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Predicting with Statistical Plus/Minus

Posted by Neil Paine on February 23, 2009

Surely most of our readers have heard about "adjusted plus/minus" at some time or another, whether through TrueHoop, Sports Illustrated, the APBRmetrics board, the many articles at 82games on the subject, or even Michael Lewis' article about Shane Battier in last week's New York Times Magazine. But for those of you who aren't familiar with the stat, it essentially tracks a player's influence on his team's point differential by comparing the team's performance when he's on the court vs. its performance with him sitting on the bench. There are also adjustments for a player's teammates, backups, opponents, and even the location of each game, and the whole mountain of data is fed through a massive linear regression equation to try and isolate the individual impact of every player. Personally, I believe this system has a lot of promise (especially with regard to measuring defense), and with further refinement it will one day be one of the better basketball metrics out there, so it was nice to see it get some more recognition this past week -- even though there are still some wrinkles that need to be ironed out.

Anyway, the other day I was fooling around with what's called "statistical plus/minus", which is basically a regression Dan Rosenbaum (the pioneer of adjusted +/-) once ran between "pure" plus/minus -- the kind you find at sites like BasketballValue.com -- and traditional box score numbers like points, blocks, assists, etc. The original goal of the regression was to try to add a more stable component to player ratings as a counterbalance to the pure +/-, which, while theoretically solid, can be wildly inconsistent for individual players from season to season. I ran the formula for every player over the past few years, but I forced 5 * the weighted average of a team's raw statistical +/- to equal that team's efficiency differential (offensive rating minus defensive rating). This is far from an ideal metric, but I found it does a reasonably credible job; for instance, here are this year's leaders in SPM (minimum 329 minutes):

Player           Tm      Pos     G       Min     SPM
----------------+----+------+-------+---------+-------
james,lebron     cle     SF      52      1955    15.90
paul,chris       nor     PG      48      1790    13.31
wade,dwyane      mia     SG      53      2018    11.63
ginobili,manu    san     SG      38      1038    7.91
duncan,tim       san     C       52      1839    7.45
roy,brandon      por     SG      49      1835    7.10
bryant,kobe      lal     SG      54      1968    6.74
kirilenko,andrei uta     SF      40      1172    6.37
kidd,jason       dal     PG      53      1878    6.12
howard,dwight    orl     C       51      1852    5.92
nelson,jameer    orl     PG      42      1307    5.89
wallace,gerald   cha     SF      43      1612    5.74
granger,danny    ind     SF      52      1882    5.33
rondo,rajon      bos     PG      56      1854    5.32
boozer,carlos    uta     PF      12      406     5.01
carter,vince     njn     SG      54      1967    4.88
turiaf,ronny     gsw     C       53      1070    4.85
iguodala,andre   phi     SF      53      2045    4.79
harris,devin     njn     PG      49      1756    4.73
robinson,nate    nyk     PG      46      1369    4.70
lewis,rashard    orl     PF      53      1947    4.31
gasol,pau        lal     PF      53      1936    4.23
garnett,kevin    bos     PF      53      1706    4.07
pierce,paul      bos     SF      56      2080    3.87
millsap,paul     uta     PF      49      1573    3.86
----------------+----+------+-------+---------+-------

Yeah, I know, there are some dudes in the top 25 that shouldn't be there, and the metric seems to have a general fondness for guys who have a good "versatility index" (PTS * AST * REB, raised to the 1/3 power)... but it's still okay. Not great, but it generally works good enough to get a broad idea of who's good and who isn't, which all we're going for here.

So I was messing around with this metric, and specifically looking at the huge leap Boston made between 2006-07 and 2007-08 (+42 wins, to be exact). Before the '08 season, we were kicking around Celtics predictions using a variety of methods, including PER and the ORtg/%Pos/DRtg framework that I used in this old article (which I promise I'll get back to... someday). And we all came up with ~50 wins for the "new-look" C's -- except for a member who used past "pure" adjusted +/- scores to predict the new roster's performance; he basically called for 65+ wins, which turned out to be dead on the money. Well, I wanted to see if you could accomplish the same thing with statistical +/-, so I projected 2008 SPM scores using data from 2005-07 and the old quick-and-dirty Bill James formula:

Proj_Y = (.5 * Y-1) + (.33 * Y-2) + (.17 * Y-3)

For the rookies, I eyeballed some past rooks and decided to give them an SPM of around -3.25. So we end up with this:

Player           Pos G  Min   Proj
----------------+--+---+----+-----
Paul Pierce      F   80 2874  6.16
Ray Allen        G   73 2624  4.88
Kevin Garnett    F   71 2328  7.97
Rajon Rondo      G   77 2306  1.61
Kendrick Perkins F   78 1912 -1.50
James Posey      F   74 1821  1.49
Eddie House      G   78 1480 -1.75
Tony Allen       G   75 1373  0.82
Glen Davis       F   69  940 -3.25
Leon Powe        F   56  809 -5.04
Brian Scalabrine F   48  512 -2.51
Sam Cassell      G   17  299  0.41
P.J. Brown       F   18  209 -2.44
Scot Pollard     C   22  173 -1.90
Gabe Pruitt      G   15   95 -3.25
----------------+--+---+----+-----
                   Eff Diff: 10.56
                        Wins 67.49

Lo and behold, you could have actually gotten 67.5 projected wins for that bunch had you predicted using SPM during the summer of 2007 (they actually won 66). So maybe there is something to this.

