
1990-91	115	115	124	*
1989-90	129	129	124
1988-89	139	135	145	*
1987-88	131	131	128
1986-87	108	108	112	*
1985-86	141	141	139
1984-85	135	135	131
1983-84	121	126	128	*
1982-83	124	124	117
1981-82	147	147	143
1980-81	135	135	122
1979-80	119	118	120	!
1978-79	116	117	127	*
1977-78	109	108	106
1976-77	105	105	107	*
1975-76	119	119	118
1974-75	121	127	130	*
1973-74	91	101	100	*
1972-73	104	104	101
1971-72	109	117	112	*
1970-71	98	116	111	*
1969-70	86	86	85
1968-69	107	107	101
1967-68	84	84	83
1966-67	70	70	74	*
1965-66	78	78	84	*
1964-65	83	83	78
1963-64	78	78	85	*
1962-63	81	81	78
1961-62	84	84	79
1960-61	90	90	85
1959-60	80	80	81
1958-59	83	84	84
1957-58	71	71	75	*
1956-57	77	72	80	*
1955-56	71	71	78	*
1954-55	74	74	71
1953-54	61	59	59
1952-53	61	61	67	*
1951-52	69	69	64
1950-51	66	66	68	*
1949-50	69	69	67
1948-49	54	54	57	*
1947-48	60	60	60
1946-47	63	63	66	*
1945-46	60	52	54	!
1944-45	78	61	65	!
1943-44	95	77	81	!
1942-43	72	66	66
1941-42	54	54	55
1940-41	44	44	47	*
1939-40	43	43	44
1938-39	44	44	44
1937-38	44	44	45
1936-37	45	45	43
1935-36	40	40	41
1934-35	47	47	48
1933-34	43	42	44	!
1932-33	44	44	44
1931-32	50	50	52	*
1930-31	43	43	48	*
1929-30	62	62	65	*
1928-29	29	29	31	*
1927-28	35	35	38	*
1926-27	32	32	35	*
1925-26		29	31	!
1924-25		36	41	!
1923-24		23	24
1922-23		34	32
1921-22		33	37	!
1920-21		33	38	!
1919-20		40	43	!

[THEAD] [/THEAD]
[TBODY] [/TBODY]

The "*" and "!" denote seasons where the VsEst is greater than the VsX or VsX* value respectively by at least 2 points. This becomes more frequent as we go further back in time.

BRIEF PLAYER COMPARISONS

This is the usual best 7-year VsX, unweighted.

Rk.	Player	VsX	VsEst	Debut
1	Wayne Gretzky	155.6	155.3	1979-80
2	Phil Esposito	130.4	124.5	1963-64
3	Gordie Howe	125.5	123.4	1946-47
4	Mario Lemieux	119.8	119.1	1984-85
5	Jaromir Jagr	114.2	111.5	1990-91
6	Bobby Orr	114.8	108.6	1966-67
7	Stan Mikita	107.8	106.9	1958-59
8	Sidney Crosby	102.4	104.5	2005-06
9	Bobby Hull	108.3	104.2	1957-58
10	Ted Lindsay	104.4	103.3	1944-45
10	Maurice Richard	102.4	103.3	1942-43
12	Marcel Dionne	103.3	103.1	1971-72
13	Guy Lafleur	104.5	102.8	1971-72
14	Jean Beliveau	105.7	102.6	1950-51
15	Bill Cowley	97.0	100.2	1934-35
16	Cy Denneny	N/A	99.8	1914-15
17	Alex Ovechkin	98.4	99.7	2005-06
18	Andy Bathgate	101.1	99.6	1952-53
19	Howie Morenz	102.2	98.9	1923-24
20	Joe Sakic	97.7	97.1	1988-89

[TBODY] [/TBODY]

IS IT WORTH IT?

It's not massively different from VsX. And there are a couple of problems:

1) VsEst uses linear extrapolation on the tail end of a distribution. I'd probably be kicked out of stats class... if I had ever taken stats. (This may also be an issue.)

2) Sometimes, the reduction in the talent pool isn't random... which is a problem when it comes to statistical arguments. There's a possibility that the healthiest players were more fit to go war (and thus the higher-end players were more likely to be away). The WHA obviously tried to poach the biggest stars from the NHL.

Thoughts?

EDIT (March 31, 2018): I modified the benchmark to include the 2nd place scorer for the first sample. I also included the debut date to see the distribution of talent over the eras in the top 20.

1910's: 1 (Denneny)
1920's: 1 (Morenz)
1930's: 1 (Cowley)
1940's: 3 (Richard, Lindsay, Howe)
1950's: 4 (Beliveau, Bathgate, Hull, Mikita)
1960's: 2 (Esposito, Orr)
1970's: 3 (Dionne, Lafleur, Gretzky)
1980's: 2 (Lemieux, Sakic)
1990's: 1 (Jagr)
2000's: 2 (Crosby, Ovechkin)

Click to read more...

 

[Canadiens1958]

Interesting but still suffers from the same issues that VsX does.

GP and TOI/G is not considered.

Also league depth while mentioned is not really considered.

Illustrate by looking at your data for 1919-20(-,40,42) and 1939-40(43,43,44)

You have one unit, app 10 player/9 skater rosters in 1919-2o in a 4 team league with a 24 game schedule, generating 9.58 TG/G. Depth is not a factor. Starters play, subs mainly sit.

