Wednesday, September 2, 2009

MVP - By the Numbers

Pythagoras Masters - Special to Cobb Times Herald

With the MVP debates raging in the Cobb World forums, The Times Herald asked noted mathematician Pythagoras Masters to break down the numbers to determine who should be taking home the hardware at the end of the season. Below is his formula for determining the Gross Production Average (GPA) of all of the top contenders for the awards, plus many other players who you might recognize. Included after all of the mathematical jargon is the GPA list, where you can see if your favorite makes the grade.

Adjusted OPS (OPS+)

OPS+, Adjusted OPS, is a closely related statistic. OPS+ is OPS adjusted for the park and the league in which the player played, but not for fielding position. An OPS+ of 100 is defined to be the league average. An OPS+ of 150 or more is excellent and 125 very good, while an OPS+ of 75 or below is poor.



The basic formula for OPS+ is







where *lgOBP is the park adjusted (Average) OBP of the league and *lgSLG is the park adjusted (Average) SLG of the league.



A common misconception is that OPS+ closely matches the ratio of a player's OPS to that of the league. In fact, due to the additive nature of the two components in OPS+, a player with an OBP and SLG both 50% better than league average in those metrics will have an OPS+ of 200 (twice the league average OPS+) while still having an OPS that is only 50% better than the average OPS of the league.



Gross Production Average

Gross Production Average or GPA is a baseball statistic created in 2003 by Aaron Gleeman as a refinement of On-Base Plus Slugging (OPS).[1] GPA attempts to solve two frequently cited problems with OPS. First, OPS gives equal weight to its two components, On Base Percentage (OBP) and Slugging Percentage (SLG). In fact, OBP contributes significantly more to scoring runs than SLG does. Sabermetricians have calculated that OBP is about 80% more valuable than SLG. A second problem with OPS is that it generates numbers on a scale unfamiliar to most baseball fans. For all the problems with traditional stats like batting average (AVG), baseball fans immediately know that a player batting .365 is significantly better than average, while a player batting .167 is significantly below average. But many fans don't immediately know how good a player with a 1.013 OPS is.



The basic formula for GPA is:





Unlike OPS, this formula both gives proper relative weight to its two component statistics and generates a number that falls on a scale similar to the familiar batting average scale.

