Batting Runs Above Position

There’s been a lot of talk around the net the past week or two about positional adjustments. Everything that a player does is relative to the production of those players around him. Both his offense and defense are compared to average and replacement levels in order to calculate that player’s relative worth. Defensively, a shortstop is compared to other shortstops but offensively, shoudl he be compared to all players in the league, or only other shortstops? How are the adjustments determined and how are they applied?

Things got going at Rob Neyer’s blog at ESPN where our own Eric Seidman was quoted trying to explain Tom Tango’s system of defensive adjustments. The idea is, to get a players total, add their offense above league replacement, defenase above position replacement, league adjustment and position adjustment. More discussion took place at Baseball Primer.

Most of Neyer’s readers had problems grasping the concept of what is labeled a “defensive” adjustment, not sure if it means players higher on the defensive spectrum are valued more because they are playing a more difficult defensive position, or if it has something to do with the offense. Tango has done studies of players at multiple positions to see, for example, how much better a shortstop who moves to second may play.However, in another thread, he calculates the average at each position by decade in order to determine the offensive differentials between the defensive positions.

This is the approach I have favored. A players value is in how hard he is to replace. At age 30, Rafael Furcal projects to hit 282/345/415 next season, a 335 wOBA, fourth highest among major league shortstops, behind only Hanley Ramirez, Derek Jeter and Jose Reyes. Furcal was highly coveted on the free agent market, and re-signed with the Dodgers for $39m over 3 years. Meanwhile, Lyle Overbay projects at 269/340/424, for an almost identical 336 wOBA. However, that puts Overbay ahead of only Mike Jacobs and Sean Casey offensively among major league first baseman. Furcal is a precious commodity at short, but if he is moved over to first base, his bat is very replaceable. There are a good number of players who can hit as well or better than Furcal, but only three of them also play shortstop.

Therefore, when calculating a player’s value, compare his defense to others at the same position, and likewise compare his offense to others at his position. An argument against this method is that if a few teams put a high offense player at a traditionally low offense position (Aaron, Mays, Mantle Snider is centerfield) that it make everyone else look less valuable in comparison. They seek a more stable baseline than a yearly average. In addition, offensive levels have changed over the years. The major leagues combined for a 295 wOBA in 1968, then rising to 348 in 1999 and 2000. I believe the answer is in a Marcel, rolling weighted mean model, where I weight the most recent season at 1.00, the year before at 0.70, the one before that at 0.49, etc. That way, the baseline is modeled on the same years, with the same weights, at the stats to which it is being compared.

I first calculated the wOBA for each position, and for all players, for each season from 1954 to 1978. Starting in 1956 (the first season with three years of data), I used Marcel to calculate the expected wOBA for each position. (Table 1). Then for each season, I took the wOBA for each position, subtracted the league mean, divided by 1.15 (to convert to runs per PA) and then multiplied by 700 to get the plus/minus run values for each position (Table 2).

 

Year

C

1B

2B

3B

SS

LF

CF

RF

DH

1956

0.323

0.348

0.308

0.331

0.302

0.348

0.345

0.343

 

1957

0.317

0.345

0.307

0.326

0.303

0.351

0.342

0.338

 

1958

0.316

0.344

0.305

0.324

0.298

0.354

0.341

0.340

 

1959

0.312

0.343

0.306

0.327

0.301

0.348

0.339

0.342

 

1960

0.308

0.344

0.302

0.326

0.301

0.348

0.339

0.339

 

1961

0.312

0.350

0.298

0.326

0.303

0.346

0.340

0.345

 

1962

0.313

0.349

0.298

0.325

0.303

0.347

0.338

0.347

 

1963

0.310

0.340

0.295

0.319

0.298

0.342

0.332

0.343

 

1964

0.308

0.336

0.291

0.319

0.299

0.340

0.328

0.341

 

1965

0.303

0.335

0.291

0.319

0.295

0.337

0.325

0.339

 

1966

0.302

0.334

0.289

0.319

0.293

0.333

0.324

0.338

 

1967

0.295

0.332

0.289

0.315

0.286

0.331

0.320

0.333

 

1968

0.291

0.328

0.285

0.308

0.277

0.327

0.315

0.327

 

1969

0.292

0.333

0.289

0.309

0.281

0.329

0.318

0.332

 

1970

0.299

0.338

0.289

0.317

0.284

0.336

0.322

0.336

 

1971

0.300

0.339

0.291

0.317

0.279

0.335

0.322

0.334

 

1972

0.299

0.339

0.289

0.312

0.275

0.333

0.320

0.329

 