1939-40, you the basic 3 line, 2 d-man pairings with subs, playing a 48 game schedule in a 7 team league,generating 4.99 TG/G. 3 lines, 2 pairings enjoyed regular playing time.

Rather obvious disparity in depth and TOI/G. This has to be considered.

% of points generated by the first unitof each team. Straightforward in the 1919-20 season, trickier for 1939-40.

Progress but plenty of room to grow.

 

[Theokritos]

A metric that takes conference/division GA imbalance in the age of unbalanced schedules into account would be the most interesting for me.

 

[blogofmike]

I like it. Perhaps variations in the talent pool (WW2, as you mentioned) will skew it, but the rules are the same for every year. It's a more constant variable, if you will. I like consistently blended averages (but have always been too lazy to calculate them) for their simplicity.

You have one unit, app 10 player/9 skater rosters in 1919-2o in a 4 team league with a 24 game schedule, generating 9.58 TG/G. Depth is not a factor. Starters play, subs mainly sit.

1939-40, you the basic 3 line, 2 d-man pairings with subs, playing a 48 game schedule in a 7 team league,generating 4.99 TG/G. 3 lines, 2 pairings enjoyed regular playing time.

Rather obvious disparity in depth and TOI/G. This has to be considered.

% of points generated by the first unitof each team. Straightforward in the 1919-20 season, trickier for 1939-40.

Would it help to use a VsEst value based on a variable pool based on league size? i.e. using fewer players to create the average for a 6-team league vs a 31-team league.

A metric that takes conference/division GA imbalance in the age of unbalanced schedules into account would be the most interesting for me.

Sort of like FootballOutsiders DYAR for scoring? Might work. If the nhl.com game-by-game data is rich enough, we may be able to have ES/PP/SH breakdowns or even be able to adjust a player's Expected Points by which goaltender they faced that day (depending on sample sizes). Last one might be a stretch though

 

[Canadiens1958]

I like it. Perhaps variations in the talent pool (WW2, as you mentioned) will skew it, but the rules are the same for every year. It's a more constant variable, if you will. I like consistently blended averages (but have always been too lazy to calculate them) for their simplicity.



Would it help to use a VsEst value based on a variable pool based on league size? i.e. using fewer players to create the average for a 6-team league vs a 31-team league.

What are you including under the rules umbrella? Given that the NHL underwent many rule changes including in season changes,pre 1967 expansion, the rules impact gets complicated.

The Vegas expansion illustrates the fragility of averages and what impacts averages.

What is a required is stratification that takes into account various aspects of deployment. This would be responsive to the depth issue.

Above we have a VsX representation over 7 seasons for leading players across eras. Fine, even interesting but it does not address depth.

Specifically how did Gretzky, Sakic other centers compare to the contemporary #1 centers on the other league teams over the same span of seasons. Repeating for #2 centers etc would go a long way towards understanding depth.

 

[blogofmike]

What are you including under the rules umbrella? Given that the NHL underwent many rule changes including in season changes,pre 1967 expansion, the rules impact gets complicated.

The rules for the calculation, to clarify. You need to read 2 sentences to know how to calculate every year, which is simpler than VSX, which has quite a few rules and exceptions.

 

[Canadiens1958]

The rules for the calculation, to clarify. You need to read 2 sentences to know how to calculate every year, which is simpler than VSX, which has quite a few rules and exceptions.

Algorithm not rules. Rules govern the sport, impacting the on ice results.

 

[Black Gold Extractor]

A metric that takes conference/division GA imbalance in the age of unbalanced schedules into account would be the most interesting for me.

This is a good point. Even in the O6 era, when there are only 5 other teams, this could have some influence. For example, would the late-50's Canadiens benefit from the fact that they don't have to face the Canadiens? Of course, the fact that other teams have to face the Canadiens would also inflate their GA. I believe that I have an iterative sequence that can narrow it down:

[Opponent GA](0) = average of all opponent GA

[Team GF](0) = team's GF

[Team GF](n) = [Team GF](n-1) x [league average GA] / [Opponent GA](n-1)

[Opponent GA](n) = [Opponent GA](n-1) - ( [Team GF](n) - [league average GF] ) / [number of opponents]

For the O6 era, after one iteration, these are the average opponent GA faced by each team.

Yr.	Avg.	BOS	CBH	DET	MTL	NYR	TOR
1966-67	209	204	207	200	215	217	209
1965-66	213	206	214	216	217	205	220
1964-65	201	196	203	203	203	195	207
1963-64	195	195	196	193	198	185	200
1962-63	208	193	218	213	211	202	212
1961-62	211	195	215	214	212	214	214
1960-61	210	207	220	212	207	202	214
1959-60	207	195	216	213	204	200	211
1958-59	203	199	203	206	203	200	206
1957-58	196	196	201	197	194	198	189
1956-57	188	190	183	194	192	180	190
1955-56	178	182	173	183	180	166	181
1954-55	177	175	166	181	171	174	192
1953-54	168	163	158	172	169	166	180
1952-53	168	170	165	165	175	160	170
1951-52	182	187	172	187	183	170	190
1950-51	190	190	172	193	194	191	198
1949-50	191	181	176	191	205	196	199
1948-49	163	160	149	161	174	167	167
1947-48	176	179	160	180	183	170	182
1946-47	190	193	168	189	202	195	190
1945-46	167	170	158	173	174	166	162
1944-45	184	176	190	182	190	175	189
1943-44	204	185	213	209	221	188	209
1942-43	181	179	181	196	178	167	182

[TBODY] [/TBODY]