Player AVG OBP SLG OPS OPS+ GPA
Pedro Franco 0.363 0.480 0.635 1.115 184 0.375
Norm Gibson 0.339 0.409 0.712 1.122 181 0.362
Chipper Harper 0.349 0.418 0.680 1.098 176 0.358
Quilvio Suarez 0.326 0.435 0.616 1.052 167 0.350
Paul Jung 0.313 0.417 0.632 1.049 165 0.346
Rodney Toombs 0.347 0.417 0.612 1.029 160 0.341
Charles Reese 0.310 0.413 0.618 1.031 161 0.340
Josh Price 0.331 0.435 0.557 0.992 153 0.335
Jamie Beimel 0.328 0.430 0.549 0.980 150 0.331
Louie Tarraga 0.324 0.388 0.616 1.004 153 0.329
Jimmie Julio 0.356 0.430 0.539 0.969 148 0.328
Kory Arnold 0.309 0.380 0.615 0.995 150 0.325
Guillermo Segui 0.333 0.407 0.564 0.971 147 0.324
Benji Ordonez 0.314 0.426 0.521 0.947 143 0.322
Joseph Pan 0.305 0.360 0.624 0.984 146 0.318
Jeremy Hernandez 0.295 0.379 0.588 0.967 144 0.318
Ernest McConnell 0.313 0.378 0.587 0.966 143 0.317
Joseph Funaki 0.282 0.331 0.670 1.001 148 0.316
Walter Stewart 0.309 0.373 0.594 0.967 143 0.316
Milt Serafini 0.301 0.415 0.518 0.933 139 0.316
Craig Lake 0.322 0.417 0.503 0.920 136 0.313
Kenny Blair 0.289 0.362 0.601 0.963 142 0.313
Shawon Lee 0.292 0.381 0.565 0.946 139 0.313
Lyle Crudale 0.308 0.398 0.533 0.932 137 0.312
Domingo Pelaez 0.294 0.357 0.605 0.962 141 0.312
Sam Lockwood 0.293 0.401 0.525 0.926 136 0.312
Hades Booker 0.309 0.381 0.560 0.941 138 0.311
Gregg Young 0.305 0.387 0.542 0.929 136 0.310
Lloyd Ross 0.340 0.440 0.442 0.882 129 0.309
Jim Henley 0.333 0.388 0.534 0.921 134 0.308
Ralph Woods 0.303 0.382 0.542 0.925 134 0.307
Lawrence Shave 0.295 0.362 0.576 0.938 136 0.307
Emmanuel Castillo 0.303 0.394 0.518 0.912 132 0.307
Michael Ong 0.319 0.370 0.561 0.931 135 0.307
Jesus Campos 0.279 0.359 0.568 0.927 133 0.304
Jose Barrios 0.288 0.384 0.519 0.903 130 0.303
Javier Rios 0.291 0.377 0.531 0.908 130 0.302
Roger Sanders 0.304 0.366 0.549 0.914 131 0.302
Kip Zeile 0.290 0.359 0.559 0.919 131 0.301
Ruben Ortega 0.273 0.345 0.580 0.924 132 0.300
Jose Ordaz 0.298 0.397 0.481 0.878 125 0.299
Angel Vazquez 0.290 0.381 0.503 0.883 125 0.297
Nick Weaver 0.272 0.341 0.574 0.915 130 0.297
Bosco Simon 0.280 0.382 0.499 0.881 125 0.297
Darryl Young 0.261 0.374 0.511 0.886 125 0.296
Jim Green 0.321 0.387 0.486 0.872 123 0.296
Vernon Jones 0.294 0.383 0.493 0.876 124 0.296
Tony Arnold 0.279 0.387 0.479 0.866 122 0.294
Garret Wells 0.293 0.381 0.490 0.870 122 0.294
Guillermo Sanchez 0.247 0.349 0.547 0.896 126 0.294
Johnny Rowe 0.292 0.355 0.535 0.890 125 0.294
R.J. Cubillan 0.279 0.361 0.521 0.882 123 0.293
Derrick Brumbaugh 0.306 0.373 0.499 0.872 122 0.293
Geronimo Liriano 0.309 0.370 0.504 0.874 122 0.293
Spud Upshaw 0.302 0.380 0.486 0.866 121 0.293
Darrell Kendall 0.283 0.359 0.524 0.883 123 0.292
Corey Green 0.281 0.341 0.554 0.895 125 0.292
Anthony Tabaka 0.271 0.359 0.521 0.880 123 0.292
Enrique Guardado 0.287 0.370 0.501 0.871 122 0.292
Jung Lee 0.311 0.374 0.492 0.867 121 0.291
Vic Flores 0.272 0.351 0.532 0.883 123 0.291
Javier Alvarez 0.294 0.388 0.462 0.851 118 0.290
Pedro Chavez 0.294 0.345 0.536 0.881 122 0.289
Sal Fox 0.304 0.377 0.477 0.853 118 0.289
Omar Rosado 0.292 0.372 0.484 0.856 118 0.288
Ben Harris 0.275 0.379 0.470 0.849 117 0.288
Jesus Henriquez 0.297 0.353 0.514 0.868 120 0.287
Frank Hutchinson 0.269 0.351 0.517 0.868 120 0.287
Ira Riggs 0.286 0.350 0.518 0.868 120 0.287
Benny Pineda 0.323 0.383 0.458 0.841 116 0.287
Wayne Wilson 0.273 0.333 0.542 0.875 120 0.285
Vladimir Fernandez 0.301 0.360 0.491 0.850 116 0.285