To further test this method, I wanted to "retrodict" the 2008-09 season so far using SPM. This time, though, I used a more sophisticated projection method, like the one we use for our official BBR projections. I also went back and found that the minute-weighted average SPM for all rookies in the lottery era was -2.16, so I assigned that value for every rookie (clearly this understates the value of your O.J. Mayos and Derrick Roses, but I wanted to keep things relatively simple). I used each player's actual minutes from this season (through Thursday's games), and efficiency differentials were converted to a winning % using this formula:

WPct = 0.498962072294257 + (0.0316764124733866 * eDiff)

Here's a rundown of how the method would have predicted things so far (all data courtesy of Dougstats):

+------------------------Actual----------------------+-Projected-+----
Team                 G  W  L  WPct  ORtg  DRtg  eDiff PeDiff projW +/-
--------------------+--+--+--+-----+-----+-----+-----+-----+----+-----
AtlantaHawks         54 32 22 0.593 109.9 108.1  1.82 -2.64   22   10
BostonCeltics        56 44 12 0.786 111.1 101.2  9.96  9.51   45   -1
CharlotteBobcats     54 22 32 0.407 104.5 106.2 -1.78 -1.40   25   -3
ChicagoBulls         54 24 30 0.444 107.0 108.7 -1.70 -1.99   24    0
ClevelandCavaliers   52 41 11 0.788 113.4 102.2 11.22  8.12   39    2
DallasMavericks      53 32 21 0.604 109.9 108.4  1.52  6.63   38   -6
DenverNuggets        54 37 17 0.685 109.9 105.9  4.01  2.81   32    5
DetroitPistons       53 27 26 0.509 106.9 107.5 -0.67  4.10   33   -6
GSWarriors           55 19 36 0.345 109.5 113.2 -3.68 -2.10   24   -5
HoustonRockets       54 33 21 0.611 109.1 105.5  3.61  7.60   40   -7
IndianaPacers        56 22 34 0.393 107.7 110.0 -2.32 -1.27   26   -4
LAClippers           55 13 42 0.236 102.8 112.1 -9.21 -3.19   22   -9
LALakers             54 44 10 0.815 115.0 106.1  8.90  8.19   41    3
MemphisGrizzlies     54 15 39 0.278 103.5 110.4 -6.91 -6.61   16   -1
MiamiHeat            53 28 25 0.528 106.9 106.9  0.00  0.00   26    2
MilwaukeeBucks       57 27 30 0.474 108.2 108.0  0.21 -3.19   23    4
MinnesotaT-wolves    53 18 35 0.340 107.2 111.1 -3.92 -5.43   17    1
NJNets               55 24 31 0.436 108.8 111.6 -2.83 -2.16   24    0
NOrleansHornets      52 32 20 0.615 110.4 107.3  3.19  5.57   35   -3
NYKnicks             53 22 31 0.415 108.3 110.9 -2.58 -0.65   25   -3
OklahomaCityThunder  54 13 41 0.241 103.9 110.0 -6.14 -8.82   12    1
OrlandoMagic         53 39 14 0.736 110.6 102.6  7.94  3.54   32    7
Philadelphia76ers    53 27 26 0.509 106.5 105.7  0.83  1.77   29   -2
PhoenixSuns          53 30 23 0.566 111.9 109.7  2.22  6.23   37   -7
PortlandTrailBlazers 53 33 20 0.623 114.1 110.0  4.10 -3.48   21   12
SacramentoKings      55 11 44 0.200 105.1 115.4-10.30 -4.49   20   -9
SanAntonioSpurs      53 36 17 0.679 108.7 105.2  3.51  4.10   33    3
TorontoRaptors       56 21 35 0.375 106.8 110.2 -3.40  1.05   30   -9
UtahJazz             55 32 23 0.582 111.0 107.8  3.15  4.55   35   -3
WashingtonWizards    54 12 42 0.222 105.4 114.0 -8.61 -4.08   20   -8
--------------------+--+--+--+-----+-----+-----+-----+-----+----+-----

That's an average error of 4.5 wins per team so far; for the sake of comparison, when projected out over 82 games, the average error vs. pythagorean record is a measly 6.4 wins, which would destroy anyone in our APBRmetrics prediction contest (in all fairness, though, this method is "cheating" considerably by knowing the actual minute totals for each player -- all it has to project is productivity, whereas before the season we all had to project both productivity and playing time). Anyway, for those interested in a closer examination, here's the data (I include each player's actual SPM scores as well as their projected SPMs):