So for the O6 players that made my original list (but only including the O6 years), the unweighted 7-year VsEst:

Player	VsEst (before adjusting for opponent GA)	VsEst (after adjusting for opponent GA)	Change
Gordie Howe	125.7	123.6	-1.7%
Ted Lindsay	105.7	104.7	-0.9%
Jean Beliveau	103.7	103.7
Maurice Richard	105.2	102.7	-2.4%
Andy Bathgate	100.9	102.4	+1.5%
Bobby Hull	101.5	99.7	-1.8%
Stan Mikita	101.1	99.6	-1.5%

[TBODY] [/TBODY]

Doing this for other seasons is going to be tougher, but the O6 era at least gives us a starting point. Bathgate is the only player who didn't play for a consistently "good" team, so he gets a boost of 1.5%. Richard sees the biggest drop due to a few of his seasons being played during WWII. Regardless, the difference after taking opponent GA isn't incredibly significant either.

So basically, the idea that players can benefit from playing for a good team has a grain of truth to it... but good players are what make a team good in the first place.

Specifics, for those who want them, follow:

Gordie Howe

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1946-47	22	22	34.4
1947-48	44	43	72.9
1948-49	37	37	67.3
1949-50	68	68	103.0
1950-51	86	85	125.0
1951-52	86	83	131.7
1952-53	95	96	147.7
1953-54	81	79	138.6
1954-55	62	60	84.5
1955-56	79	77	100.0
1956-57	89	86	108.9
1957-58	77	77	104.1
1958-59	78	77	93.9
1959-60	73	71	87.7
1960-61	72	71	84.5
1961-62	77	76	97.4
1962-63	86	84	109.1
1963-64	73	74	88.1
1964-65	76	75	98.7
1965-66	75	74	87.1
1966-67	65	68	94.4

[TBODY] [/TBODY]

Ted Lindsay

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1944-45	23	23	35.9
1945-46	17	16	29.6
1946-47	42	42	65.6
1947-48	52	51	86.4
1948-49	54	55	100.0
1949-50	78	78	118.2
1950-51	59	58	85.3
1951-52	69	67	106.3
1952-53	71	72	110.8
1953-54	62	61	107.0
1954-55	38	37	52.1
1955-56	50	48	62.3
1956-57	85	82	103.8
1957-58	39	38	51.4
1958-59	58	58	70.7
1959-60	26	25	30.9
1964-65	28	28	36.8

[TBODY] [/TBODY]

Jean Beliveau

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1950-51	2	2	2.9
1952-53	5	5	7.7
1953-54	34	34	59.6
1954-55	73	75	105.6
1955-56	88	87	113.0
1956-57	84	82	103.8
1957-58	59	60	81.1
1958-59	91	91	111.0
1959-60	74	75	92.6
1960-61	90	91	108.3
1961-62	41	41	52.6
1962-63	67	66	85.7
1963-64	78	77	91.7
1964-65	43	43	56.6
1965-66	77	76	89.4
1966-67	38	37	51.4

[TBODY] [/TBODY]

Maurice Richard

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1942-43	11	11	16.9
1943-44	54	50	61.7
1944-45	73	71	110.9
1945-46	48	46	85.2
1946-47	71	67	104.7
1947-48	53	51	86.4
1948-49	38	36	65.5
1949-50	65	61	92.4
1950-51	66	65	95.6
1951-52	44	44	69.8
1952-53	61	58	89.2
1953-54	67	67	117.5
1954-55	74	76	107.0
1955-56	71	70	90.9
1956-57	62	61	77.2
1957-58	34	34	45.9
1958-59	38	38	46.3
1959-60	35	35	43.2

[TBODY] [/TBODY]

Andy Bathgate

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1952-53	1	1	1.5
1953-54	4	4	7.0
1954-55	40	41	57.7
1955-56	66	71	92.2
1956-57	77	80	101.3
1957-58	78	77	104.1
1958-59	88	89	108.5
1959-60	74	76	93.8
1960-61	77	80	95.2
1961-62	84	83	106.4
1962-63	81	83	107.8
1963-64	77	75	89.3
1964-65	45	44	57.9
1965-66	47	46	54.1
1966-67	31	32	44.4

[TBODY] [/TBODY]

Bobby Hull

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1957-58	47	46	62.2
1958-59	50	50	61.0
1959-60	81	77	95.1
1960-61	56	54	64.3
1961-62	84	82	105.1
1962-63	62	59	76.6
1963-64	87	86	102.4
1964-65	71	70	92.1
1965-66	97	97	114.1
1966-67	80	81	112.5

[TBODY] [/TBODY]

Stan Mikita

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1958-59	1	1	1.2
1959-60	26	25	30.9
1960-61	53	51	60.7
1961-62	77	75	96.2
1962-63	76	73	94.8
1963-64	89	88	104.8
1964-65	87	86	113.2
1965-66	78	78	91.8
1966-67	97	98	136.1

[TBODY] [/TBODY]

Specifically how did Gretzky, Sakic other centers compare to the contemporary #1 centers on the other league teams over the same span of seasons. Repeating for #2 centers etc would go a long way towards understanding depth.

I probably overstated my case with regards to league depth over every season. VsEst seems to be alright at compensating for shallower periods, but it absolutely cannot account for talent compression. I think that looking at even-strength production is probably the way to go to see how deep the league was. First-liners will generally see similar conditions, but other lines are basically in the air. For example, Malkin often saw first PP time despite being the #2 C on the Penguins, which allowed Malkin to significantly outproduce your typical 2nd line center. To use another example, Henri Richard didn't produce gaudy numbers many years due to lack of PP time, but he was also the EV point leader over a 10-season stretch (1956-57 to 1965-66 with 491 EV points, ahead of Bathgate's 487 and Howe's 485 as well as Beliveau's 444).

