Adjusted Even-Strength Plus-minus 1968-2008

[overpass]

I've edited the OP to add the most recent adjusted plus-minus numbers I have, using my current method of calculating, for anyone who is interested.

Generally, the updated numbers are slightly more positive towards players on good teams, since the team adjustment is a little weaker.

I've also changed the SHGF estimator to include actual SH points, so players who scored a lot of SH points have had those moved out of the ESGF column and into the SHGF column. This change is small to non-existent for most forwards, and probably only affects Paul Coffey and Mark Howe among defencemen. It has a major effect on Wayne Gretzky's numbers.

matnor, I see what you mean about the Langway numbers being off. I don't have the 2008 numbers anymore to replace them with, so I just deleted him from the first table and included him in the second table.

plusminus, I'm still planning to get to what you posted. Not ignoring you, just busy

[Czech Your Math]

Originally Posted by plusandminus

I've studied correlations between ES icetime and ESGF+ESGA and they don't necessarily correspond very well, perhaps especially regarding forwards. For example, during 2002-03, I guy like Kowalchuk (who had a reputation as an offensive minded player) had about 1.5 times more ESGF+ESGA played than the average player.
So here we thus have our first bias. ESGF=60 and ESGA=50, will give higher "ice time" than ESGF=50 and ESGA=40, even if real ice time is the same. ?

I'm not sure ice time is so important. If a player is on ice for a much higher % of ES GF+GA than his % of his ice time, that's okay. If he's able to perform at or above the GF/GA ratio of the team as a whole, then the more volume the better for the team. If he's at a worse GF/GA level, then the high volume will negatively effect the player portion of the metric even more.

Originally Posted by plusandminus

I'm a bit against dividing ESGF by ESGA. As i wrote in another reply some day ago, I think there are better ways to do it. To use the above example, I would say that 60-50 and 50-40 is equally good, despite the latter one getting a slightly higher ratio (if I understand you right).

I don't know why you are so against calculating GF/GA ratios. They shouldn't be used randomly, but in this case they are the primary basis of the pythagorean win% calculation, so of great importance.

Whether 60/50 or 50/40 is better may depend most on context (all other things being equal). On a bad team, the extra 10/10 might be helpful, while on a good team, it may be hurtful.

Originally Posted by plusandminus

I googled, and according to wikipedia I got the impression that rather 1.8 was the "right exponent", at least in baseball?

Wouldn't shootout goals be excluded from the stats?

I saw more than one study for hockey. If 1.8 or whatever number is deemed a solid number, I have not attachment to 2.0 as exponent. It does vary by sport though, I think mainly due to differing scoring levels.

Originally Posted by plusandminus

That's 94-38 = +56 with Forsberg. And 84-87 = -3 without.
Not only did he have the league's by far best ES+/-, and scored the highest amount of ESpts, on a team that without him (and the guys who were on the ice with him) had negative +/-.

Adding ESGF+ESGA, we get 94+38=132 for him. 178+125=303 for the team.
That's an "ice time" of 43.56 % according to ESGF+ESGA.

I got 43.56 %, so at least one of us (perhaps I) may be wrong.

In reality, the correct answer seems to be 28.84 %. (if my data is correct)
So, the estimated percentage is about 1.5 times higher.

You are correct. I have realized yet another error in this hastily put together study. I had calculated player's % of team's GF and GA separately and then summed them, instead of summing them before calculating the player's % of team. I came up with this idea a couple days ago and used some existing player data for the basis of most of the calculations, but that doesn't excuse my sloppiness.

Nice job of checking my math!

Originally Posted by plusandminus

And I think three players with identical EStime, having ESGF-ESGA of 40-40 and 30-30 and 20-20 contributes equally much.

Originally Posted by plusandminus

It would be interesting to this stat listed for all the players on a team.
(I can do it myself, but not right now.)
With the risk of being called an idiot, does the sum of all players equal 100??

I don't have calculations for an entire team. I think the totals would not exactly balance, but should not be way off either.

The total for all players on the team should be somewhere around:

5 * 82 * (team's ES pythagorean win%)

note: 5 is number of skaters per goal

For a team with equal ES GF and GA, should be ~205 "ES wins"

Originally Posted by plusandminus

Pittsburgh were a bit special that year, starting the season with some very good players, just to see them drop off one by one. So Mario's stats sank deeper and deeper during the season. (If I remember right.)

Yeah, Pittsburgh was real "special" for a few years there post-Jagr.

In '94 and '96, Lemieux's R-On was slightly less than R-Off, although a big reason for that is Jagr being such a large part of the R-Off. His R-On/R-Off is great in '97 (1.97) and very good in 2001 (1.39), but a lot of that was due to those being the 1.5 seasons he played with Jagr at even strength. After that, he was mostly weak.

Originally Posted by plusandminus

A thought I have, is that one might want to seperate forwards and defencemen, since they may not be easily comparable.

An additional way of improving (or not) the method, could be to include ESpts in the calculations, to estimate how much different players contributed to their ESGF. Now I'm mainly thinking of doing it for forwards, to help seperate the offensive contributions of linemates, although it might be useful to apply (perhaps in a differnt form) to defencemen as well. To do something similar for ESGA would of course be basically impossible (unless one apply an assumption like "defencemen being more responsible for ESGA, while forwards being more responsible for ESGF").

Yes, separating forwards and defensemen is one possibilty. Would rather not do that... and what about players like Coffey that could almost be classified as either? I like using a player's ES points as a % of ESGF, but this requires even more data and doesn't address ESGA. I think the latter is probably the better way to go, or it may be better to just live with a "pure" but flawed metric.

Originally Posted by plusandminus

Finally, which you likely are aware of, this stat only tells us about players' contributions during ES. So the "rankings" here are ES only.
Creating similar stats for PP and SH would rank players differently.
For example. While Forsberg had "much better" ES stats than Naslund in 2002-03, Naslund had better PP stats.

Of course this, like adjusted plus-minus, isn't an all-encompassing metric. It's meant to shed light on even strength value. Still, about ~75% of goals occur at even strength and it's even strength play that leads to penalties, so ES play is crucial to overall value.

It's not meant to measure all aspects of the game.

[plusandminus]

I don't know why you are so against calculating GF/GA ratios. They shouldn't be used randomly, but in this case they are the primary basis of the pythagorean win% calculation, so of great importance.

I'll try to explain.

If I was asked to rank the following seasonal ES stats for players, without paying any attention at all to context, I would rank them as follow (with a tie for 2nd best):

GF-GA	GD	GF/GA	GF+GA	(GF/GA)*(GF+GA)
72-50	+22	1.440	112	161.28
60-40	+20	1.500	100	150
40-20	+20	2.000	60	120
45-30	+15	1.500	75	112.5
7- 4	+ 3	1.750	11	19.25
3- 1	+ 2	3.000	4	12

GD=GF-GA (goal difference). GS=GF+GA (goal sum).

Comments:
1. The guy with a GF/GA of 3.000 looks far too good compared to the others.
2. The lower numbers, the more extreme GF/GA. (It's a bit like pts per game. The fewer games played, the more extreme points per game.)

That's why I generally think one should be careful with using GF/GA.

Also:
3. Player ice time share during ES vary a lot between players. So does the amount time the player was not on the ice. No matter if one use real ice times, or take GF+GA, the differences are big.
4. Thus, when comparing "with" and "without", we would be comparing for example a GF/GA based on very low numbers, with a GF/GA based on very high numbers.

I'm not convinced yet regarding how good the win formula, and other formulas are at handling the things I mentioned above. Maybe they are great.

Originally Posted by Czech Your Math

I'm not sure ice time is so important. If a player is on ice for a much higher % of ES GF+GA than his % of his ice time, that's okay. If he's able to perform at or above the GF/GA ratio of the team as a whole, then the more volume the better for the team. If he's at a worse GF/GA level, then the high volume will negatively effect the player portion of the metric even more.

The above seems based a lot on GF/GA, and I think GF/GA can "lie".

Let's say we have a 2-3 result without player on ice (GF/GA=0.400).
Player on ice doing 5-3 will make his team win 7-6, despite GF/GA=1.667.
Player on ice doing 2-1will only make his team draw 4-4, despite GF/GA of 2.00.

As I said, maybe the win formula and other formulas have methods to guard for such contradictions.

Whether 60/50 or 50/40 is better may depend most on context (all other things being equal). On a bad team, the extra 10/10 might be helpful, while on a good team, it may be hurtful.

By themselves, I think both are equal. Context may make one look better, but I'm not sure GF/GA is the best way to determine that.
I may be wrong.