Ron Leon 0.285 0.351 0.507 0.858 117 0.285
Carlton Nelson 0.286 0.347 0.512 0.860 117 0.284
Abraham Traynor 0.269 0.389 0.436 0.824 112 0.284
Carl Saturria 0.313 0.365 0.479 0.845 115 0.284
Ignacio Lopez 0.298 0.358 0.489 0.846 115 0.283
Charley Porter 0.296 0.350 0.502 0.852 116 0.283
Harry Alfonseca 0.291 0.348 0.505 0.853 116 0.283
Rico Estrada 0.287 0.343 0.511 0.855 116 0.282
Brandon Miller 0.283 0.359 0.482 0.842 114 0.282
Victor Mercado 0.249 0.374 0.454 0.827 112 0.282
Brett O'Keefe 0.311 0.348 0.500 0.848 115 0.282
Tom Pettitte 0.302 0.377 0.446 0.824 111 0.281
Brook Colin 0.257 0.334 0.521 0.855 116 0.281
Marino Sierra 0.291 0.366 0.463 0.829 112 0.280
Stewart DiSarcina 0.312 0.377 0.443 0.821 111 0.280
Tony Martinez 0.290 0.412 0.380 0.792 107 0.280
Ramon Sasaki 0.307 0.365 0.464 0.829 112 0.280
Yamid Mairena 0.295 0.356 0.479 0.836 113 0.280
Sarma O'Connor 0.268 0.339 0.506 0.845 114 0.279
Peter Mullin 0.287 0.380 0.432 0.812 109 0.279
Omar DaSilva 0.249 0.349 0.487 0.836 112 0.279
Bill Norton 0.284 0.345 0.494 0.839 113 0.279
Benji Molina 0.277 0.367 0.454 0.821 110 0.279
Mike Wilson 0.268 0.347 0.489 0.835 112 0.278
Jose Cervantes 0.252 0.318 0.541 0.859 115 0.278
Luis Nunez 0.286 0.348 0.486 0.834 112 0.278
Esteban Mieses 0.254 0.338 0.503 0.840 113 0.278
Armando Chavez 0.293 0.351 0.479 0.830 111 0.278
Vinny Jang 0.264 0.338 0.501 0.840 112 0.277
Richard Nakajima 0.281 0.337 0.502 0.839 112 0.277
Ajax Worley 0.262 0.333 0.509 0.841 113 0.277
Raymond Adams 0.261 0.343 0.491 0.834 111 0.277
Justin Snopek 0.274 0.341 0.493 0.834 111 0.277
Juan Sierra 0.286 0.361 0.457 0.818 109 0.277
Pedro Rivera 0.270 0.363 0.451 0.813 108 0.276
Francis Kent 0.271 0.340 0.492 0.832 111 0.276
Kelvim Harris 0.274 0.338 0.495 0.833 111 0.276
Dick Wolf 0.288 0.363 0.450 0.813 108 0.276
Wayne Burns 0.292 0.341 0.489 0.831 110 0.276
Al Rosario 0.307 0.353 0.468 0.821 109 0.276
Clay Henry 0.294 0.359 0.453 0.812 107 0.275
Trenidad Pelaez 0.281 0.346 0.474 0.821 108 0.274
Hawk Gutierrez 0.288 0.342 0.481 0.823 109 0.274
Josh Davis 0.293 0.348 0.469 0.817 108 0.274
Harry Rios 0.290 0.356 0.453 0.809 107 0.273
James Cole 0.279 0.362 0.436 0.798 105 0.272
Al Restovich 0.284 0.342 0.471 0.813 107 0.272
Frank Abbey 0.253 0.307 0.533 0.840 110 0.271
John McGowan 0.278 0.333 0.486 0.819 107 0.271
Mitchell Marshall 0.274 0.357 0.442 0.800 104 0.271
Alex Presley 0.272 0.328 0.494 0.821 108 0.271
Brad Mann 0.248 0.321 0.506 0.826 108 0.271
Goose Benes 0.309 0.363 0.430 0.792 104 0.271
Victor Johnson 0.270 0.330 0.487 0.817 107 0.270
Ryan Saberhagen 0.265 0.325 0.493 0.817 107 0.270
Ken Puffer 0.287 0.346 0.455 0.801 104 0.269
Roosevelt Ingram 0.261 0.341 0.462 0.802 104 0.269
Phil Maddux 0.300 0.351 0.444 0.795 103 0.269
Luke Henley 0.286 0.353 0.434 0.787 101 0.267
Omar Lewis 0.304 0.346 0.446 0.792 102 0.267
Patrick Stanton 0.270 0.343 0.451 0.794 102 0.267
Wascar Lopez 0.288 0.336 0.464 0.800 103 0.267
Wilfredo Henriquez 0.280 0.351 0.436 0.786 101 0.267
Tanner Durham 0.261 0.340 0.455 0.795 102 0.267
J.P. Wilfredo 0.278 0.351 0.432 0.783 100 0.266
Felix Masato 0.260 0.340 0.450 0.790 101 0.266
Apollo Houston 0.299 0.369 0.397 0.766 98 0.265
Steven Grilli 0.276 0.326 0.473 0.798 102 0.265
Patrick Lamb 0.258 0.308 0.503 0.811 104 0.264
Miguel Matos 0.309 0.372 0.386 0.759 96 0.264
Thomas Hill 0.270 0.342 0.439 0.781 99 0.264
Curt Fox 0.283 0.339 0.444 0.783 100 0.264
