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08-24-2011, 04:28 PM
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Originally Posted by Czech Your Math View Post
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.

COLFPETER FORSBERG 8732119109828355-10.2623310.2863980.6835060.4190130.681344
COLFMILAN HEJDUK 823311510387824950.2478910.2767710.6835060.4049280.652819
DALDDERIAN HATCHER 734611979866127250.2044170.3079200.6882920.4473680.651785
COLDADAM FOOTE 764912581936627270.1949430.3008380.6835060.4401390.635082
COLDGREG DE VRIES 745813270955716380.1684690.3176850.6835060.4647870.633256
COLFALEX TANGUAY 703210292998338160.2214170.2454840.6835060.3591540.580571
WASDSERGEI GONCHAR 806314332687017-20.0630010.2815360.5532290.5088950.571896
DETDNICKLAS LIDSTROM 84481327390893610.1448990.2620090.6173100.4244360.569335
DALDPHILIPPE BOUCHER 60389874996922300.1914790.2535810.6882920.3684200.559899
DALDSERGEI ZUBOV 5942101691006517350.1785410.2613430.6882920.3796970.558238
PHIDKIM JOHNSSON 57419861926316290.1621220.2604590.6724110.3873500.549472
COLDROB BLAKE 6142103731087319350.1756890.2478910.6835060.3626750.538364
PHIDERIC WEINRICH 55409560946415300.1594650.2524860.6724110.3754930.534958
DALFMIKE MODANO 553085771047725270.1992420.2199420.6882920.3195470.518789
DALFJERE LEHTINEN 562379851038433190.2199420.2044170.6882920.2969910.516933
PHIDERIC DESJARDINS 54298370957525200.1860420.2205930.6724110.3280620.514104
OTTDWADE REDDEN 6244106601017718240.1362080.2406350.6447220.3732380.509446
BOSFGLEN MURRAY 836514829849118-70.0479450.2446880.5340160.4582030.506148
DETDMATHIEU DANDENAULT 7052122551048518190.1091700.2421600.6173100.3922820.501452
COLDDEREK MORRIS 553489751148121330.1805030.2141970.6835060.3133790.493882

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?
CBJFKENT MCDONELL 011-68120186-1-66-0.0646060.0009500.2916810.003256-0.061350
CBJFMATHIEU DARCHE 011-68120186-1-66-0.0646060.0009500.2916810.003256-0.061350


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.

COLFPETER FORSBERG 8732119109828355-10.6835060.4939390.1895671.3837860.880833
COLFMILAN HEJDUK 823311510387824950.6835060.5295590.1539471.2907070.860616
LA FZIGMUND PALFFY 6238100207310124-280.4854040.3431420.1422621.4145860.726928
PHOFLADISLAV NAGY 532881248210825-260.4963100.3656730.1306371.3572500.781797
DETDNICKLAS LIDSTROM 84481327390893610.6173100.5055860.1117241.2209790.753846
CBJFDAVID VYBORNY 442973-527615815-820.2916810.1878980.1037831.5523360.697155
PHOFDAYMOND LANGKOW 533487188210219-200.4963100.3925730.1037371.2642480.708448
NASDJASON YORK 4935844729614-240.4603790.3600000.1003791.2788300.662162
NYIDROMAN HAMRLIK 755913417718616-150.5034360.4053220.0981141.2420640.617724
STLFERIC BOGUNIECKI 512778389910924-100.5488340.4520330.0968011.2141450.781081
COLFALEX TANGUAY 703210292998338160.6835060.5872370.0962691.1639350.827143
TB DDAN BOYLE 58451034769813-220.4675430.3755520.0919911.2449480.624234
MTLDANDREI MARKOV 553792109612218-260.4742100.3824060.0918041.2400690.688438
MINFPASCAL DUPUIS 46307617809516-150.5039840.4149100.0890741.2146820.701591
CARDSEAN HILL 393473-44631175-540.3133260.2247700.0885561.3939840.568173
LA FALEXANDER FROLOV 493382128610616-200.4854040.3969510.0884531.2228310.687965
DALFJERE LEHTINEN 562379851038433190.6882920.6005660.0877261.1460720.855661
BOSFMIKE KNUBLE 65431083310211322-110.5340160.4489700.0850461.1894240.695587
TB FMARTIN ST. LOUIS 57461032779711-200.4675430.3865560.0809871.2095090.605591
STLDAL MACINNIS 695011933818619-50.5488340.4700860.0787481.1675180.655694

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? ?

CBJFDAVID VYBORNY 442973-527615815-820.2916810.1878980.1037831.5523360.697155
LA FZIGMUND PALFFY 6238100207310124-280.4854040.3431420.1422621.4145860.726928
CARDSEAN HILL 393473-44631175-540.3133260.2247700.0885561.3939840.568173
COLFPETER FORSBERG 8732119109828355-10.6835060.4939390.1895671.3837860.880833
PHOFLADISLAV NAGY 532881248210825-260.4963100.3656730.1306371.3572500.781797
COLFMILAN HEJDUK 823311510387824950.6835060.5295590.1539471.2907070.860616
CBJFGEOFF SANDERSON 424385-6878144-1-660.2916810.2268450.0648361.2858160.488236
PITFALEXEI KOVALEV 434790-6871131-4-600.2908680.2270510.0638171.2810690.455643
NASDJASON YORK 4935844729614-240.4603790.3600000.1003791.2788300.662162
FLADANDREAS LILJA 362965-31751207-450.3569020.2808980.0760041.2705750.606457
PHOFDAYMOND LANGKOW 533487188210219-200.4963100.3925730.1037371.2642480.708448
ATLFDANY HEATLEY 6162123-5285135-1-500.3545280.2838890.0706391.2488260.491870

Last edited by plusandminus: 08-24-2011 at 05:47 PM. Reason: adding more text
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