[Czech Your Math]

Originally Posted by plusandminus

If I was asked to rank the following seasonal ES stats for players, without paying any attention at all to context, I would rank them as follow (with a tie for 2nd best):

GD=GF-GA (goal difference). GS=GF+GA (goal sum).

Comments:
1. The guy with a GF/GA of 3.000 looks far too good compared to the others.
2. The lower numbers, the more extreme GF/GA. (It's a bit like pts per game. The fewer games played, the more extreme points per game.)

That's why I generally think one should be careful with using GF/GA.

The metric I've been tinkering with does not use any formula akin to (GF/GA)*(GF+GA). Neither does Overpass' adjusted plus-minus. Also, I agree that small sample sizes tend to lead to skewed results. That is why taking the best X seasons or career numbers are going to be more reliable for almost any metric.

In your 60/40 vs. 40/20 example, context is very important. First, it tells you in what environment the data was created. Second, it tells you what impact the player's performance is going to have. Since one player has 20/20 more than the other, if the R-Off of his team was > 1.0, then his performance did not help his team, while if it was < 1.0 it did help his team.

Originally Posted by plusandminus

Also:
3. Player ice time share during ES vary a lot between players. So does the amount time the player was not on the ice. No matter if one use real ice times, or take GF+GA, the differences are big.
4. Thus, when comparing "with" and "without", we would be comparing for example a GF/GA based on very low numbers, with a GF/GA based on very high numbers.

I'm not convinced yet regarding how good the win formula, and other formulas are at handling the things I mentioned above. Maybe they are great.

Again, that's why need multiple seasons to have any real solid data.

Maybe I should focus more or solely on the player's portion of the formula. I came up with the distribution of team's ES wins while thinking of some way to address Overpass' concern that players on great teams are hampered by the team's strong R-OFF. Honestly, getting credit for "just showing up" is not that great, although it's actually "playing a lot for great teams", and usually it's very good players who get lots of ice time over many years on great teams.

The player's portion is calculated by deducting his ES goals for/against from the team totals. The better the ratio and the more goals he was on ice for, the more impact it will have on the estimated win% differential, but it's more complex than multiplying the GF/GA ratio by the sum of ES GF + GA.

Originally Posted by plusandminus

The above seems based a lot on GF/GA, and I think GF/GA can "lie".

Let's say we have a 2-3 result without player on ice (GF/GA=0.400).
Player on ice doing 5-3 will make his team win 7-6, despite GF/GA=1.667.
Player on ice doing 2-1will only make his team draw 4-4, despite GF/GA of 2.00.

As I said, maybe the win formula and other formulas have methods to guard for such contradictions.

All stats can "lie", 76% of statisticians can attest to that.

I'm not using GF/GA ratio as an absolute metric. In referring to Overpass' adjusted plus-minus, I do think R-ON/R-OFF is a valuable metric. It tells you in % terms how much more effective the team was with that player on the ice than without him on the ice, and that's a valuable piece of information.

Originally Posted by plusandminus

By themselves, I think both are equal. Context may make one look better, but I'm not sure GF/GA is the best way to determine that.
I may be wrong.

They are similar, but not equal in most cases. An extra 10 GF and 10 GA is outstanding on the '75 Capitals and rather weak on a dynasty team.

[Czech Your Math]

Originally Posted by overpass

Notice that the first list has 9 of the top 10 with an R-OFF below 1. On the second list, 9 of the top 10 have an R-OFF above 1.

Thanks for posting those, I like seeing the "pure" list.

On second list, six players in top 50 with R-OFF < 1:

Bourque, Jagr, M. Howe, Lindros, Thornton, Selanne

Rather underrated group for the most part.

While Dionne, Forsberg and Lindros all helped linemates make the list, it's especially impressive to see Jagr help two separate centers (Francis, Nylander) make the list.

Perhaps I should stay with a "pure" list and just use estimated win% (player portion of ES value)? I think that would look similar to your second (100% adjusted) list.

[plusandminus]

Originally Posted by Czech Your Math

...

It seems I got a bit misunderstood when I included a (GF/GA)*(GF+GA) column. That column was just there as an example of what results it would show. It was the other columns that were the important ones. Below I have deleted that column.

GF-GA	GD	GF/GA	GF+GA
72-50	+22	1.440	112
60-40	+20	1.500	100
40-20	+20	2.000	60
45-30	+15	1.500	75
7- 4	+ 3	1.750	11
3- 1	+ 2	3.000	4

GD=GF-GA (goal difference). GS=GF+GA (goal sum).

Originally Posted by Czech Your Math

Also, I agree that small sample sizes tend to lead to skewed results. That is why taking the best X seasons or career numbers are going to be more reliable for almost any metric.

Yes. But has it been tested out how much more reliable?
I may try to examine that a bit more.

I also intend to look at game by game to see just what ES result the player had in the game ("with"), and what ES result the team had with him off ice ("without").
I know this can only be done for recent seasons, unless one wants to rely on estimated ES stats, but I still think it would be interesting to see what results it will produce. I'll get GP W D L GF-GA Pts for the players ("with") and for "without" them, and can then compare the two.

In your 60/40 vs. 40/20 example, context is very important. First, it tells you in what environment the data was created. Second, it tells you what impact the player's performance is going to have. Since one player has 20/20 more than the other, if the R-Off of his team was > 1.0, then his performance did not help his team, while if it was < 1.0 it did help his team.

I understand your example here. But I so far don't like GF/GA to be used, for reasons I have tried to put forward.

The player's portion is calculated by deducting his ES goals for/against from the team totals. The better the ratio and the more goals he was on ice for, the more impact it will have on the estimated win% differential

I understand that. That's what I call "with" and "without". And "with" may be unproportional compared to "without".

I will experiment a bit on my own to see how much it may affect the results.

All stats can "lie", 76% of statisticians can attest to that.

That was a funny statement.

They are similar, but not equal in most cases. An extra 10 GF and 10 GA is outstanding on the '75 Capitals and rather weak on a dynasty team.

Yes, I understand that.

[Czech Your Math]

Originally Posted by plusandminus

IYes. But has it been tested out how much more reliable?
I may try to examine that a bit more.

The "pure" part is the player portion. Taking the differential of the estimated pythagorean win% based on performance. What part of that do you disagree with? I understand the exponent is a bit difficult to pinpoint, but I don't think it makes much difference when comparing players, since all would be affected similarly.

The assignment of some portion of the team's success based is somewhat arbitrary and perhaps not necessary at all.

Originally Posted by plusandminus

I also intend to look at game by game to see just what ES result the player had in the game ("with"), and what ES result the team had with him off ice ("without").
I know this can only be done for recent seasons, unless one wants to rely on estimated ES stats, but I still think it would be interesting to see what results it will produce. I'll get GP W D L GF-GA Pts for the players ("with") and for "without" them, and can then compare the two.

Are you talking about ES data in games the player did not play? If you have that data, it would be interesting. However, if that's what you mean, why not just look at total results (record, GF, GA). I've calculated the actual vs. expected win% for a few players, and could also calculated expected win % using pythagorean based on GF/GA.

If you're bringing ice time into the picture, I don't consider that very important in comparison.

Originally Posted by plusandminus

I understand that. That's what I call "with" and "without". And "with" may be unproportional compared to "without".

I will experiment a bit on my own to see how much it may affect the results.

With and without, yes it's a fairly simple concept.
I don't understand what you mean by unproportional.

[plusandminus]

Below is an example to illustrate the principle of looking at every single game to determine ES contributions. Everything in the table is ES only. 2002-03 season.

x=without player. tot (or t)=with player+without player
W D L = won draw loss
Pts=Pts, win=2, draw=1, loss=0
I need to keep table names short. Ask if unclear.

I think only games where the player were on the ice on a goal (no matter what type of goal) are counted. The missing games are all 0-0 for the player.
(Better would be to include all the games the player participated in, but unfortunately that informations seems to be depleted because of a disk crash several years ago.)

Just an example.

