The fits below were obtained by fitting total runs for the 14 AL teams for the 2009 season.
2009 League averages:
AB Runs BA OBP SLG OPS OOPS R1_est OOPS2 R2_est
AL 5569 781 .266 .335 .428 .763 1.098 776 1.206 779
NL 5493 718 .259 .330 .409 .739 1.069 734 1.143 738
OOPS == 2*OBP + SLG; OOPS2== OOPS^2
R1_est = -910 + 1350 * (2.45 * OBP + SLG)
R2_est = 646 * OOPS^2
OOPS2 has the advantage of zero offset (Runs=0 at x=0) with only 1 parameter. The fractional change in OOPS2 is equal to the fractional change in predicted runs. That is not true for the common run estimators, which predict negative runs for very low values of the independent variables.
One could define OOPS2_BA as 0.266 * OOPS^2/1.206 for the AL. Or, OOPS2+ = 100* OOPS^2/1.206.
2009 stats:
AVG OBP SLG OPS OOPS OOPS2 OOPS2+ OOPS2_BA
Guerrero .295 .334 .460 .794 1.128 1.272 106 .281
Dunn .267 .398 .529 .928 1.325 1.756 146(AL) .387
Pujols .327 .443 .658 1.101 1.544 2.384 198 .526
Mauer .365 .444 .587 1.031 1.475 2.176 180 .480
Youkilis .306 .413 .548 .961 1.374 1.888 157 .416
Teixeira .292 .383 .565 .948 1.331 1.772 147 .391
A-Rod .286 .402 .532 .933 1.336 1.785 148 .394
Swisher .249 .371 .498 .869 1.240 1.538 127 .339
Abreu .293 .390 .435 .825 1.215 1.476 122 .326
Damon .282 .365 .489 .854 1.219 1.486 123 .328
Matsui .274 .367 .509 .876 1.243 1.545 128 .341
Jeter .334 .406 .465 .871 1.277 1.631 135 .360
V_Mart .303 .381 .480 .861 1.242 1.543 128 .340
Posada .285 .363 .522 .885 1.248 1.558 129 .344
J Molina .217 .292 .268 .560 0.852 0.728 60 .160
Cervelli .298 .309 .372 .682 0.990 0.980 81 .216
Varitek .209 .313 .390 .703 1.016 1.032 86 .228
Melky .274 .336 .416 .752 1.088 1.184 98 .261
Gardner .270 .345 .379 .724 1.069 1.143 95 .252
Granderson.249 .327 .453 .780 1.107 1.225 102 .270
Cameron(NL).250 .342 .452 .795 1.136 1.290 107(AL) .285
==================================================
KaleidaGraph Results:
KG: RUNS_OPS.qpc:
y = a + b * x
Value Error
a -811.8 160.7
b 2087.2 210.33
Chisq 8089.1 NA
R 0.9441 NA
RUNS = -810 + 2090 * OPS
CHI2 = 8090 ==> sig = 25 runs; R = 0.944
Note that CHI2 in both KG and ProFit basically assume sig=1;
i.e., Chi2 = SUM [ (y-y_fit)^2 ].