 

[Canadiens1958]

This is a good point. Even in the O6 era, when there are only 5 other teams, this could have some influence. For example, would the late-50's Canadiens benefit from the fact that they don't have to face the Canadiens? Of course, the fact that other teams have to face the Canadiens would also inflate their GA. I believe that I have an iterative sequence that can narrow it down:

[Opponent GA](0) = average of all opponent GA

[Team GF](0) = team's GF

[Team GF](n) = [Team GF](n-1) x [league average GA] / [Opponent GA](n-1)

[Opponent GA](n) = [Opponent GA](n-1) - ( [Team GF](n) - [league average GF] ) / [number of opponents]

For the O6 era, after one iteration, these are the average opponent GA faced by each team.

Yr.	Avg.	BOS	CBH	DET	MTL	NYR	TOR
1966-67	209	204	207	200	215	217	209
1965-66	213	206	214	216	217	205	220
1964-65	201	196	203	203	203	195	207
1963-64	195	195	196	193	198	185	200
1962-63	208	193	218	213	211	202	212
1961-62	211	195	215	214	212	214	214
1960-61	210	207	220	212	207	202	214
1959-60	207	195	216	213	204	200	211
1958-59	203	199	203	206	203	200	206
1957-58	196	196	201	197	194	198	189
1956-57	188	190	183	194	192	180	190
1955-56	178	182	173	183	180	166	181
1954-55	177	175	166	181	171	174	192
1953-54	168	163	158	172	169	166	180
1952-53	168	170	165	165	175	160	170
1951-52	182	187	172	187	183	170	190
1950-51	190	190	172	193	194	191	198
1949-50	191	181	176	191	205	196	199
1948-49	163	160	149	161	174	167	167
1947-48	176	179	160	180	183	170	182
1946-47	190	193	168	189	202	195	190
1945-46	167	170	158	173	174	166	162
1944-45	184	176	190	182	190	175	189
1943-44	204	185	213	209	221	188	209
1942-43	181	179	181	196	178	167	182

[TBODY] [/TBODY]

So for the O6 players that made my original list (but only including the O6 years), the unweighted 7-year VsEst:

Player	VsEst (before adjusting for opponent GA)	VsEst (after adjusting for opponent GA)	Change
Gordie Howe	125.7	123.6	-1.7%
Ted Lindsay	105.7	104.7	-0.9%
Jean Beliveau	103.7	103.7
Maurice Richard	105.2	102.7	-2.4%
Andy Bathgate	100.9	102.4	+1.5%
Bobby Hull	101.5	99.7	-1.8%
Stan Mikita	101.1	99.6	-1.5%

[TBODY] [/TBODY]

Doing this for other seasons is going to be tougher, but the O6 era at least gives us a starting point. Bathgate is the only player who didn't play for a consistently "good" team, so he gets a boost of 1.5%. Richard sees the biggest drop due to a few of his seasons being played during WWII. Regardless, the difference after taking opponent GA isn't incredibly significant either.

So basically, the idea that players can benefit from playing for a good team has a grain of truth to it... but good players are what make a team good in the first place.

Specifics, for those who want them, follow:

Gordie Howe

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1946-47	22	22	34.4
1947-48	44	43	72.9
1948-49	37	37	67.3
1949-50	68	68	103.0
1950-51	86	85	125.0
1951-52	86	83	131.7
1952-53	95	96	147.7
1953-54	81	79	138.6
1954-55	62	60	84.5
1955-56	79	77	100.0
1956-57	89	86	108.9
1957-58	77	77	104.1
1958-59	78	77	93.9
1959-60	73	71	87.7
1960-61	72	71	84.5
1961-62	77	76	97.4
1962-63	86	84	109.1
1963-64	73	74	88.1
1964-65	76	75	98.7
1965-66	75	74	87.1
1966-67	65	68	94.4

[TBODY] [/TBODY]

Ted Lindsay

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1944-45	23	23	35.9
1945-46	17	16	29.6
1946-47	42	42	65.6
1947-48	52	51	86.4
1948-49	54	55	100.0
1949-50	78	78	118.2
1950-51	59	58	85.3
1951-52	69	67	106.3
1952-53	71	72	110.8
1953-54	62	61	107.0
1954-55	38	37	52.1
1955-56	50	48	62.3
1956-57	85	82	103.8
1957-58	39	38	51.4
1958-59	58	58	70.7
1959-60	26	25	30.9
1964-65	28	28	36.8

[TBODY] [/TBODY]

Jean Beliveau

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1950-51	2	2	2.9
1952-53	5	5	7.7
1953-54	34	34	59.6
1954-55	73	75	105.6
1955-56	88	87	113.0
1956-57	84	82	103.8
1957-58	59	60	81.1
1958-59	91	91	111.0
1959-60	74	75	92.6
1960-61	90	91	108.3
1961-62	41	41	52.6
1962-63	67	66	85.7
1963-64	78	77	91.7
1964-65	43	43	56.6
1965-66	77	76	89.4
1966-67	38	37	51.4

[TBODY] [/TBODY]