Team	Pos	Name	Game	+/-	x+/-	Pts	xPts	totPts	Pts-x	tot-x	W	D	L	xW	xD	xL	tW	tD	tL
COL	C	PETER FORSBERG	68	55	1	97	61	91	36	30	40	17	11	21	19	28	39	13	16
COL	R	MILAN HEJDUK	73	49	-1	98	72	94	26	22	37	24	12	27	18	28	41	12	20
LA	R	ZIGMUND PALFFY	71	24	-26	86	53	71	33	18	30	26	15	17	19	35	25	21	25
DAL	R	JERE LEHTINEN	64	33	21	89	72	86	17	14	34	21	9	27	18	19	34	18	12
DAL	D	DERIAN HATCHER	75	27	27	90	85	99	5	14	36	18	21	32	21	22	40	19	16
TB	R	MARTIN ST. LOUIS	70	7	-19	78	54	67	24	13	29	20	21	16	22	32	25	17	28
COL	L	ALEX TANGUAY	69	38	10	88	76	89	12	13	35	18	16	31	14	24	38	13	18
DET	D	NICKLAS LIDSTROM	80	36	2	95	84	97	11	13	37	21	22	31	22	27	40	17	23
NJ	R	JAMIE LANGENBRUNNER	59	16	14	66	62	75	4	13	25	16	18	22	18	19	32	11	16

How to read the table:
Forsberg was +55 during ES, without him Colorado was +1 during ES. Forsberg was 40-11-17 (W-L-D) during ES. That would have resulted in 97 pts in 68 games. It seems he (and his units) helped getting Colorado 30 more "ES points" (91 instead of 61). Again, everything is ES only, and only games where player where on the ice on a goal is counted.

Sorted another way, it would look like:

Team	Pos	Name	Game	+/-	x+/-	Pts	xPts	totPts	Pts-x	tot-x	W	D	L	xW	xD	xL	totW	totD	totL
CBJ	R	DAVID VYBORNY	59	15	-63	71	32	37	39	5	24	23	12	9	14	36	14	9	36
COL	C	PETER FORSBERG	68	55	1	97	61	91	36	30	40	17	11	21	19	28	39	13	16
LA	R	ZIGMUND PALFFY	71	24	-26	86	53	71	33	18	30	26	15	17	19	35	25	21	25
CAR	D	SEAN HILL	66	5	-44	69	42	52	27	10	22	25	19	11	20	35	20	12	34
COL	R	MILAN HEJDUK	73	49	-1	98	72	94	26	22	37	24	12	27	18	28	41	12	20
MTL	D	ANDREI MARKOV	71	18	-23	88	62	66	26	4	32	24	15	20	22	29	25	16	30
TB	R	MARTIN ST. LOUIS	70	7	-19	78	54	67	24	13	29	20	21	16	22	32	25	17	28
CBJ	L	GEOFF SANDERSON	71	-1	-56	70	47	42	23	-5	20	30	21	13	21	37	14	14	43
LA	L	ALEXANDER FROLOV	58	16	-16	69	48	59	21	11	28	13	17	19	10	29	22	15	21
TB	C	VACLAV PROSPAL	70	7	-21	81	60	67	21	7	27	27	16	16	28	26	25	17	28

The difference between Vyborny on the ice, and Vyborny off the ice, is hugh. +15 with, -63 without. With him, 71 points in 59 games, without him only 32 points in 59 games. His contributions however only helped Columbus get 5 more points more than if he had been +/- 0 in every game. Same data and limitations as above.

Just an example. Just intended as something to add to the debate.
I know important stats are missing for older data. Again, just an example.

Pts, xPts and totPts can be used to tell us about pts per game:

Team	Pos	Name	Game	ES+/-	xES+/-	Pts	xPts	totPts	Pts-xPts	totPts-xPts
ATL	C	KAMIL PIROS	2	4	-2	2.000	0.000	1.500	2.000	1.500
WAS	D	MICHAEL FARRELL	1	1	-1	2.000	0.000	1.000	2.000	1.000
NAS	D	TOMAS KLOUCEK	1	1	-1	2.000	0.000	1.000	2.000	1.000
VAN	R	PAT KAVANAGH	2	2	-2	2.000	0.000	1.000	2.000	1.000

I personally find totals more useful.

Results does seem more useful if for example only taking those with minimum of 41 games:

Team	Pos	Name	Game	ES+/-	xES+/-	Pts	xPts	totPts	Pts-xPts	totPts-xPts
COL	C	PETER FORSBERG	68	55	1	1.426	0.897	1.338	0.529	0.441
COL	R	MILAN HEJDUK	73	49	-1	1.342	0.986	1.288	0.356	0.301
LA	R	ZIGMUND PALFFY	71	24	-26	1.211	0.746	1.000	0.465	0.254
NJ	R	JAMIE LANGENBRUNNER	59	16	14	1.119	1.051	1.271	0.068	0.220
DAL	R	JERE LEHTINEN	64	33	21	1.391	1.125	1.344	0.266	0.219
PHO	L	LADISLAV NAGY	62	24	-10	1.210	0.952	1.145	0.258	0.194
LA	L	ALEXANDER FROLOV	58	16	-16	1.190	0.828	1.017	0.362	0.190
COL	L	ALEX TANGUAY	69	38	10	1.275	1.101	1.290	0.174	0.188
DAL	D	DERIAN HATCHER	75	27	27	1.200	1.133	1.320	0.067	0.187
STL	R	ERIC BOGUNIECKI	43	11	-10	1.186	0.721	0.907	0.465	0.186

I prefer the totals (first two tables in this post) more than the averages.

Perhaps, though, "Pts as a total" might be wisely combined with "xPts per game".

Dividing, or dividing with square root, would give:

Team	Pos	Name	Game	ES+/-	xES+/-	Pts	PtsG	xPts	totPts	totPts2	totPts3
COL	C	PETER FORSBERG	68	55	1	97	1.426	0.897	1.338	108.13114	102.41445
LA	R	ZIGMUND PALFFY	71	24	-26	86	1.211	0.746	1.000	115.20754	99.538178
COL	R	MILAN HEJDUK	73	49	-1	98	1.342	0.986	1.288	99.361111	98.678208
CBJ	R	DAVID VYBORNY	59	15	-63	71	1.203	0.542	0.627	130.90625	96.407176
MTL	D	ANDREI MARKOV	71	18	-23	88	1.239	0.873	0.930	100.7741	94.170744
STL	D	AL MACINNIS	78	19	-3	92	1.179	0.962	1.038	95.680000	93.821959
DET	D	NICKLAS LIDSTROM	80	36	2	95	1.188	1.050	1.212	90.476190	92.710506
TB	C	BRAD RICHARDS	75	8	-17	82	1.093	0.840	0.973	97.619047	89.469334
STL	D	BARRET JACKMAN	74	17	-6	87	1.176	0.959	1.014	90.676056	88.819012
TB	R	MARTIN ST. LOUIS	70	7	-19	78	1.114	0.771	0.957	101.11111	88.806906
NYR	C	ERIC LINDROS	75	15	-3	87	1.160	0.960	1.053	90.625	88.794003
WAS	D	SERGEI GONCHAR	75	17	-5	86	1.147	0.960	1.040	89.583333	87.773382

TotPts2=Pts/(xPts/Games). TotPts3=Pts/sqrt(xPts/Games)

I'm not saying this last table above gives the best results, just that it uses another way of combining "with" and "without".

Maybe the results of the "win formula" and/or overpass' method would be fairly similar (or not).

I think this is an interesting way to look at things. I know one needs some data that are not available for "old" seasons, but still. And the results here may be compared to the other methods in this thread, to see how they correspond to each other.


Edit:
The above should basically work for all eras, no matter how high or low scoring. Only thing to adjust for would be GP per season (for teams, i.e. 82 nowadays, 80 during Gretzy's prime).
It should also take care of injuries. If a player misses a game, he simply gets 0 pts for that game. It should be very easy to aggregate different seasons to get career totals (if it wasn't for necessary data missing).

[seventieslord]

OK.
I've studied correlations between ES icetime and ESGF+ESGA and they don't necessarily correspond very well, perhaps especially regarding forwards. For example, during 2002-03, I guy like Kowalchuk (who had a reputation as an offensive minded player) had about 1.5 times more ESGF+ESGA played than the average player.
So here we thus have our first bias. ESGF=60 and ESGA=50, will give higher "ice time" than ESGF=50 and ESGA=40, even if real ice time is the same. ?

I'm surprised CYM didn't mention/ask this, but... did you mean he had about 1.5 times the "average" player? or the average of his own team? there are only so many minutes to go around, and I find it unlikely that he would be that far off of his own team's average. If you compare him to another team, sure, his icetime figures would look wonky. but that's not what a model that uses GF & GA to calculate icetime does.

Also, Kovalchuk is about the most extreme example of a "high risk, high reward" type player. Watching the guy play it is clear he is going to cause both more goals for and more goals against while on the ice. If there was ever a player who would be an outlier whose GF/GA figures might cause an estimation model to lie, it would be him. With that said, that's no reason to throw out such a model.