Player          Tm      Pos     G       Min     SPM     pSPM
---------------+----+------+-------+---------+-------+-------
johnson,joe     atl     SG      52      2059    1.76    0.85
bibby,mike      atl     PG      53      1850    2.85    -0.14
williams,marvin atl     SF      50      1748    0.32    -1.91
smith,josh      atl     PF      42      1476    1.80    3.68
horford,al      atl     C       40      1274    2.15    -1.03
evans,maurice   atl     SG      54      1206    -1.99   -1.07
murray,ronald   atl     PG      52      1172    -2.42   -3.37
pachulia,zaza   atl     C       50      1014    -1.20   -1.19
jones,solomon   atl     C       45      539     0.11    -1.80
law,acie        atl     PG      42      445     -5.58   -3.43
west,mario      atl     SG      31      84      2.78    0.09
morris,randolph atl     C       16      64      -6.76   -1.80
hunter,othello  atl     SG      10      34      -10.63  -2.16
gardner,thomas  atl     SG      5       27      -25.58  -0.60
ATLANTA                                         1.82    -2.64
---------------+----+------+-------+---------+-------+-------
pierce,paul     bos     SF      56      2080    3.87    4.81
allen,ray       bos     SG      56      2021    3.02    3.08
rondo,rajon     bos     PG      56      1854    5.32    1.65
garnett,kevin   bos     PF      53      1706    4.07    6.42
perkins,k       bos     C       50      1436    -0.22   0.02
house,eddie     bos     PG      55      953     1.85    -0.75
davis,glen      bos     C       54      951     -2.36   -1.18
powe,leon       bos     PF      56      890     -0.36   -1.33
allen,tony      bos     SG      40      760     -0.34   -0.39
scalabrine,b    bos     PF      37      454     -1.56   -1.97
pruitt,gabe     bos     PG      33      286     -4.39   -0.49
o'bryant,p      bos     C       26      110     -4.52   -0.17
walker,bill     bos     SG      8       54      -2.13   -2.16
BOSTON                                          9.96    9.51
---------------+----+------+-------+---------+-------+-------
felton,raymond  cha     PG      54      2054    0.69    -1.10
okafor,emeka    cha     PF      54      1839    -0.71   -0.58
wallace,gerald  cha     SF      43      1612    5.74    4.53
augustin,d.j.   cha     PG      44      1248    -0.29   -2.16
diaw,boris      cha     PF      31      1179    0.71    0.17
bell,raja       cha     SG      23      807     0.00    0.64
morrison,adam   cha     SF      44      667     -5.69   -4.31
richardson,j    cha     SG      14      492     2.20    2.99
carroll,matt    cha     SG      34      481     -4.74   -1.23
dudley,jared    cha     SF      20      427     0.20    -0.13
howard,juwan    cha     PF      24      353     -3.16   -3.59
brown,shannon   cha     SG      30      340     -3.24   -2.36
mohammed,nazr   cha     C       35      310     -7.93   -1.67
may,sean        cha     PF      18      250     -11.18  0.32
diop,desagana   cha     C       13      224     1.65    1.01
hollins,ryan    cha     C       18      183     4.29    -0.75
singletary,sean cha     PG      24      182     -6.13   -2.16
ajinca,alexis   cha     C       29      175     -6.60   -2.16
martin,cartier  cha     PF      8       107     1.71    -2.16
radmanovic,vlad cha     PF      4       107     2.86    -0.58
jones,dwayne    cha     C       6       52      -15.97  -0.32
brown,andre     cha     PF      4       41      -14.84  -3.08
johnson,linton  cha     SG      2       13      -4.50   -1.08
CHARLOTTE                                       -1.78   -1.40
---------------+----+------+-------+---------+-------+-------
rose,derrick    chi     PG      54      1989    -1.71   -2.16
gordon,ben      chi     SG      54      1944    0.15    0.57
deng,luol       chi     SF      43      1484    -0.66   0.83
thomas,tyrus    chi     PF      51      1307    1.22    0.38
nocioni,andres  chi     SF      53      1281    -1.88   -0.74
noah,joakim     chi     C       52      1115    3.66    1.15
gooden,drew     chi     PF      31      920     -2.81   -2.67
hughes,larry    chi     SG      30      792     0.21    -0.95
sefolosha,thabo chi     SG      43      735     -0.44   -1.68
gray,aaron      chi     C       45      662     -0.83   -0.58
hinrich,kirk    chi     PG      23      611     1.34    1.77
hunter,lindsey  chi     PG      22      238     -4.72   -0.97
simmons,cedric  chi     PF      12      62      1.51    -2.34
nichols,d       chi     SF      2       6       -25.52  -0.77
CHICAGO                                         -1.70   -1.99
---------------+----+------+-------+---------+-------+-------
james,lebron    cle     SF      52      1955    15.90   10.60
williams,mo     cle     PG      52      1794    0.93    0.10
varejao,a       cle     C       52      1441    0.48    -0.09
west,delonte    cle     SG      37      1236    3.41    0.35
wallace,ben     cle     C       49      1193    1.40    2.89
gibson,daniel   cle     PG      47      1169    -0.94   0.02
szczerbiak,w    cle     SF      49      1049    -1.42   -0.87
ilgauskas,z     cle     C       36      973     -0.51   0.69
pavlovic,sasha  cle     SG      46      731     -1.21   -2.89
hickson,j.j.    cle     PF      45      533     -6.40   -2.16
jackson,darnell cle     PF      27      179     -11.08  -2.16
kinsey,tarence  cle     SF      31      145     -3.63   -1.62
wright,lorenzen cle     C       15      87      -10.07  -2.16
williams,jawad  cle     PF      9       12      -14.53  -2.16
johnson,trey    cle     SG      2       11      -29.72  -2.16
CLEVELAND                                       11.22   8.12
---------------+----+------+-------+---------+-------+-------
nowitzki,dirk   dal     PF      52      1950    3.27    6.80
kidd,jason      dal     PG      53      1878    6.12    3.28
terry,jason     dal     PG      50      1683    2.78    2.28
dampier,erick   dal     C       53      1258    2.51    0.25
howard,josh     dal     SF      36      1182    -0.27   2.02
bass,brandon    dal     PF      52      1024    -4.39   -2.54
barea,juan_jose dal     PG      50      935     -4.16   -1.85
wright,antoine  dal     SG      36      742     -2.17   -2.83
george,devean   dal     SF      33      576     -3.31   -2.36
diop,desagana   dal     C       34      451     -1.66   1.01
singleton,james dal     PF      36      405     -3.81   -0.52
green,gerald    dal     SF      25      269     -7.26   -2.86
williams,shawne dal     SF      15      169     -9.88   -1.31
stackhouse,j    dal     SG      8       142     -11.00  -1.69
carroll,matt    dal     SG      10      86      -10.70  -1.23