1973

0.299

0.339

0.294

0.316

0.272

0.334

0.321

0.329

0.318

1974

0.299

0.337

0.294

0.315

0.274

0.334

0.321

0.328

0.313

1975

0.301

0.338

0.296

0.316

0.273

0.333

0.321

0.329

0.315

1976

0.298

0.334

0.294

0.314

0.275

0.330

0.319

0.327

0.313

1977

0.306

0.337

0.296

0.319

0.275

0.332

0.321

0.334

0.319

1978

0.305

0.335

0.295

0.319

0.278

0.332

0.319

0.335

0.318

1979

0.307

0.338

0.298

0.321

0.280

0.333

0.323

0.338

0.321

1980

0.307

0.339

0.297

0.320

0.281

0.335

0.321

0.336

0.324

1981

0.304

0.334

0.295

0.320

0.279

0.332

0.319

0.332

0.321

1982

0.305

0.334

0.297

0.321

0.282

0.333

0.319

0.331

0.325

1983

0.305

0.334

0.299

0.323

0.285

0.333

0.319

0.328

0.329

1984

0.303

0.335

0.300

0.320

0.284

0.332

0.321

0.331

0.329

1985

0.303

0.338

0.303

0.321

0.285

0.331

0.321

0.332

0.325

1986

0.303

0.339

0.305

0.323

0.288

0.332

0.322

0.333

0.327

1987

0.302

0.346

0.308

0.328

0.292

0.335

0.327

0.337

0.330

1988

0.300

0.342

0.304

0.323

0.291

0.332

0.322

0.335

0.328

1989

0.297

0.343

0.305

0.319

0.288

0.331

0.317

0.332

0.324

1990

0.300

0.343

0.306

0.317

0.289

0.331

0.320

0.330

0.322

1991

0.298

0.340

0.308

0.317

0.290

0.329

0.320

0.330

0.327

1992

0.298

0.339

0.308

0.317

0.290

0.326

0.319

0.327

0.327

1993

0.303

0.344

0.310

0.321

0.294

0.331

0.322

0.329

0.328

1994

0.307

0.351

0.315

0.325

0.299

0.336

0.326

0.337

0.337

1995

0.310

0.355

0.316

0.330

0.301

0.339

0.326

0.342

0.343

1996

0.314

0.359

0.316

0.334

0.305

0.345

0.330

0.346

0.349

1997

0.317

0.362

0.319

0.334

0.306

0.343

0.331

0.350

0.348

1998

0.316

0.364

0.320

0.335

0.307

0.343

0.332

0.352

0.350

1999

0.319

0.366

0.324

0.337

0.312

0.346

0.335

0.356

0.354

2000

0.323

0.370

0.327

0.338

0.315

0.352

0.337

0.358

0.356

2001

0.319

0.368

0.326

0.337

0.315

0.353

0.335

0.357

0.352

2002

0.315

0.366

0.323

0.334

0.315

0.353

0.334

0.357

0.349

2003

0.315

0.364

0.323

0.331

0.314

0.354

0.333

0.356

0.348

2004

0.316

0.363

0.323

0.335

0.315

0.355

0.334

0.353

0.347

2005

0.314

0.361

0.324

0.336

0.315

0.352

0.333

0.351

0.345

2006

0.317

0.363

0.324

0.340

0.317

0.352

0.332

0.351

0.347

2007

0.316

0.361

0.326

0.340

0.319

0.351

0.332

0.350

0.348

2008

0.316

0.359

0.327

0.339

0.318

0.349

0.331

0.349

0.345

 

 

 

 

 

 

 

 

 

 

Year

C

1B

2B

3B

SS

LF

CF

RF

DH

1956

-4.9

10.2

-14.1

-0.3

-17.5

10.1

8.4

6.9

 

1957

-7.4

9.6

-13.4

-1.9

-15.6

13.4

8.1

5.8

 

1958

-7.5

9.4

-14.1

-2.3

-18.2

15.6

8.0

7.4

 

1959

-9.6

9.3

-13.1

-0.3

-16.4

12.3

7.2

8.8

 

1960

-11.0

10.8

-14.9

0.0

-15.3

13.2

7.8

7.4

 

1961

-9.8

13.8

-17.8

-1.1

-15.3

10.8

7.7

10.2

 

1962

-9.2

13.2

-17.9

-1.9

-15.3

11.6

6.2

11.8

 

1963

-7.7

10.6

-16.7

-2.0

-15.3

11.7

5.5

12.5

 

1964

-7.6

9.5

-18.0

-0.8

-13.0

12.0

4.2

12.5

 

1965

-9.4

10.0

-16.5

0.2

-14.0

11.4

4.2

12.6

 