If I was asked to rank the following seasonal ES stats for players, without paying any attention at all to context, I would rank them as follow (with a tie for 2nd best):

GF-GA GD GF/GA GF+GA (GF/GA)*(GF+GA)
72-50 +22 1.440 112 161.28
60-40 +20 1.500 100 150
40-20 +20 2.000 60 120
45-30 +15 1.500 75 112.5
7- 4 + 3 1.750 11 19.25
3- 1 + 2 3.000 4 12
GD=GF-GA (goal difference). GS=GF+GA (goal sum).

Comments:
1. The guy with a GF/GA of 3.000 looks far too good compared to the others.
2. The lower numbers, the more extreme GF/GA. (It's a bit like pts per game. The fewer games played, the more extreme points per game.)

That's why I generally think one should be careful with using GF/GA.

I have an even more compelling reason to throw out the bottom player - any calculation done on him would be based on an obscenely low number of game situations. It's a poor sample size and is practically meaningless. Of course, if it got further in the season and he was 40-13, then we'd have something to talk about, and whether he was outperforming the 72-50 player would be a worthy question to ask.

[plusandminus]

Originally Posted by seventieslord

I'm surprised CYM didn't mention/ask this, but... did you mean he had about 1.5 times the "average" player? or the average of his own team? there are only so many minutes to go around, and I find it unlikely that he would be that far off of his own team's average. If you compare him to another team, sure, his icetime figures would look wonky. but that's not what a model that uses GF & GA to calculate icetime does.

Thanks for asking. I compare only with his team's totals.

Below are what it looks like. I have only included players with GF+GA >= 20. (Expect even larger differences for the other players.)
I think the raw data I assembled and corrected should be near 100 % correct.
The rightmost column shows GF+GA per 60 minutes. I have divided all those values by league average, to make it easier to compare.

Highest:

Team	Name	pos	ESTOI	EStoi%	ESGFGA%	diff	ESGFGA	normESGFGAper60min
CAR	BRUNO ST. JACQUES	D	297	0.081	0.138	0.057	35	1.577
CHI	BURKE HENRY	D	250	0.065	0.094	0.029	29	1.552
ATL	ILYA KOVALCHUK	F	1153	0.305	0.379	0.074	130	1.509
NYR	REM MURRAY	F	398	0.105	0.155	0.050	44	1.479
EDM	MIKE COMRIE	F	910	0.241	0.328	0.086	100	1.470
CHI	ERIC DAZE	F	722	0.188	0.257	0.070	79	1.464
LA	ADAM DEADMARSH	F	265	0.071	0.106	0.035	29	1.464
COL	PETER FORSBERG	F	1091	0.288	0.419	0.131	119	1.459
BOS	JOE THORNTON	F	1285	0.340	0.433	0.093	140	1.458
ATL	KIRILL SAFRONOV	D	414	0.110	0.131	0.022	45	1.454
TOR	ALEXANDER MOGILNY	F	943	0.258	0.348	0.090	102	1.447
TOR	KAREL PILAR	D	245	0.067	0.089	0.022	26	1.420
BOS	GLEN MURRAY	F	1400	0.371	0.458	0.087	148	1.414
ATL	DANY HEATLEY	F	1164	0.308	0.359	0.051	123	1.414
NYI	ROMAN HAMRLIK	D	1281	0.355	0.460	0.106	134	1.400
PIT	MARIO LEMIEUX	F	1082	0.286	0.387	0.101	113	1.397
MTL	NIKLAS SUNDSTROM	F	384	0.098	0.129	0.031	40	1.394
PHO	LANDON WILSON	F	328	0.089	0.125	0.036	34	1.387
SJ	NICHOLAS DIMITRAKOS	F	244	0.065	0.089	0.023	25	1.371
BOS	MIKE KNUBLE	F	1061	0.281	0.334	0.053	108	1.362

Lowest:

Team	Name	pos	ESTOI	EStoi%	ESGFGA%	diff	ESGFGA	normESGFGAper60min
WAS	BRIAN SUTHERBY	F	554	0.146	0.096	-0.05	27	0.652
PIT	IAN MORAN	F	1053	0.278	0.175	-0.10	51	0.648
CGY	STEVE BEGIN	F	436	0.118	0.078	-0.04	21	0.644
STL	TYSON NASH	F	532	0.142	0.087	-0.05	25	0.629
TOR	RICHARD JACKMAN	D	535	0.146	0.085	-0.06	25	0.625
FLA	IGOR ULANOV	D	823	0.215	0.146	-0.07	38	0.618
MIN	JASON MARSHALL	F	462	0.119	0.084	-0.04	21	0.608
TB	ALEXANDER SVITOV	F	511	0.132	0.083	-0.05	23	0.602
CAR	JAROSLAV SVOBODA	F	549	0.150	0.095	-0.05	24	0.585
TOR	PAUL HEALEY	F	458	0.125	0.068	-0.06	20	0.584
BUF	VACLAV VARADA	F	525	0.139	0.082	-0.06	22	0.561
CGY	STEVE MONTADOR	D	627	0.170	0.096	-0.07	26	0.555
STL	SHJON PODEIN	F	540	0.144	0.073	-0.07	21	0.520
COL	SERGE AUBIN	F	700	0.185	0.095	-0.09	27	0.516
PIT	IAN MORAN	D	1053	0.278	0.134	-0.14	39	0.496

Biggest differences between real ES%, and ES% estimated by GF+GA:

Team	Name	pos	ESTOI	EStoi%	ESGFGA%	diff	ESGFGA	normESGFGAper60min
PIT	IAN MORAN	D	1053	0.278	0.134	-0.14	39	0.496
COL	PETER FORSBERG	F	1091	0.288	0.419	0.131	119	1.459
NYI	MATTIAS TIMANDER	D	1159	0.321	0.213	-0.11	62	0.716
NYI	ROMAN HAMRLIK	D	1281	0.355	0.460	0.106	134	1.400
PIT	MARIO LEMIEUX	F	1082	0.286	0.387	0.101	113	1.397
PHO	OSSI VAANANEN	D	1056	0.287	0.192	-0.10	52	0.659
PIT	IAN MORAN	F	1053	0.278	0.175	-0.10	51	0.648
STL	PAVOL DEMITRA	F	1151	0.308	0.406	0.098	116	1.348
TB	VINCENT LECAVALIER	F	1134	0.293	0.390	0.097	108	1.274
BOS	JOE THORNTON	F	1285	0.340	0.433	0.093	140	1.458
WAS	SERGEI GONCHAR	D	1584	0.417	0.509	0.092	143	1.208
TOR	ALEXANDER MOGILNY	F	943	0.258	0.348	0.090	102	1.447
CGY	STEPHANE YELLE	F	1054	0.285	0.200	-0.09	54	0.686
COL	SERGE AUBIN	F	700	0.185	0.095	-0.09	27	0.516
BOS	GLEN MURRAY	F	1400	0.371	0.458	0.087	148	1.414
EDM	MIKE COMRIE	F	910	0.241	0.328	0.086	100	1.470
COL	MILAN HEJDUK	F	1219	0.322	0.405	0.083	115	1.262
TB	MARTIN ST. LOUIS	F	1123	0.290	0.372	0.082	103	1.227
FLA	OLLI JOKINEN	F	1168	0.305	0.385	0.080	100	1.146
BOS	SEAN O'DONNELL	D	1150	0.305	0.229	-0.08	74	0.861
VAN	TODD BERTUZZI	F	1223	0.334	0.413	0.079	117	1.280
DET	MATHIEU DANDENAULT	D	1203	0.314	0.392	0.078	122	1.357
PHO	PAUL MARA	D	1129	0.307	0.384	0.077	104	1.233
FLA	IVAN NOVOSELTSEV	F	960	0.250	0.327	0.077	85	1.185
MIN	MARIAN GABORIK	F	1078	0.278	0.355	0.077	89	1.105
ATL	ILYA KOVALCHUK	F	1153	0.305	0.379	0.074	130	1.509

This makes, in my opinion, GF+GA a bit unreliable when using it to determine ice time. Maybe there are steps involved in the calculations that takes care of that, so that it really doesn't matter that much. But I felt a need to point it out.

Also, Kovalchuk is about the most extreme example of a "high risk, high reward" type player. Watching the guy play it is clear he is going to cause both more goals for and more goals against while on the ice. If there was ever a player who would be an outlier whose GF/GA figures might cause an estimation model to lie, it would be him. With that said, that's no reason to throw out such a model.

Agree about Kowalchuk. But there were lots of other players like him. And plenty of the opposite kind too, i.e. players with "low risk getting scored on, but also low risk for their opponents to be scored on".