hollins,ryan    dal     C       9       76      -15.86  -0.75
DALLAS                                          1.52    6.63
---------------+----+------+-------+---------+-------+-------
hilario,nene    den     C       53      1730    3.70    0.21
billups,c       den     PG      49      1698    3.59    5.56
martin,kenyon   den     PF      48      1606    1.61    -0.57
smith,j.r.      den     SG      53      1441    0.23    0.41
carter,anthony  den     PG      54      1325    -1.57   -0.32
anthony,carmelo den     SF      39      1323    2.13    2.93
kleiza,linas    den     SF      54      1255    -3.19   -1.82
jones,dahntay   den     SG      52      1022    -2.32   -3.17
andersen,chris  den     C       43      815     3.19    -0.45
balkman,renaldo den     SF      33      421     1.52    1.18
iverson,allen   den     PG      3       122     -1.52   2.22
atkins,chucky   den     PG      16      118     -9.36   -0.50
petro,johan     den     C       11      64      -8.34   -4.05
weems,sonny     den     SG      7       35      -18.65  -2.16
howard,juwan    den     PF      3       23      4.21    -3.59
samb,cheick     den     C       6       23      -8.69   -0.11
DENVER                                          4.01    2.81
---------------+----+------+-------+---------+-------+-------
prince,tayshaun det     SF      53      1975    0.46    0.45
iverson,allen   det     PG      48      1841    0.37    2.22
wallace,rasheed det     C       49      1641    1.13    3.20
stuckey,rodney  det     PG      51      1584    0.47    -0.27
hamilton,rip    det     SG      45      1493    -0.36   0.96
mcdyess,antonio det     PF      34      898     0.00    -0.14
afflalo,arron   det     SG      51      803     -3.13   -1.22
maxiell,jason   det     PF      49      785     -0.97   -0.61
johnson,amir    det     PF      44      742     1.53    2.54
brown,kwame     det     C       32      473     -2.99   -1.73
bynum,will      det     PG      29      246     -6.23   -0.71
herrmann,walter det     SF      31      243     -2.16   -1.58
billups,c       det     PG      2       69      4.71    5.56
acker,alex      det     SG      7       21      1.61    -0.37
sharpe,walter   det     PF      3       7       -16.56  -2.16
DETROIT                                         -0.67   4.10
---------------+----+------+-------+---------+-------+-------
jackson,stephen gsw     SF      45      1817    0.05    -0.33
biedrins,andris gsw     C       50      1547    3.48    0.56
azubuike,k      gsw     SG      50      1537    -1.32   -1.90
crawford,jamal  gsw     SG      38      1451    -2.59   0.32
watson,c.j.     gsw     PG      52      1260    -0.85   -1.29
maggette,corey  gsw     SF      36      1183    -0.31   2.04
turiaf,ronny    gsw     C       53      1070    4.85    1.38
morrow,anthony  gsw     SG      41      763     -1.67   -2.16
belinelli,marco gsw     SG      32      679     -3.81   -1.89
wright,brandan  gsw     PF      31      523     -1.25   -0.92
randolph,a      gsw     PF      37      487     -5.30   -2.16
ellis,monta     gsw     SG      12      399     -6.97   -0.06
kurz,rob        gsw     SF      23      240     -1.39   -2.16
nelson,demarcus gsw     PG      13      171     -7.79   -2.16
harrington,al   gsw     PF      5       166     -4.17   -0.39
williams,marcus gsw     PG      11      56      -12.22  -3.95
davidson,j      gsw     PF      6       13      -28.18  -1.66
GOLDENSTATE                                     -3.68   -2.10
---------------+----+------+-------+---------+-------+-------
ming,yao        hou     C       51      1664    3.08    3.10
alston,rafer    hou     PG      48      1590    0.33    0.64
scola,luis      hou     PF      54      1557    -0.27   -0.25
artest,ron      hou     SF      41      1400    3.12    3.34
mcgrady,tracy   hou     SG      35      1182    2.19    4.76
brooks,aaron    hou     PG      52      1180    -1.21   -0.64
landry,carl     hou     PF      54      1125    -0.14   0.82
battier,shane   hou     SF      32      1020    2.50    2.92
wafer,von       hou     SG      35      699     -0.85   -2.43
barry,brent     hou     SG      36      652     0.36    2.56
hayes,chuck     hou     PF      49      607     -2.40   1.07
head,luther     hou     SG      22      321     -5.05   -0.15
mutombo,dikembe hou     C       4       20      -14.07  -1.90
dorsey,joey     hou     PF      3       6       -3.38   -2.16
HOUSTON                                         3.61    7.60
---------------+----+------+-------+---------+-------+-------
granger,danny   ind     SF      52      1882    5.33    1.48
jack,jarrett    ind     SG      56      1735    -2.91   -0.77
murphy,troy     ind     PF      51      1701    1.67    0.42
ford,t.j.       ind     PG      49      1508    -0.16   -0.19
foster,jeff     ind     C       51      1251    1.14    0.75
daniels,marquis ind     SG      41      1231    -2.59   -1.80
rush,brandon    ind     SG      49      1022    -6.15   -2.16
nesterovic,r    ind     C       49      939     -0.34   -0.20
hibbert,roy     ind     C       45      546     1.63    -2.16
graham,stephen  ind     SF      37      497     -8.88   -1.25
dunleavy,mike   ind     SG      18      493     -1.77   1.00
diener,travis   ind     PG      36      483     -0.12   -0.75
mcroberts,josh  ind     PF      19      151     -5.24   -0.11
baston,maceo    ind     PF      17      146     -1.80   0.29
INDIANA                                         -2.32   -1.27
---------------+----+------+-------+---------+-------+-------
thornton,al     lac     SF      55      2070    -3.52   -2.67
gordon,eric     lac     SG      55      1818    0.17    -2.16
camby,marcus    lac     C       43      1439    3.28    3.59
davis,baron     lac     PG      41      1420    0.76    3.89
randolph,zach   lac     PF      21      760     0.17    -0.85
davis,ricky     lac     SF      31      689     -5.61   -0.48
novak,steve     lac     PF      45      670     -2.37   -0.67
jones,fred      lac     SG      26      660     -0.45   -0.64
skinner,brian   lac     C       39      649     -4.67   -2.71
collins,mardy   lac     SG      30      635     -3.04   -3.01
kaman,chris     lac     C       15      532     -0.12   -1.99
jordan,deandre  lac     C       34      473     -4.20   -2.16
mobley,cuttino  lac     SG      11      364     -5.74   -1.26
davis,paul      lac     C       27      321     -4.86   -1.24
hart,jason      lac     PG      29      311     -6.81   -2.01
taylor,mike     lac     PG      24      283     -8.74   -2.16