Maurice Richard

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1942-43	11	11	16.9
1943-44	54	50	61.7
1944-45	73	71	110.9
1945-46	48	46	85.2
1946-47	71	67	104.7
1947-48	53	51	86.4
1948-49	38	36	65.5
1949-50	65	61	92.4
1950-51	66	65	95.6
1951-52	44	44	69.8
1952-53	61	58	89.2
1953-54	67	67	117.5
1954-55	74	76	107.0
1955-56	71	70	90.9
1956-57	62	61	77.2
1957-58	34	34	45.9
1958-59	38	38	46.3
1959-60	35	35	43.2

[TBODY] [/TBODY]

Andy Bathgate

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1952-53	1	1	1.5
1953-54	4	4	7.0
1954-55	40	41	57.7
1955-56	66	71	92.2
1956-57	77	80	101.3
1957-58	78	77	104.1
1958-59	88	89	108.5
1959-60	74	76	93.8
1960-61	77	80	95.2
1961-62	84	83	106.4
1962-63	81	83	107.8
1963-64	77	75	89.3
1964-65	45	44	57.9
1965-66	47	46	54.1
1966-67	31	32	44.4

[TBODY] [/TBODY]

Bobby Hull

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1957-58	47	46	62.2
1958-59	50	50	61.0
1959-60	81	77	95.1
1960-61	56	54	64.3
1961-62	84	82	105.1
1962-63	62	59	76.6
1963-64	87	86	102.4
1964-65	71	70	92.1
1965-66	97	97	114.1
1966-67	80	81	112.5

[TBODY] [/TBODY]

Stan Mikita

Spoiler

Season	PTS	Adj. PTS	Adj. VsEst
1958-59	1	1	1.2
1959-60	26	25	30.9
1960-61	53	51	60.7
1961-62	77	75	96.2
1962-63	76	73	94.8
1963-64	89	88	104.8
1964-65	87	86	113.2
1965-66	78	78	91.8
1966-67	97	98	136.1

[TBODY] [/TBODY]

I probably overstated my case with regards to league depth over every season. VsEst seems to be alright at compensating for shallower periods, but it absolutely cannot account for talent compression. I think that looking at even-strength production is probably the way to go to see how deep the league was. First-liners will generally see similar conditions, but other lines are basically in the air. For example, Malkin often saw first PP time despite being the #2 C on the Penguins, which allowed Malkin to significantly outproduce your typical 2nd line center. To use another example, Henri Richard didn't produce gaudy numbers many years due to lack of PP time, but he was also the EV point leader over a 10-season stretch (1956-57 to 1965-66 with 491 EV points, ahead of Bathgate's 487 and Howe's 485 as well as Beliveau's 444).

Do not think so. Basic problem is that there is no consensus definition of depth and deployment is not taken into account.

The trend is to define lines in terms of offensive performance as opposed to deployment.

That Malkin gets #1 PP opportunities is a function of deployment. The faceoff now is always in the penalized team's defensive zone after a penalty.Not the situation previously.

Similarly the Beliveau and Henri Richard situation. Looking only at the center ES scoring does not convey the actual strengths of the respective lines. Richard played with Moore a much better LW than Beliveau ever had during the years considered, RW tended to wash.

Which line of the two was the foundation line - that generated the match-ups. Against Boston it did not matter but against Chicago -Hull,Detroit - Howe, New York - Bathgate, Toronto - Mahovlich it did. The Richard line was the foundation line.

Defining and applying deployment is rather straightforward thru 1928-29, basically a one line game.But as the rosters increased allowing for 2 to 4 lines and 2-3 pairings it gets trickier. ES is part of the answer but VsXand derivatives, should also contribute. Specfically you have a global VsX but it is also possible to generate VsX for ES and PP situations that would go along way towards explaining the global differences.

Also it is possible to benchmark offensive VsX over a length of time for each strata - first liners,second liners,etc.

 

[daver]

I think in general that anything besides first place needs context when comparing a 2nd, 3rd, 4th place etc... vs. the same for a player from a different era.

Should Crosby's Top 3 Art Ross placings hold higher value than those of a player from the 06 for example? Should Howe's Top 5 Art Ross finishes from the 06 era be given the same value as a Top 5 finish in a 30 team league?

I would hesitate to say that a 10th place from the current NHL = 5th place in the 06 but rather treat this dynamic as a tiebreaker for players with similar raw point and PPG finishes.

 

[Black Gold Extractor]

The trend is to define lines in terms of offensive performance as opposed to deployment.

That Malkin gets #1 PP opportunities is a function of deployment. The faceoff now is always in the penalized team's defensive zone after a penalty.Not the situation previously.

Similarly the Beliveau and Henri Richard situation. Looking only at the center ES scoring does not convey the actual strengths of the respective lines. Richard played with Moore a much better LW than Beliveau ever had during the years considered, RW tended to wash.

Which line of the two was the foundation line - that generated the match-ups. Against Boston it did not matter but against Chicago -Hull,Detroit - Howe, New York - Bathgate, Toronto - Mahovlich it did. The Richard line was the foundation line.

There are a few posters who conflate league size with league depth. It's fair to say that if Richard was on another team in some hypothetical 12-team NHL at that time, he could have been a "typical" elite 1st-line center with #1 PP time. He led one ten-year stretch in EV scoring and was third in plus-minus for forwards from 1959-60 through 1965-66 (+116, behind only Mikita's +134 and Wharram's +117, and way ahead of Beliveau's +49). As you say, Richard was also tasked with facing off against the toughest lines.