I have an even more compelling reason to throw out the bottom player - any calculation done on him would be based on an obscenely low number of game situations. It's a poor sample size and is practically meaningless. Of course, if it got further in the season and he was 40-13, then we'd have something to talk about, and whether he was outperforming the 72-50 player would be a worthy question to ask.

I agree. Unfortunately, the lower numbers the more "extreme" results. And the higher numbers, the less "extreme" results. But problem is that that rule continues to be true even for high numbers. The 40-13 case will still be slightly more vulnerable than the 72-50 case (I think, but that case it might be negligable).

Anyway, I don't like dividing GF by GA, because to me it only makes sense when
GF+GA is equally big for every player.
(But maybe there is something built in in overpass' method, that takes care of that.)

I look at it like this:
A: Player being 40-20 actually helped his team improve by +20.
B: Player being 30-15 actually helped his team improve by +15.
Both have the same GF/GA (2.0). But I think what matters is GF-GA.
Let's say B was 30-12 instead, raising his GF/GA to 2.5. That may make him look like a better player when looking at GF/GA. But he would have helped his team improve by +18.
During the whole season, I think a player's goal is to help their team improve by as many goals as possible, by getting as good GF-GA as possible.

[plusandminus]

I had to edit the part about (and with) the tables in my last post.
(I made a change before posting on the board, so that you would see if player played L, C, R, but that flawed the results, since some forwards played on more than one position, so I had to call all forwards F. If there is some guy playing both D and F, which is rare, the stats for that guy may be unreliable.)

[overpass]

plusminus, I'll try to address your concerns about the use of GF/GA ratios.

First, my adjusted plus-minus metric does not use the player's on-ice GF/GA ratio (R-ON) in the calculations. Only the difference is used, as in regular plus-minus.

The R-OFF ratio is used to calculate the team adjustment component, in conjunction with the sum of GA and GF. So the adjustment scales with the number of GF and GA, just as with regular plus-minus

I really don't think your concerns about the use of ratios apply to this metric. The ratios are useful for a quick overview of the on/off ice relationship of the player and team, but are incomplete without a measure of quantity. Adjusted plus-minus includes a measure of quantity.

[plusandminus]

Originally Posted by overpass

plusminus, I'll try to address your concerns about the use of GF/GA ratios.

First, my adjusted plus-minus metric does not use the player's on-ice GF/GA ratio (R-ON) in the calculations. Only the difference is used, as in regular plus-minus.

Thanks for clarifying.

The R-OFF ratio is used to calculate the team adjustment component, in conjunction with the sum of GA and GF. So the adjustment scales with the number of GF and GA, just as with regular plus-minus

I think I may understand. I think I perhaps need to try it out myself to be sure.

I really don't think your concerns about the use of ratios apply to this metric. The ratios are useful for a quick overview of the on/off ice relationship of the player and team, but are incomplete without a measure of quantity. Adjusted plus-minus includes a measure of quantity.

OK.

Sorry if I may have gotten things wrong. I think I need to re-produce myself what you are doing, to be sure I've understood things right.

[seventieslord]

Originally Posted by plusandminus

Thanks for asking. I compare only with his team's totals.

Below are what it looks like. I have only included players with GF+GA >= 20. (Expect even larger differences for the other players.)
I think the raw data I assembled and corrected should be near 100 % correct.
The rightmost column shows GF+GA per 60 minutes. I have divided all those values by league average, to make it easier to compare.

Highest:

Lowest:

Biggest differences between real ES%, and ES% estimated by GF+GA:


This makes, in my opinion, GF+GA a bit unreliable when using it to determine ice time. Maybe there are steps involved in the calculations that takes care of that, so that it really doesn't matter that much. But I felt a need to point it out.

To be honest, I think this reveals how effective a model that uses GF/GA can be.

they actaually do include an adjustment based on the line or pairing the player was on, because as you can see, goals are more frequent on a per-minute basis when the higher minute players are out there. So this will partially mitigate the effect that you're seeing, an effect that is pretty small to begin with.

I mean, if you want to try to approximate icetime across the board from 1967-onwards, be my guest. But can you improve on what exists enough that it is worth the time it would take?

As for Kovalchuk, considering two other Thrashers are in your top-20, he doesn't appear to really be that much of an outlier on his team. He just barely makes the bottom list that you provided, and only because it is based on a "raw" difference and not a percentage difference (if it was based on that, he would not be anywhere near the top)

I agree. Unfortunately, the lower numbers the more "extreme" results. And the higher numbers, the less "extreme" results. But problem is that that rule continues to be true even for high numbers. The 40-13 case will still be slightly more vulnerable than the 72-50 case (I think, but that case it might be negligable).

Anyway, I don't like dividing GF by GA, because to me it only makes sense when
GF+GA is equally big for every player.
(But maybe there is something built in in overpass' method, that takes care of that.)

I look at it like this:
A: Player being 40-20 actually helped his team improve by +20.
B: Player being 30-15 actually helped his team improve by +15.
Both have the same GF/GA (2.0). But I think what matters is GF-GA.
Let's say B was 30-12 instead, raising his GF/GA to 2.5. That may make him look like a better player when looking at GF/GA. But he would have helped his team improve by +18.
During the whole season, I think a player's goal is to help their team improve by as many goals as possible, by getting as good GF-GA as possible.

Keep in mind that generally when we talk about r-on and r-ff we are talking about very large sample sizes - seasons at the very least, and generally blocks of seasons, or careers. Like you, I don't see any value in the micro aspect, these 10-20-game segments and single game scenarios you are providing.

overpass, as usual, did a much better job than I could have done, fuddling my way through descriptions of statistics in "normal people" words and terms.

[plusandminus]

Originally Posted by overpass

Glossary of Terms:

SFrac: Season Fraction. 1.00 is a full season. I prefer it to games played because it gives a 48 game season, a 74 game season, an 80 game season or an 82 game season the same weight.
$ESGF: Even-strength goals for, normalized to a 200 ESG scoring environment and with estimated SH goals removed.
$ESGA: Even-strength goals against, normalized to a 200 ESG scoring environment and with estimated SH goals removed.
R-ON: Even strength GF/GA ratio when the player is on the ice.
R-OFF: Even-strength GF/GA ratio when the player is off the ice.
XEV+/-: Expected even-strength plus-minus, which is an estimate of the plus-minus that an average player would post with the same teammates. The calculation is described above.
EV+/-: Even –strength plus-minus, which is simply plus-minus with estimated shorthanded goals removed and normalized to a 200 ESG environment.
AdjEV+/-: Adjusted even-strength plus-minus, which is even-strength plus-minus minus expected even-strength plus-minus. This is the final number.
The following three stats evaluate special teams play and are not related to adjusted plus-minus. I’m including them in the table for a quick reference to the player’s contributions outside of even-strength play.
PP% : The % of the team’s power play goals for that the player was on the ice for.
SH%: The % of the team’s power play goals against that the player was on the ice for.
$PPP/G: Power play points per game, normalized to a 70 PPG environment and with pre-1988 PP assists estimated.

Results
Here are the top 60 in career adjusted even-strength plus-minus, as well as the players in the HOH Top 100 and several others who were strongly considered for voting.

Sorry, but I'm still a bit confused.
The text says $ESGF and $ESGA are adjusted to 200 ESG scoring environment.
The $ prefix makes me think "adjusted to 200 ESG scoring environment".
The text says EV+/- is also adjusted to 200 ESG scoring environment. ?

If it had been named "$EV+/-", I would have been pretty sure it's $ESGF-$ESGA, because $ tells me that it's "adjusted to 200 ESG scoring environment".
My question is... Is EV+/- = $ESGF-$ESGA ?

The text also says:

To calculate the adjusted plus-minus, I take the player’s on-ice total goals for and against as given. I calculate an expected plus-minus for the player, based on his team’s off-ice performance.

"As given", does that mean they are not "adjusted to 200 ESG scoring environment"?


Example, using made up seasonal stats for one player and his team.

Everything is ES only.
"without" or "w" means when player was off the ice.
GD (goal difference) = GF-GA.

Lge aver ESGF per team

teamGD

teamGF

teamGA

playerGD

playerGF

playerGA

withoutGD

withoutGF

withoutGA

pGF/pGA

wGF/wGA

100

+20

60

40

+10

24

14

+10

36

26

1.714

1.385

Lge aver ESGF per team

$teamGD

$teamGF

$teamGA

$playerGD

$playerGF

$playerGA

$withoutGD

$withoutGF

$withoutGA

pGF/pGA

wGF/wGA

200

+40

120

80

+20

48

28

+20

72

52

1.714

1.385

Are the $ values above true? Is that how the ""adjusted to 200 ESG scoring environment" values are calculated?