thomas,tim      lac     PF      10      220     -6.85   -0.33
samb,cheick     lac     C       10      52      -15.61  -0.11
acker,alex      lac     SG      1       12      -22.28  -0.37
LACLIPPERS                                      -9.21   -3.19
---------------+----+------+-------+---------+-------+-------
bryant,kobe     lal     SG      54      1968    6.74    7.27
gasol,pau       lal     PF      53      1936    4.23    4.18
fisher,derek    lal     PG      54      1698    0.78    -0.33
odom,lamar      lal     PF      51      1430    1.68    1.72
bynum,andrew    lal     C       46      1336    1.76    0.36
ariza,trevor    lal     SF      54      1289    3.57    0.96
vujacic,sasha   lal     SG      52      855     2.07    -1.21
radmanovic,vlad lal     PF      46      767     -2.98   -0.58
farmar,jordan   lal     PG      37      707     -2.29   -1.32
walton,luke     lal     SF      37      585     -4.18   -1.21
powell,josh     lal     PF      33      312     -8.72   -3.95
mihm,chris      lal     C       18      103     -5.86   -2.01
yue,sun         lal     SF      10      29      -20.34  -2.16
morrison,adam   lal     SF      1       7       -22.95  -4.31
brown,shannon   lal     SG      1       6       -55.67  -2.36
mbenga,dj       lal     C       1       3       17.77   -0.95
LALAKERS                                        8.90    8.19
---------------+----+------+-------+---------+-------+-------
mayo,o.j.       mem     SG      54      2034    -0.86   -2.16
gay,rudy        mem     SF      51      1909    -2.08   -0.15
gasol,marc      mem     C       54      1620    1.27    -2.16
conley,mike     mem     PG      54      1484    -1.05   -1.42
warrick,hakim   mem     PF      54      1383    -1.94   -2.73
lowry,kyle      mem     PG      49      1060    0.73    1.53
arthur,darrell  mem     PF      48      943     -4.93   -2.16
ross,quinton    mem     SG      47      821     -3.72   -1.57
milicic,darko   mem     C       36      725     -0.17   -1.24
buckner,greg    mem     SG      42      544     -2.61   -0.25
jaric,marko     mem     PG      27      263     -6.83   0.29
miles,darius    mem     SF      18      198     0.49    -1.97
crittenton,j    mem     PG      7       44      -1.91   -2.49
haddadi,hamed   mem     C       4       14      10.92   -2.16
MEMPHIS                                         -6.91   -6.61
---------------+----+------+-------+---------+-------+-------
wade,dwyane     mia     SG      53      2018    11.63   6.68
haslem,udonis   mia     PF      52      1798    -3.04   -2.43
chalmers,mario  mia     PG      53      1671    1.61    -2.16
marion,shawn    mia     PF      42      1517    0.13    4.45
cook,daequan    mia     SG      49      1264    -2.85   -2.85
beasley,michael mia     PF      52      1255    -5.68   -2.16
anthony,joel    mia     C       50      889     0.30    -0.99
quinn,chris     mia     PG      47      771     -1.13   -0.13
diawara,y       mia     SG      45      569     -5.56   -2.44
magloire,jamaal mia     C       35      413     -5.11   -5.81
jones,james     mia     PF      16      205     -6.81   -0.30
blount,mark     mia     C       17      186     -10.43  -4.90
banks,marcus    mia     PG      16      164     -2.70   -1.20
livingston,s    mia     PG      4       41      -8.19   -0.87
o'neal,jermaine mia     C       1       27      0.35    1.20
wright,dorell   mia     SF      1       6       -15.22  -0.67
moon,jamario    mia     SF      1       5       -12.55  1.45
MIAMI                                           0.00    0.00
---------------+----+------+-------+---------+-------+-------
jefferson,r     mil     SF      57      2061    0.39    1.02
ridnour,luke    mil     PG      49      1526    1.53    -0.74
mbah_a_moute,l  mil     SF      57      1440    -1.76   -2.16
sessions,ramon  mil     PG      54      1404    1.83    -0.27
villanueva,c    mil     PF      53      1350    3.35    -2.37
redd,michael    mil     SG      33      1201    1.97    2.15
bogut,andrew    mil     C       36      1125    0.30    1.01
bell,charlie    mil     SG      45      1081    -3.59   -0.39
gadzuric,dan    mil     C       46      602     0.68    -2.25
elson,francisco mil     C       38      568     -2.37   -3.12
alexander,joe   mil     PF      40      451     -4.17   -2.16
lue,tyronn      mil     PG      30      392     -3.18   -2.22
allen,malik     mil     PF      29      343     -4.55   -3.73
bogans,keith    mil     SG      5       97      -1.60   -0.09
croshere,austin mil     PF      11      78      -1.31   -0.86
gill,eddie      mil     PG      4       36      5.14    -0.03
jones,damon     mil     PG      5       32      -7.43   -1.77
MILWAUKEE                                       0.21    -3.19
---------------+----+------+-------+---------+-------+-------
foye,randy      min     PG      53      1909    0.19    -1.06
jefferson,al    min     C       50      1832    2.42    0.25
gomes,ryan      min     SF      53      1668    -2.26   -1.15
miller,mike     min     SG      44      1375    0.70    1.15
telfair,s       min     PG      48      1278    -3.42   -2.65
love,kevin      min     PF      53      1274    -1.09   -2.16
smith,craig     min     PF      49      974     -0.34   -1.16
mccants,rashad  min     SG      34      635     -4.50   -1.65
carney,rodney   min     SG      42      619     -4.04   -1.96
ollie,kevin     min     PG      24      401     1.35    -2.36
cardinal,brian  min     PF      37      351     1.06    -0.70
brewer,corey    min     SF      15      308     -0.25   -2.36
collins,jason   min     C       14      164     -6.11   -2.94
madsen,mark     min     C       11      59      -7.49   -2.15
booth,calvin    min     C       1       1       -4.75   0.05
MINNESOTA                                       -3.92   -5.43
---------------+----+------+-------+---------+-------+-------
carter,vince    njn     SG      54      1967    4.88    4.67
harris,devin    njn     PG      49      1756    4.73    1.88
lopez,brook     njn     C       55      1640    -2.58   -2.16
dooling,keyon   njn     PG      52      1357    -0.94   -1.29
hayes,jarvis    njn     SF      50      1265    -4.35   -2.10
simmons,bobby   njn     SF      46      1195    -0.50   -1.05
jianlian,yi     njn     PF      39      1003    -3.80   -3.36
anderson,ryan   njn     PF      48      945     -1.64   -2.16
boone,josh      njn     PF      42      726     -1.34   -1.83
hassell,trenton njn     SF      33      614     -3.12   -2.46
najera,eduardo  njn     PF      27      319     -3.91   0.49
douglas-roberts njn     SG      24      214     -8.08   -2.16