Tony Cruz 0.286 0.351 0.421 0.772 98 0.263
Ira Black 0.284 0.369 0.389 0.757 96 0.263
Jose Gandarillas 0.271 0.356 0.409 0.765 97 0.262
Dorian Woolf 0.246 0.322 0.468 0.791 100 0.262
Mark Hocking 0.272 0.333 0.448 0.781 99 0.262
Sammy Bennett 0.235 0.304 0.498 0.802 102 0.261
Todd Hemphill 0.304 0.354 0.406 0.760 95 0.261
Brace Davey 0.220 0.313 0.479 0.791 100 0.261
Charley Morton 0.266 0.366 0.380 0.747 93 0.260
Tito Sisco 0.280 0.352 0.400 0.752 94 0.258
Carl Alexander 0.270 0.350 0.399 0.749 93 0.257
Rob Leonard 0.285 0.354 0.391 0.745 92 0.257
Luis Espinoza 0.277 0.351 0.396 0.747 92 0.257
Trent Billingsley 0.265 0.363 0.374 0.737 91 0.257
Lewis Allen 0.268 0.325 0.441 0.766 95 0.257
Alex Liriano 0.257 0.328 0.435 0.763 94 0.256
Darrin Barkley 0.284 0.357 0.382 0.739 91 0.256
Bo Rhodes 0.261 0.324 0.440 0.765 94 0.256
Frank Hartgraves 0.267 0.337 0.415 0.752 93 0.255
Vladimir Espinosa 0.266 0.337 0.415 0.751 93 0.255
Larry Gant 0.249 0.326 0.431 0.757 93 0.254
Louie Lee 0.269 0.346 0.394 0.740 90 0.254
Raul Palacios 0.290 0.346 0.394 0.740 90 0.254
Darryl Bates 0.249 0.333 0.416 0.750 92 0.254
Erubiel Bonilla 0.269 0.324 0.432 0.756 93 0.254
Alex Brantley 0.230 0.296 0.480 0.776 95 0.253
Ken Daniels 0.268 0.336 0.402 0.738 89 0.252
Buck Fuller 0.249 0.310 0.448 0.757 92 0.252
Harpo Hurst 0.274 0.333 0.399 0.732 88 0.250
Steven Clayton 0.225 0.304 0.447 0.750 90 0.249
Luis Mercado 0.264 0.340 0.380 0.720 85 0.248
Santiago Matos 0.247 0.291 0.468 0.759 91 0.248
John Helms 0.292 0.314 0.428 0.741 88 0.248
Arnold Fitzgerald 0.235 0.333 0.389 0.723 85 0.247
David Kwon 0.262 0.320 0.410 0.730 86 0.247
Alexander Erickson 0.254 0.306 0.432 0.738 87 0.246
Alex Guzman 0.293 0.357 0.340 0.698 81 0.246
Gregg Durbin 0.261 0.316 0.413 0.729 86 0.245
Raymond Sanford 0.256 0.309 0.422 0.731 86 0.245
Greg Tyson 0.231 0.305 0.424 0.730 85 0.243
Alfredo Cruz 0.253 0.315 0.402 0.717 83 0.242
Dickie Huff 0.295 0.350 0.338 0.688 79 0.242
James Lowry 0.228 0.332 0.367 0.698 80 0.241
Norm Ripken 0.274 0.323 0.379 0.702 80 0.240
Dude Barry 0.261 0.326 0.373 0.699 80 0.240
Joel Valentin 0.255 0.341 0.346 0.688 78 0.240
Tomas Diaz 0.249 0.306 0.401 0.706 80 0.238
Marc Reagan 0.266 0.326 0.363 0.690 78 0.237
William Chang 0.251 0.322 0.367 0.689 77 0.236
Larry Sabel 0.238 0.307 0.389 0.696 78 0.235
Ted O'Donnell 0.271 0.338 0.333 0.671 74 0.235
Tomas Lee 0.252 0.308 0.386 0.693 77 0.235
Danny Browning 0.272 0.328 0.350 0.678 75 0.235
Napoleon Scott 0.265 0.327 0.344 0.671 74 0.233
Rico Cruz 0.248 0.303 0.385 0.689 76 0.233
Theodore Starr 0.268 0.296 0.392 0.688 75 0.231
Chipper Woods 0.254 0.320 0.346 0.666 72 0.231
John Simpson 0.260 0.321 0.333 0.654 69 0.228
Dennis Ashby 0.265 0.283 0.400 0.682 73 0.227
Kiko Wall 0.242 0.302 0.361 0.662 70 0.226
Emmanuel Contreras 0.229 0.282 0.389 0.672 71 0.224
Tim Smith 0.229 0.288 0.374 0.662 69 0.223
Alan Peterson 0.232 0.298 0.352 0.650 67 0.222
Willie Kotsay 0.249 0.303 0.340 0.643 66 0.221
Erv Castillo 0.234 0.295 0.351 0.646 66 0.221
Donte Shelby 0.228 0.297 0.343 0.640 65 0.219
Ismael Delgado 0.211 0.301 0.334 0.636 64 0.219
Andres Liriano 0.239 0.323 0.290 0.613 60 0.218
Paul Roth 0.264 0.306 0.300 0.606 57 0.213
Gerald Murata 0.220 0.275 0.349 0.623 59 0.211
Albert Burnett 0.248 0.331 0.234 0.400 50 0.207
Fernando Belliard 0.233 0.275 0.324 0.598 54 0.205
D'Angelo Romero 0.245 0.292 0.288 0.579 51 0.203
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