If the above is correct, then how do we use the different variables to calculate the missing columns?
R-On? R-Off?


Can someone write down the formula's for calculating the values, using the variables of the tables above?

And can we write "rOn" and "rOff" instead of "R-On" and "R-Off", to make it easier to understand the formulas? ("-" can otherwise be interpreted as a minus sign. But we don't take R minus On, and R minus Off, right? If, I'm even more confused.)

The expected plus-minus is calculated using the off-ice performance regressed partially to even, as a player should be expected to play somewhat better than a set of bad teammates or worse than a set of good teammates.

I understand the regression thing. But I'm confused about other things, including what exactly to regress (I guess it's "wGF/wGA"). ? Is rOff = "wGF/wGA" regressed to even?

I then calculate an actual plus-minus, which differs from official NHL plus-minus in that it is normalized to a scoring environment of 200 even-strength goal per season and does not include shorthanded goals. I subtract the “expected plus-minus” from the “actual plus-minus” to generate an adjusted plus-minus number.

I think I need an example to understand.

[overpass]

Originally Posted by plusandminus

Sorry, but I'm still a bit confused.
The text says $ESGF and $ESGA are adjusted to 200 ESG scoring environment.
The $ prefix makes me think "adjusted to 200 ESG scoring environment".
The text says EV+/- is also adjusted to 200 ESG scoring environment. ?

If it had been named "$EV+/-", I would have been pretty sure it's $ESGF-$ESGA, because $ tells me that it's "adjusted to 200 ESG scoring environment".
My question is... Is EV+/- = $ESGF-$ESGA ?


The text also says:


"As given", does that mean they are not "adjusted to 200 ESG scoring environment"?

All numbers are adjusted to the 200 ESG per team-season scoring environment. Yes, EV+/- is simply $ESGF-$ESGA. "As given" still means scoring-adjusted numbers.

Originally Posted by plusandminus

Example, using made up seasonal stats for one player and his team.

Everything is ES only.
"without" or "w" means when player was off the ice.
GD (goal difference) = GF-GA.



Are the $ values above true? Is that how the ""adjusted to 200 ESG scoring environment" values are calculated?

All correct. I don't scoring-level adjust the off-ice numbers, since I only use them to calculate a ratio, but if you did want to adjust for scoring level that would be correct.

Originally Posted by plusandminus

If the above is correct, then how do we use the different variables to calculate the missing columns?
R-On? R-Off?

Can someone write down the formula's for calculating the values, using the variables of the tables above?

And can we write "rOn" and "rOff" instead of "R-On" and "R-Off", to make it easier to understand the formulas? ("-" can otherwise be interpreted as a minus sign. But we don't take R minus On, and R minus Off, right? If, I'm even more confused.)

R-ON = $ESGF/$ESGA. For single seasons, multiple seasons, or careers.

R-OFF = (TeamESGF-PlayerESGF)/(TeamESGA-PlayerESGA) for a single season. For multiple seasons, take the sum of the XEV+/-, $ESGF, and $ESGA, and calculate by turning around the formula for XEV+/-

XEV+/- = ($ESGF+$ESGA)/(1+R-OFF^0.65)*R-OFF^0.65 - ($ESGF+$ESGA)/(1+R-OFF^0.65)

EV+/- = $ESGF - $ESGA

AEV+/- = (EV+/-) - (XEV+/-)

Originally Posted by plusandminus

I understand the regression thing. But I'm confused about other things, including what exactly to regress (I guess it's "wGF/wGA"). ? Is rOff = "wGF/wGA" regressed to even?

I think I need an example to understand.

Adjusted plus-minus applies the regression to the ratio rOff in the XEV calculation. It's simply rOff^0.65, which regresses rOff toward 1. If I understand your terms correctly, wGF/wGA = rOff as I present it. I have never presented the regressed rOff value alone.

Full example:

Player X has 60 ESGF, 45 ESGA. His team has 140 ESGF, 155 ESGA. League scoring level is 150 ESGA/team.

$ESGF = 60*200/150 = 80
$ESGA = 45*200/150 = 60

rOn = 60/45 = 1.33
rOff = (140-60)/(155-45) = 80/110 = 0.73

XEV+/- = (80+60)*(0.73^0.65)/(1+0.73^0.65) - (80+60)/(1+0.73^0.65)
= 140*0.81/1.81 - 140/1.81
= 63 - 77
= -14

EV+/- = 80 - 60 = 20

AEV+/- = 20 - 14 = 34

[plusandminus]

Originally Posted by overpass

(Formulas.)

OK, I post my results for 2002-03 season using overpass' formulas. I have not adjusted to era, since I only look at one season. I used .65 as the "regress to even" number. Let me know if numbers are wrong. (Please don't overfocus on the number of decimals shown. I want them there for verifying purposes.)

Lowest expected +/-:

Team	Pos	Name	TOIshare	+/-	+/- without player	rOn	rOff	exp+/-	adj+/-
PIT	F	MARIO LEMIEUX	0.2856	-15	-49	0.7656	0.5702	-20.4062	5.4062
CBJ	D	LUKE RICHARDSON	0.4065	-26	-41	0.6709	0.6204	-20.3193	-5.6806
CBJ	D	JAROSLAV SPACEK	0.3544	-19	-48	0.7206	0.5966	-19.4554	0.4554
ATL	F	DANY HEATLEY	0.3079	-1	-50	0.9839	0.6296	-18.3552	17.3552
PIT	F	ALEXEI KOVALEV	0.2415	-4	-60	0.9149	0.5420	-17.6831	13.6831
PIT	D	DICK TARNSTROM	0.2631	-7	-57	0.8600	0.5547	-17.5984	10.5984
CBJ	F	DAVID VYBORNY	0.2859	15	-82	1.5172	0.4810	-17.0432	32.0432
CBJ	F	GEOFF SANDERSON	0.2760	-1	-66	0.9767	0.5417	-16.7163	15.7163
PIT	F	MARTIN STRAKA	0.2428	-6	-58	0.8723	0.5573	-16.5250	10.5250
CAR	D	SEAN HILL	0.3440	5	-54	1.1471	0.5385	-14.4917	19.4917

(Comment: Dominated by Pittsburgh and Columbus players.)

Highest expected +/-:

Team	Pos	Name	TOIshare	+/-	+/- without player	rOn	rOff	exp+/-	adj+/-
COL	F	JOE SAKIC	0.2269	9	45	1.2500	1.5696	11.7839	-2.7839
PHI	D	ERIC WEINRICH	0.3580	15	30	1.3750	1.4688	11.8073	3.1926
PHI	D	KIM JOHNSSON	0.3605	16	29	1.3902	1.4603	11.9996	4.0004
DAL	D	RICHARD MATVICHUK	0.2767	-5	57	0.8611	1.8028	12.6784	-17.6784
COL	D	ROB BLAKE	0.3652	19	35	1.4524	1.4795	13.0408	5.9591
DAL	D	DERIAN HATCHER	0.4141	27	25	1.5870	1.4098	13.2289	13.7710
VAN	D	BRENT SOPEL	0.3782	-10	35	0.8246	1.4861	13.3167	-23.3168
COL	D	ADAM FOOTE	0.3842	27	27	1.5510	1.4091	13.8747	13.1252
DAL	D	SERGEI ZUBOV	0.3819	17	35	1.4048	1.5385	14.0487	2.9512
COL	F	STEVEN REINPRECHT	0.2496	-9	63	0.8125	1.9403	18.4572	-27.4572
COL	D	GREG DE VRIES	0.4051	16	38	1.2759	1.6667	21.7152	-5.7152

Comment: Some Colorado, some Philadelphia, some Dallas.