williams,sean   njn     C       20      205     -5.81   -0.63
swift,stromile  njn     C       6       63      -10.02  -2.75
ager,maurice    njn     SG      16      57      -13.41  -2.98
NEWJERSEY                                       -2.83   -2.16
---------------+----+------+-------+---------+-------+-------
paul,chris      nor     PG      48      1790    13.31   8.11
west,david      nor     PF      46      1732    0.46    1.47
stojakovic,peja nor     SF      46      1570    -0.89   0.58
posey,james     nor     SF      52      1484    1.45    1.69
butler,rasual   nor     SF      52      1478    -1.21   -2.37
chandler,tyson  nor     C       32      997     -1.67   0.82
armstrong,h     nor     C       48      735     -4.69   -2.24
brown,devin     nor     SF      44      680     -3.08   -1.32
daniels,antonio nor     PG      31      465     -3.38   -0.39
marks,sean      nor     C       33      428     -6.35   -0.44
peterson,morris nor     SG      28      363     -2.71   -0.20
wright,julian   nor     SF      30      292     -5.63   0.11
ely,melvin      nor     C       21      254     -6.05   -3.06
bowen,ryan      nor     PF      13      144     4.42    -0.52
james,mike      nor     PG      8       73      -8.21   -0.89
NEWORLEANS                                      3.19    5.57
---------------+----+------+-------+---------+-------+-------
duhon,chris     nyk     PG      52      2023    0.60    0.37
lee,david       nyk     PF      53      1876    0.34    1.29
chandler,wilson nyk     SF      53      1704    -1.70   -1.05
harrington,al   nyk     PF      40      1407    -1.53   -0.39
richardson,q    nyk     SF      49      1407    -1.88   -0.93
robinson,nate   nyk     PG      46      1369    4.70    0.99
thomas,tim      nyk     SF      36      771     -0.21   -0.33
jeffries,jared  nyk     SF      32      726     -2.19   -0.75
crawford,jamal  nyk     SG      11      393     -2.31   0.32
randolph,zach   nyk     PF      11      388     -1.39   -0.85
roberson,a      nyk     PG      23      253     -2.34   -1.04
gallinari,d     nyk     SF      16      230     0.11    -2.16
rose,malik      nyk     PF      18      158     -15.93  -3.19
collins,mardy   nyk     SG      9       75      -9.11   -3.01
james,jerome    nyk     C       2       10      -18.15  -2.89
curry,eddy      nyk     C       1       3       -17.88  -3.98
NEWYORK                                         -2.58   -0.65
---------------+----+------+-------+---------+-------+-------
durant,kevin    okl     SF      53      2122    3.01    -0.62
green,jeff      okl     PF      54      1995    0.08    -2.60
westbrook,r     okl     PG      54      1714    1.02    -2.16
watson,earl     okl     PG      54      1429    -5.20   -0.36
collison,nick   okl     PF      47      1199    0.79    -0.88
mason,desmond   okl     SF      39      1059    -5.20   -4.00
wilcox,chris    okl     PF      37      720     -4.52   -0.85
smith,joe       okl     PF      36      691     -1.99   -2.07
weaver,kyle     okl     SG      29      519     -0.88   -2.16
wilkins,damien  okl     SG      31      511     -5.04   -0.90
krstic,nenad    okl     C       18      418     -3.56   -3.20
petro,johan     okl     C       22      343     -7.52   -4.05
swift,robert    okl     C       17      244     -0.14   -2.51
atkins,chucky   okl     PG      6       67      -3.94   -0.50
sene,mouhamed   okl     C       5       24      -11.35  -1.29
hill,steven     okl     C       1       2       -13.38  -2.16
OKLAHOMACITY                                    -6.14   -8.82
---------------+----+------+-------+---------+-------+-------
lewis,rashard   orl     PF      53      1947    4.31    3.48
turkoglu,hedo   orl     SF      52      1909    1.73    2.53
howard,dwight   orl     C       51      1852    5.92    2.24
nelson,jameer   orl     PG      42      1307    5.89    0.88
lee,courtney    orl     SG      48      1080    -0.72   -2.16
johnson,anthony orl     PG      53      1016    -1.01   -1.64
bogans,keith    orl     SG      36      785     -1.20   -0.09
pietrus,mickael orl     SF      30      781     0.07    -1.09
battie,tony     orl     C       51      779     -3.64   -2.36
redick,j.j.     orl     SG      39      683     -2.59   -0.79
gortat,marcin   orl     C       34      352     -1.05   -0.10
cook,brian      orl     PF      21      147     -8.86   -1.92
lue,tyronn      orl     PG      4       54      -4.28   -2.22
richardson,j    orl     SF      5       38      -11.99  -2.04
foyle,adonal    orl     C       5       28      -15.07  -1.49
ORLANDO                                         7.94    3.54
---------------+----+------+-------+---------+-------+-------
iguodala,andre  phi     SF      53      2045    4.79    4.24
miller,andre    phi     PG      53      1893    3.61    1.18
young,thaddeus  phi     SF      53      1809    -1.81   -0.07
dalembert,s     phi     C       53      1313    -4.19   -1.25
williams,louis  phi     PG      52      1191    0.01    0.15
green,willie    phi     SG      52      1133    -2.33   -3.53
brand,elton     phi     PF      29      921     -3.33   4.99
speights,m      phi     PF      50      767     1.88    -2.16
evans,reggie    phi     PF      50      638     -2.67   -2.86
ivey,royal      phi     PG      42      500     0.23    -2.56
ratliff,theo    phi     C       25      278     1.94    0.15
rush,kareem     phi     SG      21      169     -6.11   -3.22
marshall,d      phi     PF      12      86      7.20    -1.41
PHILADELPHIA                                    0.83    1.77
---------------+----+------+-------+---------+-------+-------
stoudemire,a    pho     C       53      1949    2.50    3.97
nash,steve      pho     PG      48      1606    -1.29   1.66
hill,grant      pho     SF      53      1515    0.73    0.88
o'neal,shaq     pho     C       46      1397    3.32    1.31
barnes,matt     pho     PF      48      1216    -1.09   -0.19
barbosa,leandro pho     SG      48      1103    2.87    1.44
richardson,j    pho     SG      29      1001    1.28    2.99
bell,raja       pho     SG      22      711     -1.30   0.64
amundson,louis  pho     PF      47      573     -0.85   -1.03
diaw,boris      pho     PF      22      536     -1.56   0.17
lopez,robin     pho     C       35      371     -1.88   -2.16
dragic,goran    pho     PG      28      357     -5.94   -2.16
dudley,jared    pho     SF      20      157     4.44    -0.13
tucker,alando   pho     SF      13      126     -8.30   -0.80
singletary,sean pho     PG      13      121     -2.63   -2.16