It does appear that Richard saw more EV ice time, at least from 1959-60 onward, with 938 non-PP events in 634 games (1.48 per game). Beliveau saw 878 non-PP events in 622 games (1.41 per game). Richard probably averaged less than one extra shift per game.

I think that Beliveau is more accomplished than Richard, but that obscures their actual abilities due to deployment. That's the crux of the whole "depth" issue, I suspect.

Defining and applying deployment is rather straightforward thru 1928-29, basically a one line game.But as the rosters increased allowing for 2 to 4 lines and 2-3 pairings it gets trickier. ES is part of the answer but VsXand derivatives, should also contribute. Specfically you have a global VsX but it is also possible to generate VsX for ES and PP situations that would go along way towards explaining the global differences.

Also it is possible to benchmark offensive VsX over a length of time for each strata - first liners,second liners,etc.

I do think that breaking down VsX for EV and PP situations is a good idea, though that would require some more effort. I'll look into that later.

I think in general that anything besides first place needs context when comparing a 2nd, 3rd, 4th place etc... vs. the same for a player from a different era.

I would hesitate to say that a 10th place from the current NHL = 5th place in the 06 but rather treat this dynamic as a tiebreaker for players with similar raw point and PPG finishes.

This is too harsh of an adjustment. From my previous work, 5th in the O6 era is roughly the same as 7th now (or 7th in the O6 era is roughly the same as 10th now... both indicate a 1.4x factor).

VsEst does try to take this into account. For example, from 2013-14 through 2015-16, VsEst predicts that the highest non-outlier scorer should have been 85 points each season. The actual 2nd-place scorers were 87, 86, and 89 points respectively, which indicates that the league was deep enough to generate a few marginal outliers consistently. In fact, post-2005 lockout, only 2005-06 and 2016-17 failed to produce a non-outlier that couldn't match the VsEst estimate. (Although if you look at it strictly as an estimate of 2nd place, you could argue that Jagr's 123 blew away the 110 point estimate, and Crosby definitely could have passed the 92 point estimate had he missed fewer games.)

Just looking at the 7-year VsX going to VsEst, you'll find that Crosby has gone up 2.6% from 102.4 to 105.1, and Ovechkin has gone up 2.1% from 98.4 to 100.5. Going from VsX to VsEst, Crosby (1, 1, 2, 2, 3, 3, 3) manages to move up past Beliveau (1, 2, 2, 3, 3, 3, 3), Dionne (1, 2, 2, 2, 3, 4, 5), and Lafleur (1, 1, 1, 3, 3, 4, 36). Purely in terms of regular season scoring over their best 7 years, this makes sense.

To look at another example when the league was shallower, going from VsX to VsEst, Morenz is bumped down from 102.2 to 100.0. (His 1927-28 regular season is still by far the most dominant season prior to Howe, though, with a VsEst score of 134.2.)

 

[Black Gold Extractor]

Here's the full list of VsEst benchmarks for goals, assists, and points from 1919-20 to 2016-17.

Spoiler

VsEst Benchmarks	Goals	Assists	Points
2016-17	41	61	92
2015-16	43	58	86
2014-15	43	58	85
2013-14	41	63	85
2012-13	27	39	58
2011-12	43	62	90
2010-11	44	62	99
2009-10	49	69	105
2008-09	45	72	102
2007-08	49	64	104
2006-07	48	75	109
2005-06	56	72	113
2003-04	41	56	86
2002-03	47	63	105
2001-02	42	54	84
2000-01	48	69	103
1999-00	46	56	92
1998-99	45	60	106
1997-98	52	67	95
1996-97	52	66	104
1995-96	57	88	128
1994-95	33	44	66
1993-94	58	78	117
1992-93	67	92	147
1991-92	51	84	117
1990-91	52	83	124
1989-90	60	81	124
1988-89	60	90	145
1987-88	55	87	128
1986-87	58	69	112
1985-86	59	86	139
1984-85	64	81	131
1983-84	57	76	128
1982-83	62	71	117
1981-82	60	88	143
1980-81	60	79	122
1979-80	56	71	120
1978-79	53	74	127
1977-78	51	72	106
1976-77	52	71	107
1975-76	56	75	118
1974-75	53	78	130
1973-74	53	68	100
1972-73	46	67	101
1971-72	52	62	112
1970-71	45	64	111
1969-70	41	55	85
1968-69	50	58	101
1967-68	40	49	83
1966-67	31	49	74
1965-66	32	48	84
1964-65	31	46	78
1963-64	33	52	85
1962-63	38	50	78
1961-62	34	49	79
1960-61	37	54	85
1959-60	36	47	81
1958-59	41	52	84
1957-58	34	45	75
1956-57	37	49	80
1955-56	36	47	78
1954-55	36	45	71
1953-54	30	36	59
1952-53	31	41	67
1951-52	31	40	64
1950-51	32	43	68
1949-50	31	37	67
1948-49	27	32	57
1947-48	29	34	60
1946-47	31	37	66
1945-46	30	29	54
1944-45	31	40	65
1943-44	38	46	81
1942-43	30	45	66
1941-42	26	34	55
1940-41	24	27	47
1939-40	24	26	44
1938-39	23	31	44
1937-38	24	26	45
1936-37	23	26	43
1935-36	22	25	41
1934-35	23	30	48
1933-34	24	24	44
1932-33	26	25	44
1931-32	29	29	52
1930-31	30	26	48
1929-30	42	28	65
1928-29	19	12	31
1927-28	26	14	38
1926-27	22	12	35
1925-26	29	11	31
1924-25	28	14	41
1923-24	18	7	24
1922-23	23	12	32
1921-22	27	15	37
1920-21	28	10	38
1919-20	30	12	43