1966

-9.0

10.4

-16.8

1.4

-14.4

9.7

4.7

12.7

 

1967

-10.8

11.5

-15.0

1.4

-16.5

11.1

4.3

12.3

 

1968

-10.1

12.2

-13.7

-0.1

-18.5

11.8

4.7

11.9

 

1969

-11.5

13.7

-13.4

-0.9

-18.1

10.8

4.4

13.1

 

1970

-10.1

13.7

-16.2

0.9

-19.4

12.7

4.3

12.3

 

1971

-9.0

14.6

-14.4

1.1

-21.6

12.1

4.2

11.4

 

1972

-8.3

16.5

-14.4

0.0

-22.5

12.6

4.4

10.0

 

1973

-8.6

15.6

-12.2

1.4

-25.0

12.4

4.8

9.5

1.2

1974

-8.4

14.4

-11.7

1.1

-23.9

12.4

4.8

9.3

-0.3

1975

-7.9

14.5

-10.8

1.2

-24.7

11.5

4.5

9.4

0.3

1976

-8.6

13.7

-11.0

1.5

-22.6

11.1

4.2

9.0

1.0

1977

-6.2

13.2

-11.9

2.1

-24.6

10.1

3.3

11.2

1.7

1978

-6.0

12.2

-12.4

2.0

-22.8

10.1

2.5

11.8

1.6

1979

-6.4

12.4

-12.2

2.0

-23.3

9.4

3.0

12.3

1.8

1980

-6.8

12.7

-12.5

1.5

-22.6

10.5

2.1

11.2

3.7

1981

-6.6

11.7

-12.4

2.7

-21.9

10.2

2.1

10.4

3.6

1982

-7.0

11.0

-11.8

3.0

-21.0

10.0

1.8

9.2

5.1

1983

-7.6

10.6

-10.8

3.4

-19.4

9.8

1.3

6.8

7.2

1984

-8.6

11.1

-10.1

2.0

-20.4

9.0

2.2

8.8

7.0

1985

-8.8

12.3

-8.7

2.0

-19.7

8.0

1.8

8.6

4.2

1986

-9.8

12.1

-8.8

2.6

-19.0

7.7

1.9

8.5

4.9

1987

-12.5

14.3

-9.2

2.8

-19.0

7.6

2.4

8.8

4.2

1988

-11.9

13.7

-9.7

2.0

-17.6

7.4

1.6

9.5

5.0

1989

-12.4

15.4

-7.6

1.2

-17.8

8.2

0.0

8.6

3.9

1990

-11.1

15.6

-7.2

-0.3

-17.7

8.3

1.3

7.5

2.7

1991

-11.8

13.8

-5.9

-0.2

-16.8

6.8

1.2

7.7

5.6

1992

-11.5

13.5

-5.4

0.4

-16.3

6.0

1.7

6.2

6.0

1993

-10.7

14.7

-6.1

0.4

-15.7

6.6

1.2

5.4

4.6

1994

-11.6

15.6

-6.6

-0.3

-16.0

6.2

0.4

7.1

6.6

1995

-11.6

16.2

-7.5

0.7

-16.9

6.4

-1.5

8.1

8.7

1996

-11.4

16.0

-9.8

0.8

-16.6

7.5

-1.5

8.3

9.9

1997

-10.3

17.2

-9.2

0.1

-17.0

5.5

-1.7

9.5

8.8

1998

-11.5

17.5

-9.1

0.0

-16.7

4.9

-1.9

10.5

9.6

1999

-11.7

16.7

-8.4

-0.5

-16.2

4.8

-1.8

10.9

9.8

2000

-11.1

17.7

-8.7

-1.8

-16.0

6.4

-2.3

10.1

9.0

2001

-12.9

17.4

-8.4

-1.5

-15.3

7.9

-2.7

10.6

7.2

2002

-13.8

17.2

-9.2

-2.6

-14.1

9.0

-2.6

11.5

6.8

2003

-13.3

16.5

-8.7

-3.9

-13.9

10.0

-2.6

11.3

6.9

2004

-13.1

15.2

-8.7

-1.5

-13.8

10.7

-2.2

9.6

5.9

2005

-13.4

15.0

-7.4

-0.3

-13.1

9.2

-2.2

8.8

5.0

2006

-12.4

15.4

-8.2

1.2

-12.6

8.9

-3.4

7.7

5.4

2007

-13.3

14.4

-6.9

1.4

-11.6

8.1

-3.5

7.6

6.2

2008

-12.7

13.9

-6.1

1.5

-11.6

7.3

-3.4

7.8

5.1

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