brown,dee       pho     PG      2       28      -10.83  -0.88
PHOENIX                                         2.22    6.23
---------------+----+------+-------+---------+-------+-------
aldridge,l      por     PF      53      1938    1.56    0.45
roy,brandon     por     SG      49      1835    7.10    3.32
outlaw,travis   por     SF      52      1423    -1.22   -0.73
fernandez,rudy  por     PG      52      1364    2.16    -2.16
blake,steve     por     PG      40      1217    1.43    -1.17
przybilla,joel  por     C       53      1171    -1.38   -1.50
oden,greg       por     C       46      1051    0.67    -2.16
batum,nicolas   por     SF      53      925     0.63    -2.16
rodriguez,s     por     PG      53      898     -2.53   -2.51
bayless,jerryd  por     PG      32      480     -3.77   -2.16
frye,channing   por     PF      38      422     -6.21   -2.31
diogu,ike       por     PF      19      72      -17.85  -2.63
randolph,s      por     C       3       8       -13.57  -0.39
webster,martell por     SF      1       5       -18.04  -1.89
PORTLAND                                        4.10    -3.48
---------------+----+------+-------+---------+-------+-------
salmons,john    sac     SG      53      1980    0.09    -1.04
udrih,beno      sac     PG      53      1596    -2.49   -2.42
thompson,jason  sac     PF      55      1448    -4.14   -2.16
hawes,spencer   sac     C       51      1391    -3.32   -2.56
miller,brad     sac     C       43      1358    1.39    1.62
martin,kevin    sac     SG      33      1256    1.48    2.25
garcia,f        sac     SF      38      1002    0.93    0.35
jackson,bobby   sac     SG      51      953     -3.26   0.39
moore,mikki     sac     PF      46      749     -2.84   -1.25
brown,bobby     sac     PG      47      677     -8.39   -2.16
greene,donte    sac     SF      30      387     -8.58   -2.16
williams,s      sac     PF      30      303     -7.28   -3.23
douby,quincy    sac     PG      20      227     -6.27   -3.49
thomas,kenny    sac     PF      7       57      0.57    -2.36
SACRAMENTO                                      -10.30  -4.49
---------------+----+------+-------+---------+-------+-------
duncan,tim      san     C       52      1839    7.45    5.87
mason,roger     san     PG      53      1628    -2.22   -1.42
parker,tony     san     PG      43      1467    0.13    1.26
finley,michael  san     SF      52      1453    -3.17   -1.80
bonner,matt     san     PF      52      1229    3.33    -0.47
bowen,bruce     san     SF      53      1069    -1.80   -0.34
ginobili,manu   san     SG      38      1038    7.91    7.42
hill,george     san     PG      51      915     -0.38   -2.16
thomas,kurt     san     C       50      811     0.00    -1.26
udoka,ime       san     SF      38      474     -5.58   0.38
oberto,fabricio san     PF      38      469     -0.38   0.27
tolliver,a      san     C       19      208     -4.75   -2.16
vaughn,jacque   san     PG      18      195     -9.26   -3.11
farmer,desmon   san     SG      3       54      -11.10  -0.16
hairston,malik  san     SG      7       44      -1.40   -2.16
croshere,austin san     PF      3       23      -17.29  -0.86
ahearn,blake    san     PG      3       18      1.70    -0.59
SANANTONIO                                      3.51    4.10
---------------+----+------+-------+---------+-------+-------
bosh,chris      tor     PF      51      1949    3.62    4.22
parker,anthony  tor     SG      54      1772    -0.46   1.34
bargnani,andrea tor     PF      56      1708    -2.68   -2.19
calderon,jose   tor     PG      42      1444    2.78    1.53
moon,jamario    tor     SF      54      1378    3.12    1.45
kapono,jason    tor     SF      54      1303    -4.89   -2.52
o'neal,jermaine tor     C       41      1217    -1.23   1.20
graham,joey     tor     SF      53      1093    -2.80   -2.87
ukic,roko       tor     SG      46      572     -5.53   -2.16
solomon,will    tor     PG      39      544     -4.18   -2.16
humphries,kris  tor     C       29      269     -1.48   -2.51
voskuhl,jake    tor     C       24      156     -9.25   -1.54
adams,hassan    tor     SF      12      52      -15.93  -1.39
marion,shawn    tor     SF      1       40      6.72    4.45
jawai,nathan    tor     C       4       13      -29.73  -2.16
banks,marcus    tor     PG      1       12      -2.37   -1.20
TORONTO                                         -3.40   1.05
---------------+----+------+-------+---------+-------+-------
brewer,ronnie   uta     SG      54      1713    0.99    1.99
okur,mehmet     uta     C       46      1606    1.35    1.60
millsap,paul    uta     PF      49      1573    3.86    1.80
williams,deron  uta     PG      41      1481    0.93    0.19
miles,c.j.      uta     SG      50      1205    -1.06   -0.93
korver,kyle     uta     SF      51      1181    -1.47   -0.26
kirilenko,a     uta     SF      40      1172    6.37    5.07
price,ronnie    uta     PG      42      699     -3.44   -1.04
knight,brevin   uta     PG      47      666     -2.98   0.31
koufos,kosta    uta     PF      48      568     -2.16   -2.16
harpring,matt   uta     SF      41      493     -1.97   -1.21
boozer,carlos   uta     PF      12      406     5.01    2.87
almond,morris   uta     SG      25      258     -8.94   -0.43
fesenko,kyrylo  uta     C       18      143     1.25    -0.75
collins,jarron  uta     C       17      137     -5.36   -0.87
UTAH                                            3.15    4.55
---------------+----+------+-------+---------+-------+-------
jamison,antawn  was     PF      54      2083    2.52    0.79
butler,caron    was     SF      49      1902    2.24    2.44
young,nick      was     SG      54      1179    -5.46   -3.56
mcguire,dominic was     SF      51      1117    -0.96   -1.99
blatche,andray  was     C       45      1052    0.12    -0.56
james,mike      was     PG      35      1029    -4.51   -0.89
songaila,darius was     PF      53      984     -3.04   -2.15
stevenson,d     was     SG      32      886     -4.49   -1.70
mcgee,javale    was     C       48      734     -3.66   -2.16
dixon,juan      was     SG      35      550     -6.17   -2.46
crittenton,j    was     PG      30      491     -2.53   -2.49
thomas,etan     was     C       26      303     -6.47   -1.79
daniels,antonio was     PG      13      289     -2.11   -0.39
brown,dee       was     PG      17      232     -3.57   -0.88
pecherov,o      was     PF      17      141     -15.14  -2.13
WASHINGTON                                      -8.61   -4.08
---------------+----+------+-------+---------+-------+-------

