View Single Post
08-24-2011, 04:28 PM
#193
plusandminus
Registered User

Join Date: Mar 2011
Posts: 980
vCash: 500
Quote:
 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

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