## Correlations Between Various Rating Methods

For each of the 1994-95 NBA teams, I have calculated several different measures of evaluating teams, including three linear weights measures (Barra, Credits, and HGS), as well as the Correlated Gaussian method and the Pythagorean method. An ideal statistic correlates with the actual winning percentage of the team perfectly; in other words, it has a correlation of 1.000. As can be seen at the bottom of the table, the Correlated Gaussian method does the best, followed closely by the Pythagorean Method. The Linear Weights methods all do relatively poorly, indicating that their use provides relatively little information about the potential for winning.
```Tm      Barra  Credits  HGS  CorrGauss%         Pyth%  Actual%
ATL     12286   8751    7378.6  0.550           0.571   0.512
BOS     12494   9127    7812.4  0.485           0.474   0.427
CHA     12669   9501    7842.7  0.600           0.633   0.610
CHI     12937   9463    8024.5  0.635           0.690   0.573
CLV     11404   8200    6983    0.519           0.528   0.524
DAL     12802   9229    7966.2  0.410           0.388   0.439
DEN     13015   9483    8080.6  0.519           0.528   0.500
DET     12233   8819    7438.1  0.281           0.235   0.341
GSW     12911   9335    7977.9  0.338           0.305   0.317
HOU     13315   9858    8103    0.560           0.580   0.573
IND     12514   9221    7922.6  0.617           0.656   0.634
LAC     12068   8329    7365.4  0.265           0.183   0.207
LAL     13617   9853    8349.9  0.493           0.491   0.585
MIA     12268   8947    7584.6  0.441           0.391   0.390
MIL     12024   8558    7353.1  0.361           0.331   0.415
MIN     11388   8132    7143.1  0.243           0.182   0.256
NJN     12693   9146    7836.8  0.387           0.359   0.366
NYK     12458   9213    7700.8  0.601           0.624   0.671
ORL     14282  10585    9037.2  0.684           0.750   0.695
PHI     11990   8399    7274.1  0.350           0.298   0.293
PHO     13727  10347    8646.6  0.630           0.643   0.720
POR     13192   9423    8090.7  0.607           0.651   0.537
SAC     12324   8828    7665.6  0.467           0.458   0.476
SAS     13604  10115    8535.2  0.715           0.722   0.756
SEA     14183  10538    8983.7  0.720           0.781   0.695
UTA     13731  10489    8945.3  0.721           0.784   0.732
WAS     12196   8726    7426.7  0.262           0.290   0.256

Correl  0.714  0.799    0.7441  0.958           0.949
```
Using 1994-95 NBA Team Statistics
```Barra = PTS+REB+AST+2*STL+2*BLK-TO-0.5*(FGA-FGM)
(From his ESPNet article)

Credits = PTS+REB+AST+STL+BLK-TO-(FGA-FGM)-(FTA-FTM)

1.4*FGM+FTM+0.85*OR+0.5*DefR+AST+STL+1.4*BLK-0.8*TO-
0.6*(FGA-FGM)
(From HoopStats, by Joshua Trupin and Gerald Secor Couzens.)

CorrGaus% = NORM{[PPG-Opp.PPG]/[Var(PPG)+Var(Opp.PPG) -
2*Cov(PPG,Opp.PPF)]}, where NORM means to take the percentile of the
normal (mean=0, variance=1) distribution having the value in braces, etc.
See explanation in Bell Curve article.)
Pyth% = Pts^16.5/(Pts^16.5 + Opp. Pts^16.5)
= Off. Rtg^16.5/(Off. Rtg^16.5 + Def. Rtg^16.5)
(From The Basketball Hoopla, by L. Dean Oliver.)

Actual% = Actual Winning Percentage of the team

Correl. = Statistical correlation between the columnar statistics and actual
winning percentage.
```