So is SPM a great boxscore-based method to rank players? I don't really think so, seeing as it's meant merely as a complement to "pure" adjusted +/-. But at the same time, it does exhibit at least some ability to effectively predict a future team's performance based on the weighted projected SPMs of its players. And that means it's worth looking at this summer when free agency is over and you're trying to ascertain which teams will be better and which will be worse in 2010. (Hmm, do I sense a future column topic here?)

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3 Responses to “Predicting with Statistical Plus/Minus”

  1. art Says:

    I looked at a few players (not those obvious superstars) that I think they are the most valuable players on their respective teams and they all are rated high (highest or 2nd highest rating on their respective teams) by your SPM. I also looked at a few players that I think they are detrimental to team-oriented offense and defense despite they score more (because they shoot a lot), they all are ranked relatively low among their team main rotation players (ie, playing 25+ min). Thus, I like your SPM which relatively accurately reflects a player’s value. At least your SPM is much, much, much better than Cuban’s rating system. As soon as I saw Telfair (a backup-caliber PG) and B-Gordon (an extremely selfish small ball-hog) are ranked so high and Roy and the likes are nowhere to be found, I know Cuban’s system is useless. I like your “Versatility Index” which is much, much better than “PER” that overemphasizes scores and encourages ball-hogs. Keep up the good work!

  2. Art Stancill Says:

    Your blog keeps getting better and better! Your older articles are not as good as newer ones you have a lot more creativity and originality now. Keep it up!

  3. Witt Says:

    Lojra Falas