Best adjusted +/-:

Team	Pos	Name	TOIshare	+/-	+/- without player	rOn	rOff	exp+/-	adj+/-
COL	F	PETER FORSBERG	0.2885	55	-1	2.7188	0.9880	-0.4688	55.4688
COL	F	MILAN HEJDUK	0.3223	49	5	2.4848	1.0610	2.2119	46.7881
DET	D	NICKLAS LIDSTROM	0.3878	36	1	1.7500	1.0112	0.4793	35.5207
LA	F	ZIGMUND PALFFY	0.3235	24	-28	1.6316	0.7228	-10.5125	34.5125
PHO	F	LADISLAV NAGY	0.3002	25	-26	1.8929	0.7593	-7.2309	32.2309
COL	F	ALEX TANGUAY	0.3104	38	16	2.1875	1.1928	5.8372	32.1627
CBJ	F	DAVID VYBORNY	0.2859	15	-82	1.5172	0.4810	-17.0432	32.0432
DAL	F	JERE LEHTINEN	0.2803	33	19	2.4348	1.2262	5.2278	27.7722
STL	F	ERIC BOGUNIECKI	0.2453	24	-10	1.8889	0.9083	-2.4386	26.4385
BOS	F	MIKE KNUBLE	0.2811	22	-11	1.5116	0.9027	-3.5934	25.5934
PHO	F	DAYMOND LANGKOW	0.3225	19	-20	1.5588	0.8039	-6.1608	25.1607
MTL	D	ANDREI MARKOV	0.3408	18	-26	1.4865	0.7869	-7.1518	25.1517

Comment: Similar to the method I used and posted yesterday (post #184). Forsberg atop here too. Hejduk higher, as is Tanguay, which I think is not so good. Lidstrom higher. Vyborny lower, I think he should be higher, as I think +15 with vs -82 "without" is a huge difference. Palffy, Lehtinen, Boguniecki on my list too.
Martin St Louis, who was high on my list(s), is missing here. He's 25th here. Perhaps it has to do with how he distributed his ESGF and ESGF game by game.


Best adjusted (if not "regressing R-Off to even"):

Team	Pos	Name	TOIshare	+/-	+/- without player	rOn	rOff	exp+/-	adj+/-
COL	F	PETER FORSBERG	0.2885	55	-1	2.7188	0.9880	-0.7212	55.7212
COL	F	MILAN HEJDUK	0.3223	49	5	2.4848	1.0610	3.4023	45.5976
CBJ	F	DAVID VYBORNY	0.2859	15	-82	1.5172	0.4810	-25.58120	40.5812
LA	F	ZIGMUND PALFFY	0.3235	24	-28	1.6316	0.7228	-16.0919	40.0919
PHO	F	LADISLAV NAGY	0.3002	25	-26	1.8929	0.7593	-11.0842	36.0842
DET	D	NICKLAS LIDSTROM	0.3878	36	1	1.7500	1.0112	0.7374	35.26257
COL	F	ALEX TANGUAY	0.3104	38	16	2.1875	1.1928	8.9670	29.0330
MTL	D	ANDREI MARKOV	0.3408	18	-26	1.4865	0.7869	-10.9724	28.9724
NYI	D	ROMAN HAMRLIK	0.3548	16	-15	1.2712	0.8256	-12.8025	28.8025
PHO	F	DAYMOND LANGKOW	0.3225	19	-20	1.5588	0.8039	-9.4565	28.4565
STL	F	ERIC BOGUNIECKI	0.2453	24	-10	1.8889	0.9083	-3.7500	27.7500
BOS	F	MIKE KNUBLE	0.2811	22	-11	1.5116	0.9027	-5.5256	27.5255
ATL	F	DANY HEATLEY	0.3079	-1	-50	0.9839	0.6296	-27.9545	26.9545
CAR	D	SEAN HILL	0.3440	5	-54	1.1471	0.5385	-21.9000	26.9000
TB	D	DAN BOYLE	0.3600	13	-22	1.2889	0.7755	-13.0229	26.0229

Comment: At first glance it looks "better", in that linemates appear a bit more separated. But experience has shown me that regressing "when player off the ice" to even usually gives better results. (By the way, 6 Europeans atop.)



Although I like to compare the results to "my" mentioned method (see post #184), my method is not perfect. I need to find a way to include games where the player played but wasn't on the ice on any ES goals either way. Plus think more about it. Good things with it are that it doesn't need to pay attention to ice time, and doesn't have to adjust to "different GPG in different eras".

Now that I may know how overpass have done the calculations, and have been able to (hopefully) reproduce the results, my impression is that overpass' technique gives good results considered how relatively simple it is.
By simple, I mean that it only depends on ESGF and ESGA (and adjustment for ESGF per season), and that basically the only "tricky" part was the formula to calculate the expected +/-. That formula seem to produce interestingly good results.
(I did however not understand how it was done until it was written down in detail.)

The things I "don't like" about it, may be mostly present when looking at single seasons. When aggregating seasons, it might become alright (as players will play on other lines, on teams differently strong, etc). That is also what overpass have said.

Thanks overpass for explaining more in detail. It currently seems as if most of my "suspicions" regarding your method may have been a bit overstated.

Hopefully I will be able to reproduce czechyourmath's method too... eventually.

[plusandminus]

Originally Posted by Czech Your Math

I have an alternative that might be fairer to players on great teams without using somewhat arbitrary regressions to the mean. It's not exactly comparable to adjusted plus-minus, but it uses much of the same methodology. For lack of a better term, I might call it "even strength value". It has two primary components:

1. Player's share of team success at even strength
2. Player's marginal (additional) success at even strength

Once you calculate each component, simply add them together.

Player's share of team success at ES is calculated as:

82 * (Team Exp. ES Win %) * (Player's ESGF + ESGA) / (Team's ESGF + ESGA)

where Team Expected ES Win % = (ESGF)^N / (ESGF^N + ESGA^N)

this is the pythagorean win formula; N = 2 (or another number if supported by data)

Player's marginal contribution to team success is calculated as follows:

Subtract the player's ESGF and ESGA from the team's totals.
Recalculate the ES Win % from the new numbers (this is ES Win % without player).
Subtract Team Exp. ES Win % from ES Win % without player.
Multiply the difference in Win % by 82 to yield player's marginal contribution.

Then add player's share of team success ES and player's marginal contribution to team success at ES to get "ES Value" (whatever is proper term). The results are in the same ballpark as plus-minus.

Is the above still true? Or did you come up with changes to improve further?

Anyway, I tried to calculate according to how I interpreted the instructions, and below are my results for the 2002-03 season.
Columns starting with "x" is "without" player, i.e. teamStat - playerStat. GS = goal sum (GF+GA).
I haven't multiplied anything by 82. Should be OK anyway, right?

You are welcome to check my math for errors and/or misunderstandings.

Team	Pos	Name	GF	GA	GS	xGS	xGF	xGA	+/-	x+/-	playerWin	xWin	teamWin	pmargCont	Win
COL	F	PETER FORSBERG	87	32	119	109	82	83	55	-1	0.262331	0.286398	0.683506	0.419013	0.681344
COL	F	MILAN HEJDUK	82	33	115	103	87	82	49	5	0.247891	0.276771	0.683506	0.404928	0.652819
DAL	D	DERIAN HATCHER	73	46	119	79	86	61	27	25	0.204417	0.307920	0.688292	0.447368	0.651785
COL	D	ADAM FOOTE	76	49	125	81	93	66	27	27	0.194943	0.300838	0.683506	0.440139	0.635082
COL	D	GREG DE VRIES	74	58	132	70	95	57	16	38	0.168469	0.317685	0.683506	0.464787	0.633256
COL	F	ALEX TANGUAY	70	32	102	92	99	83	38	16	0.221417	0.245484	0.683506	0.359154	0.580571
WAS	D	SERGEI GONCHAR	80	63	143	32	68	70	17	-2	0.063001	0.281536	0.553229	0.508895	0.571896
DET	D	NICKLAS LIDSTROM	84	48	132	73	90	89	36	1	0.144899	0.262009	0.617310	0.424436	0.569335
DAL	D	PHILIPPE BOUCHER	60	38	98	74	99	69	22	30	0.191479	0.253581	0.688292	0.368420	0.559899
DAL	D	SERGEI ZUBOV	59	42	101	69	100	65	17	35	0.178541	0.261343	0.688292	0.379697	0.558238
PHI	D	KIM JOHNSSON	57	41	98	61	92	63	16	29	0.162122	0.260459	0.672411	0.387350	0.549472
COL	D	ROB BLAKE	61	42	103	73	108	73	19	35	0.175689	0.247891	0.683506	0.362675	0.538364
PHI	D	ERIC WEINRICH	55	40	95	60	94	64	15	30	0.159465	0.252486	0.672411	0.375493	0.534958
DAL	F	MIKE MODANO	55	30	85	77	104	77	25	27	0.199242	0.219942	0.688292	0.319547	0.518789
DAL	F	JERE LEHTINEN	56	23	79	85	103	84	33	19	0.219942	0.204417	0.688292	0.296991	0.516933
PHI	D	ERIC DESJARDINS	54	29	83	70	95	75	25	20	0.186042	0.220593	0.672411	0.328062	0.514104
OTT	D	WADE REDDEN	62	44	106	60	101	77	18	24	0.136208	0.240635	0.644722	0.373238	0.509446
BOS	F	GLEN MURRAY	83	65	148	29	84	91	18	-7	0.047945	0.244688	0.534016	0.458203	0.506148
DET	D	MATHIEU DANDENAULT	70	52	122	55	104	85	18	19	0.109170	0.242160	0.617310	0.392282	0.501452
COL	D	DEREK MORRIS	55	34	89	75	114	81	21	33	0.180503	0.214197	0.683506	0.313379	0.493882

Forsberg atop here too. But I think there are far too much Colorado dominance at the top. Basically, it seems to list the players with highest ESGF+ESGA on the teams.
We see some familiar names from the other two methods, like Hejduk, Lehtinen, Tanguay, but also many new.