[TBODY] [/TBODY]

Top 25 7-year VsEst goal-scorers (that I have found, anyway), with the benchmark normalized to 50:

Rk.	VsX Rk.	Player	VsX	VsEst	Best 7 Top-10 Finishes	Debut
1	1	Bobby Hull	70.2	69.0	(1, 1, 1, 1, 1, 1, 1)	1957-58
2	2	Maurice Richard	67.2	65.1	(1, 1, 1, 1, 1, 2, 2)	1942-43
3	3	Gordie Howe	65.5	63.7	(1, 1, 1, 1, 1, 2, 2)	1946-47
4	4	Phil Esposito	62.1	61.5	(1, 1, 1, 1, 1, 1, 2)	1963-64
5	5	Alex Ovechkin	59.2	60.1	(1, 1, 1, 1, 1, 1, 2)	2005-06
6	6	Wayne Gretzky	59.0	58.9	(1, 1, 1, 1, 1, 3, 4)	1979-80
7	7	Brett Hull	56.3	55.1	(1, 1, 1, 2, 6, 8, 9)	1986-87
8	8	Mario Lemieux	54.5	54.9	(1, 1, 1, 3, 3, 3, 7)	1984-85
9		Babe Dye		53.8	(1, 1, 1, 2, 2, 2, 8)	1919-20
10	11	Mike Bossy	52.9	53.2	(1, 1, 2, 2, 2, 3, 3)	1977-78
11	10	Charlie Conacher	54.3	51.2	(1, 1, 1, 1, 1)	1929-30
12	12	Bill Cook	52.7	51.0	(1, 1, 1, 2, 5, 6, 6)	1926-27
13	15	Nels Stewart	50.7	50.5	(1, 1, 2, 3, 3, 4, 4)	1925-26
14	9	Jean Beliveau	54.4	50.3	(1, 1, 2, 3, 3, 4, 5)	1950-51
15	22	Howie Morenz	48.3	50.1	(1, 2, 3, 3, 3, 4, 5)	1923-24
16		Cy Denneny		50.0	(1, 2, 2, 3, 3, 4, 4)	1914-15
17	17	Steven Stamkos	50.4	49.9	(1, 1, 2, 2, 2, 7)	2008-09
18	14	Frank Mahovlich	50.8	49.6	(2, 2, 2, 2, 3, 4, 6)	1956-57
19	19	Stan Mikita	50.0	49.4	(2, 2, 2, 3, 4, 5, 6)	1958-59
20	16	Jaromir Jagr	50.4	49.3	(2, 2, 2, 2, 3, 4, 6)	1990-91
21	18	Pavel Bure	50.3	49.1	(1, 1, 1, 3, 5)	1991-92
22	13	Bernie Geoffrion	51.2	48.4	(1, 1, 3, 3, 5, 5, 8)	1950-51
23	24	Guy Lafleur	48.2	48.1	(1, 2, 2, 2, 3, 7)	1971-72
24	24	Marcel Dionne	48.2	47.9	(2, 2, 3, 4, 5, 5, 8)	1971-72
25	21	Ted Lindsay	48.4	47.5	(1, 2, 2, 3, 5, 6, 6)	1944-45

[TBODY] [/TBODY]

Distribution throughout the decades:

1910's: 2 (Denneny, Dye)
1920's: 4 (Morenz, Stewart, Cook, Conacher)
1930's: 0 (??? I probably missed someone...)
1940's: 3 (Richard, Lindsay, Howe)
1950's: 5 (Geoffrion, Beliveau, Mahovlich, Hull, Mikita)
1960's: 1 (Esposito)
1970's: 4 (Dionne, Lafleur, Bossy, Gretzky)
1980's: 2 (Lemieux, Hull)
1990's: 2 (Jagr, Bure)
2000's: 2 (Ovechkin, Stamkos)

 

[Black Gold Extractor]

Top 25 7-year VsEst assist-talliers, with the benchmark normalized to 50:

Rk.	Player	VsEst	Best 7 Top-10 Finishes	Debut
1	Wayne Gretzky	82.0	(1, 1, 1, 1, 1, 1, 1)	1979-80
2	Bobby Orr	64.5	(1, 1, 1, 1, 1, 2)	1966-67
3	Frank Boucher	59.6	(1, 1, 1, 2, 2, 2, 2)	1921-22
4	Phil Esposito	56.2	(1, 1, 1, 2, 2, 2, 2)	1963-64
5	Joe Thornton	55.4	(1, 1, 1, 2, 2, 2, 2)	1997-98
6	Stan Mikita	54.9	(1, 1, 1, 2, 2, 2, 4)	1958-59
7	Mario Lemieux	54.6	(1, 1, 1, 2, 2, 2, 3)	1984-85
8	Bill Cowley	53.9	(1, 1, 1, 2, 3, 5, 6)	1934-35
9	Elmer Lach	53.6	(1, 1, 1, 2, 4, 5, 5)	1940-41
10	Gordie Howe	53.2	(1, 1, 1, 2, 3, 3, 3)	1946-47
11	Adam Oates	52.3	(1, 1, 1, 2, 2, 3, 3)	1985-86
12	Andy Bathgate	52.1	(1, 1, 2, 2, 2, 2, 3)	1952-53
13	Ted Lindsay	51.6	(1, 1, 3, 3, 3, 4, 7)	1944-45
14	Henrik Sedin	51.5	(1, 1, 1, 4, 4, 5, 8)	2000-01
15	Jaromir Jagr	51.3	(1, 1, 1, 3, 3, 3, 5)	1990-91
16	Paul Coffey	50.0	(2, 2, 2, 3, 4, 4, 5)	1980-81
17	Sidney Crosby	49.3	(1, 2, 2, 2, 3, 7, 8)	2005-06
18	Bobby Clarke	48.8	(1, 1, 3, 4, 5, 6, 8)	1969-70
18	Marcel Dionne	48.8	(2, 2, 3, 3, 3, 4, 9)	1971-72
18	Nicklas Backstrom	48.8	(1, 2, 3, 3, 3, 3, 7)	2007-08
21	Jean Beliveau	48.7	(1, 1, 2, 2, 2, 3, 4)	1950-51
22	Bryan Trottier	48.5	(1, 1, 4, 5, 5, 5, 5)	1975-76
23	Ron Francis	48.2	(1, 1, 3, 4, 4, 5, 7)	1981-82
24	Doug Bentley	48.0	(1, 1, 4, 5, 5, 9, 9)	1939-40
25	Guy Lafleur	47.7	(1, 2, 2, 3, 3, 5)	1971-72

[TBODY] [/TBODY]

Distribution throughout the decades based on their debut:

1910's: 0
1920's: 1 (Boucher)
1930's: 2 (Cowley, Bentley)
1940's: 3 (Lach, Lindsay, Howe)
1950's: 3 (Beliveau, Bathgate, Mikita)
1960's: 3 (Esposito, Orr, Clarke)
1970's: 4 (Dionne, Lafleur, Trottier, Gretzky)
1980's: 4 (Coffey, Francis, Lemieux, Oates)
1990's: 2 (Jagr, Thornton)
2000's: 3 (Sedin, Crosby, Backstrom)

 

[Canadiens1958]

Top 25 7-year VsEst assist-talliers, with the benchmark normalized to 50:

Rk.	Player	VsEst	Best 7 Top-10 Finishes	Debut
1	Wayne Gretzky	82.0	(1, 1, 1, 1, 1, 1, 1)	1979-80
2	Bobby Orr	64.5	(1, 1, 1, 1, 1, 2)	1966-67
3	Frank Boucher	59.6	(1, 1, 1, 2, 2, 2, 2)	1921-22
4	Phil Esposito	56.2	(1, 1, 1, 2, 2, 2, 2)	1963-64
5	Joe Thornton	55.4	(1, 1, 1, 2, 2, 2, 2)	1997-98
6	Stan Mikita	54.9	(1, 1, 1, 2, 2, 2, 4)	1958-59
7	Mario Lemieux	54.6	(1, 1, 1, 2, 2, 2, 3)	1984-85
8	Bill Cowley	53.9	(1, 1, 1, 2, 3, 5, 6)	1934-35
9	Elmer Lach	53.6	(1, 1, 1, 2, 4, 5, 5)	1940-41
10	Gordie Howe	53.2	(1, 1, 1, 2, 3, 3, 3)	1946-47
11	Adam Oates	52.3	(1, 1, 1, 2, 2, 3, 3)	1985-86
12	Andy Bathgate	52.1	(1, 1, 2, 2, 2, 2, 3)	1952-53
13	Ted Lindsay	51.6	(1, 1, 3, 3, 3, 4, 7)	1944-45
14	Henrik Sedin	51.5	(1, 1, 1, 4, 4, 5, 8)	2000-01
15	Jaromir Jagr	51.3	(1, 1, 1, 3, 3, 3, 5)	1990-91
16	Paul Coffey	50.0	(2, 2, 2, 3, 4, 4, 5)	1980-81
17	Sidney Crosby	49.3	(1, 2, 2, 2, 3, 7, 8)	2005-06
18	Bobby Clarke	48.8	(1, 1, 3, 4, 5, 6, 8)	1969-70
18	Marcel Dionne	48.8	(2, 2, 3, 3, 3, 4, 9)	1971-72
18	Nicklas Backstrom	48.8	(1, 2, 3, 3, 3, 3, 7)	2007-08
21	Jean Beliveau	48.7	(1, 1, 2, 2, 2, 3, 4)	1950-51
22	Bryan Trottier	48.5	(1, 1, 4, 5, 5, 5, 5)	1975-76
23	Ron Francis	48.2	(1, 1, 3, 4, 4, 5, 7)	1981-82
24	Doug Bentley	48.0	(1, 1, 4, 5, 5, 9, 9)	1939-40
25	Guy Lafleur	47.7	(1, 2, 2, 3, 3, 5)	1971-72

[TBODY] [/TBODY]

Distribution throughout the decades based on their debut:

1910's: 0
1920's: 1 (Boucher)
1930's: 2 (Cowley, Bentley)
1940's: 3 (Lach, Lindsay, Howe)
1950's: 3 (Beliveau, Bathgate, Mikita)
1960's: 3 (Esposito, Orr, Clarke)
1970's: 4 (Dionne, Lafleur, Trottier, Gretzky)
1980's: 4 (Coffey, Francis, Lemieux, Oates)
1990's: 2 (Jagr, Thornton)
2000's: 3 (Sedin, Crosby, Backstrom)

Very nice. Especially revealing about the pre-70 game schedule players when assists were awarded in a very conservative fashion.