"Chi2" = sum[ (y-y_fit)^2 ]
VAR = "Chi2" / (N-1)
sig = sqrt(VAR) = sqrt( "Chi2" / (N-1) ) = sqrt( "Chi2"/13 )
SS_err = "Chi2"
SS_tot = SUM [ (y-y_avg)^2 ]
SS_reg = SUM [ (y_fit-y_avg)^2 ]
R^2 = 1 - SS_err/SS_tot = 1 - "Chi2"/SS_tot
standard error in R is sqrt[ (1-R^2) / (N-2) ]
For RUNS_OPS.qpc: R^2 = 0.8914 = 1 - 8089/SS_tot, or SS_tot = 74,460
(check: KG gives Variance=5728; 5728 x 13 = 74464)
for this data set, R = SQRT( 1 - "Chi2"/74460 )
From Kaleidagraph fits for AL 2009:
Stat R Chisq sig
AVG 0.840 21914 41.1
SLG 0.867 18497 37.7
OBP 0.915 12078 30.5
OPS 0.944 8089 24.9
OOPS 0.953 6836 22.9
OOPS2 0.948 7486 24.0
wOBA 0.953 6834 22.9
ProFit:
eq(1) 0.954 6740 22.8
eq(2) 0.959 5930 21.4
===================================================
ProFit Results:
function Fred(OBP, SLG, b, c,d : real);
begin;
y := b*(c*OBP + SLG) + d;
end;
iterations: 19
------------------------
Chi squared = 6743.2299
Parameters: Standard deviations:
b = 1353.3799 ∆b = 458.7910
c = 2.4512 ∆c = 1.3064
d = -910.4042 ∆d = 166.6370
RUNS = -910 + 1350 * (2.45 * OBP + SLG) eq(1)
CHI2 = 6740 ==> sig = 23 runs; R = 0.954
===================================================
=================================================
function Fred(BB_PA, S_PA, D_PA, T_PA, HR_PA, b,c,d,e,f : real);
begin;
y := b + c * (d*BB_PA + S_PA + e*D_PA + 1.6*T_PA + f*HR_PA)
end;
Iterations: 14
-------------------------------------------
Chi squared = 5932.8988
Parameters: Standard deviations:
b = -1024.8696 ∆b = 241.3729
c = 5185.8310 ∆c = 1007.9237
d = 0.7774 ∆d = 0.2233
e = 1.4131 ∆e = 0.3643
f = 1.7033 ∆f = 0.3541
RUNS = -1020 + 5200 * (0.77*BB_PA + 1B_PA + 1.4*2B_PA + 1.6*3B_PA + 1.7*HR_PA) eq(2)
CHI2 = 5930 ==> sig = 21.4 runs; R = 0.959
=================================================
for comparison (http://www.insidethebook.com/woba.shtml)lists
HR 1.70, 3B 1.37, 2B 1.08, 1B 0.77, NIBB 0.62, equivalent to:
BB 0.81, 1B 1.00, 2B 1.40, 3B 1.78, HR 2.21
---------------------------------------------------from
http://www.hardballtimes.com/main/statpages/glossary/
GPA= Gross Production Average, a variation of OPS, but more accurate and easier to interpret. The exact formula is (1.8*OBP + SLG)/4, adjusted for ballpark factor. The scale of GPA is similar to BA: .200 is lousy, .265 is around average and .300 is a star. A simple formula for converting GPA to runs is PA*1.356*(GPA^1.77).
---------------------------------------------------
from http://www.baseball-fever.com/showthread.php?t=66363
"the best correlation with runs comes from (1.8*OBA + SLG), or something in that range"
---------------------------------------------------
from http://www.tangotiger.net/wiki/index.php?title=Linear_Weights
R = .49S + .61D + 1.14T + 1.50HR + .33W + .14SB + .73SF, roughly:
BB 0.67, 1B 1.00, 2B 1.24, 3B 2.33, HR 3.06
---------------------------------------------------
from http://www.tangotiger.net/wiki/index.php?title=Batting_Runs
BR = .47S + .85D + 1.02T + 1.40HR + .33(W + HB), roughly:
BB 0.70, 1B 1.00, 2B 1.81, 3B 2.17, HR 2.98
---------------------------------------------------
from http://www.baseballmusings.com/archives/005962.php
RG = -5.84 + 22.92 (OBP) + 7.21 (SLG) + e, roughly:
RUNS = -950 + 1170 * (3.18 * OBP + SLG) R^2 = 0.92
---------------------------------------------------
from http://cyrilmorong.com/Havoc.htm
The table below summarizes the correlation and r-squared that various stats had
with team runs from 2001-03:
Stat Correlation R-squared
AVG 0.858 0.736
SLG 0.917 0.842
OBP 0.891 0.794
OPS 0.950 0.903
SB/G -0.032 0.001
Net SB/G 0.136 0.018
SB% 0.303 0.092