Have I missed something in my calculations?

While I think "my" method and overpass' method ended up with quite similar results, I think this method gives the most "different" results. That does not necessarily have to bad, but looking at the table it does not seem to care much about "how good" the player played. Guys like Foote and DeVries don't look special +/- wise when comparing them to how Colorado did when they were off the ice.
The list is very much dominated by defencemen.
The only forwards on the list are: Forsberg-Hejduk-Tanguay, Modano-Lethinen and G.Murray. Among forwards will soon follow Bertuzzi-Naslund-Morrison (in between them are a few other forwards), all close to each other.

Shoudn't there be some consideration paid to GF-GA, or GF/(GF+GA), or even GF/GA?
Maybe I've missed something?

Edit: By the way, some guys ended up with slightly negative numbers. Is that OK?
Worst:

Team	Pos	Name	GF	GA	GS	xGS	xGF	xGA	+/-	x+/-	playerWin	xWin	teamWin	pmargCont	Win
CBJ	F	KENT MCDONELL	0	1	1	-68	120	186	-1	-66	-0.064606	0.000950	0.291681	0.003256	-0.061350
CBJ	F	MATHIEU DARCHE	0	1	1	-68	120	186	-1	-66	-0.064606	0.000950	0.291681	0.003256	-0.061350

Edit:

I experimented a bit more.
teamWin = team win formula
xWin = appplying win formula but with "without" stats instead of team stats. ("Without"=team-player.)
Then the differences between the two.
playerWin = applying win formula but with player stats instead of team stats. Gives strange results for players with low numbers.
The results below looks far "better" than the ones above.
One thing I suspect is still missing, is to add something more to it. I think we know below much "difference" the player did, but I think there might be something more added? (Perhaps something to do with (playerGF+playerGA) / (teamGF+teamGA)?? I'm very tired now, by will continue probably tomorrow.

Team	Pos	Name	GF	GA	GS	xGS	xGF	xGA	+/-	x+/-	teamWin	xWin	Diff	Diff%	playerWin
COL	F	PETER FORSBERG	87	32	119	109	82	83	55	-1	0.683506	0.493939	0.189567	1.383786	0.880833
COL	F	MILAN HEJDUK	82	33	115	103	87	82	49	5	0.683506	0.529559	0.153947	1.290707	0.860616
LA	F	ZIGMUND PALFFY	62	38	100	20	73	101	24	-28	0.485404	0.343142	0.142262	1.414586	0.726928
PHO	F	LADISLAV NAGY	53	28	81	24	82	108	25	-26	0.496310	0.365673	0.130637	1.357250	0.781797
DET	D	NICKLAS LIDSTROM	84	48	132	73	90	89	36	1	0.617310	0.505586	0.111724	1.220979	0.753846
CBJ	F	DAVID VYBORNY	44	29	73	-52	76	158	15	-82	0.291681	0.187898	0.103783	1.552336	0.697155
PHO	F	DAYMOND LANGKOW	53	34	87	18	82	102	19	-20	0.496310	0.392573	0.103737	1.264248	0.708448
NAS	D	JASON YORK	49	35	84	4	72	96	14	-24	0.460379	0.360000	0.100379	1.278830	0.662162
NYI	D	ROMAN HAMRLIK	75	59	134	17	71	86	16	-15	0.503436	0.405322	0.098114	1.242064	0.617724
STL	F	ERIC BOGUNIECKI	51	27	78	38	99	109	24	-10	0.548834	0.452033	0.096801	1.214145	0.781081
COL	F	ALEX TANGUAY	70	32	102	92	99	83	38	16	0.683506	0.587237	0.096269	1.163935	0.827143
TB	D	DAN BOYLE	58	45	103	4	76	98	13	-22	0.467543	0.375552	0.091991	1.244948	0.624234
MTL	D	ANDREI MARKOV	55	37	92	10	96	122	18	-26	0.474210	0.382406	0.091804	1.240069	0.688438
MIN	F	PASCAL DUPUIS	46	30	76	17	80	95	16	-15	0.503984	0.414910	0.089074	1.214682	0.701591
CAR	D	SEAN HILL	39	34	73	-44	63	117	5	-54	0.313326	0.224770	0.088556	1.393984	0.568173
LA	F	ALEXANDER FROLOV	49	33	82	12	86	106	16	-20	0.485404	0.396951	0.088453	1.222831	0.687965
DAL	F	JERE LEHTINEN	56	23	79	85	103	84	33	19	0.688292	0.600566	0.087726	1.146072	0.855661
BOS	F	MIKE KNUBLE	65	43	108	33	102	113	22	-11	0.534016	0.448970	0.085046	1.189424	0.695587
TB	F	MARTIN ST. LOUIS	57	46	103	2	77	97	11	-20	0.467543	0.386556	0.080987	1.209509	0.605591
STL	D	AL MACINNIS	69	50	119	33	81	86	19	-5	0.548834	0.470086	0.078748	1.167518	0.655694

Results looks much more similar to the other methods (those "by overpass" and "by me").

Dividing instead gives different results, see below. But those above are "better", right? ?

Team	Pos	Name	GF	GA	GS	xGS	xGF	xGA	+/-	x+/-	teamWin	xWin	Diff	Diff%	playerWin
CBJ	F	DAVID VYBORNY	44	29	73	-52	76	158	15	-82	0.291681	0.187898	0.103783	1.552336	0.697155
LA	F	ZIGMUND PALFFY	62	38	100	20	73	101	24	-28	0.485404	0.343142	0.142262	1.414586	0.726928
CAR	D	SEAN HILL	39	34	73	-44	63	117	5	-54	0.313326	0.224770	0.088556	1.393984	0.568173
COL	F	PETER FORSBERG	87	32	119	109	82	83	55	-1	0.683506	0.493939	0.189567	1.383786	0.880833
PHO	F	LADISLAV NAGY	53	28	81	24	82	108	25	-26	0.496310	0.365673	0.130637	1.357250	0.781797
COL	F	MILAN HEJDUK	82	33	115	103	87	82	49	5	0.683506	0.529559	0.153947	1.290707	0.860616
CBJ	F	GEOFF SANDERSON	42	43	85	-68	78	144	-1	-66	0.291681	0.226845	0.064836	1.285816	0.488236
PIT	F	ALEXEI KOVALEV	43	47	90	-68	71	131	-4	-60	0.290868	0.227051	0.063817	1.281069	0.455643
NAS	D	JASON YORK	49	35	84	4	72	96	14	-24	0.460379	0.360000	0.100379	1.278830	0.662162
FLA	D	ANDREAS LILJA	36	29	65	-31	75	120	7	-45	0.356902	0.280898	0.076004	1.270575	0.606457
PHO	F	DAYMOND LANGKOW	53	34	87	18	82	102	19	-20	0.496310	0.392573	0.103737	1.264248	0.708448
ATL	F	DANY HEATLEY	61	62	123	-52	85	135	-1	-50	0.354528	0.283889	0.070639	1.248826	0.491870

[plusandminus]

I added text to the previous, perhaps confused, post. Not sure if it became less or more confused. Very tired now.

[OrrNumber4]

This is just a fantastic thread. Thought I would bump it up so other's could see it. Should be pinned.

[Sixbladeknife]

This is amazing stuff, very insightful! Do you have / are you willing to share the year-to-year spreadsheets? A friend of mine and I are trying to rank the best players since 1990, and this information would be very useful.

[overpass]

Originally Posted by Sixbladeknife

This is amazing stuff, very insightful! Do you have / are you willing to share the year-to-year spreadsheets? A friend of mine and I are trying to rank the best players since 1990, and this information would be very useful.

Just posted it here.

http://hfboards.hockeysfuture.com/sh....php?t=1270041

I don't fully endorse the single season plus-minus ratings as significant. There's a lot of random variation still at the season level. But I do find it useful for looking at groups of seasons like, say, Gretzky's Edmonton years compared to his LA years. Or for looking peak seasons (over several years) for any player.