The Batter/Pitcher Match Up

by Dan Levitt

[ Webmaster's Note: The following article in the By the Numbers newsletter of Statistical Analysis Committee of SABR and appears here courtesy of the author. ]

One of the key questions facing baseball modelers revolves around determining of the outcome of the batter/pitcher match-up. When a .310 hitter faces a pitcher with a batting average against (OAV) of .290 what should the resulting batting average be? At first glance it may appear that the result should be the average of the two, i.e. .300. Upon reflection, however, this solution is flawed. Assuming a .260 league average, the .290 pitcher is worse than average. Therefore, the batter should hit for a higher average against this pitcher than his overall average.

Bill James in his 1983 Baseball Abstract introduces the log5 method for addressing this calculation. He credits the formula below for evaluating the batter/pitcher match-up to Dallas Adams.

Where PitAvg equals batting average against the pitcher.

In the above example this formula would be:

which evaluates to .343.

Does James' theoretical calculation hold true in actual play? The Stats Baseball Scoreboard 1996 contains a study that allows us to empirically test the validity of the above formula. Stats, in an essay titled "Who Hits Who?", looked at how batters hit in 1995 against three pitcher classes: Good (top third), Average (middle third), and Poor (bottom third). Stats' sample included all batters with at least 446 PA and pitchers who faced at least 100 batters.

The appendix to the Stats essay presented the batter data for all 136 batters with at least 446 PA. By breaking the batters into the same three groups (top, middle, and bottom third), we can create nine different comparisons in each league. That is, how do good hitters do against good pitchers, average hitters against poor pitchers, etc.

As an example of the batter calculation methodology, below I have listed the top 24 AL hitters by batting average (i.e. the top third) including how they did against the three classes of pitchers as reported by Stats. In total there were 72 AL hitters with 446 or more plate appearances and 64 in the NL.

Player

Team

AB

PA

Avg

VsGood

VsAve

VsPoor

Martinez, Edgar

Sea

511

639

.356

.285

.274

.308

Knoblauch, Chuck

Min

538

629

.333

.291

.382

.347

Salmon, Tim

Cal

537

638

.330

.310

.301

.390

NYA

460

541

.324

.276

.360

.306

Murray, Eddie

Cle

436

480

.323

.301

.312

.336

Surhoff, B.J.

Mil

415

462

.320

.277

.341

.361

Davis, Chili

Cal

424

522

.318

.248

.365

.273

Belle, Albert

Cle

546

629

.317

.264

.332

.357

Baerga, Carlos

Cle

557

600

.314

.280

.307

.342

Puckett, Kirby

Min

538

602

.314

.264

.324

.371

Thome, Jim

Cle

452

557

.314

.261

.290

.403

Seitzer, Kevin

Mil

492

570

.311

.291

.309

.363

Joyner, Wally

KC

465

550

.310

.265

.302

.353

Lofton, Kenny

Cle

481

529

.310

.286

.235

.412

Palmeiro, Rafael

Bal

554

624

.310

.273

.310

.338

Ramirez, Manny

Cle

484

571

.308

.233

.340

.333

Thomas, Frank

ChA

493

647

.308

.296

.297

.321

Naehring, Tim

Bos

433

520

.307

.263

.374

.283

Williams, Bernie

NYA

563

648

.307

.266

.347

.293

Canseco, Jose

Bos

396

450

.306

.299

.308

.302

Johnson, Lance

ChA

607

645

.306

.247

.302

.380

Rodriguez, Ivan

Tex

492

517

.303

.271

.315

.331

Clark, Will

Tex

454

537

.302

.318

.300

.289

Alomar, Roberto

Tor

517

577

.300

.258

.288

.361

Sub-Total Good Batters

.315

.276

.317

.340

Note that the above subtotals are simple averages; they are not weighted by at bats.

In the next table below I calculated the opponents batting average for each of the three pitching categories.

 OAV (Opponents Batting Average) Calculation 206AL Pitchers with 100+BFP AB H OAV OAV Top Third (69) 22,101 5,146 .233 OAV Mid Third (68) 26,917 7,340 .273 OAV Bot   Third (69) 18,054 5,533 .306 Overall for 206 67,072 18,019 .269 192 NL Pitchers with 100+ BFP AB H OAV OAV Top Third (64) 20,691 4,712 .228 OAV Mid Third (64) 26,225 6,885 .263 OAV Bot   Third (64) 18,768 5,609 .299 Overall for 192 65,684 17,206 .262

For example, the above tables indicate that when batters with an overall average of .315 face good pitchers (overall average against of .233), they will hit approximately .276. This ties out almost perfectly with James' formula which predicts a batting average of .275 when a .315 hitter faces a .233 pitcher given a league average of .269.

In fact, as the final table indicates, the actual batting averages in the eighteen situations (nine comparisons in each league) correlate extremely well with the formula. In other words, at least by this 1995 data, James' formula for predicting the outcome of the batter versus pitcher matchup holds up extremely well.

 Summary of Batter versus Pitcher Matchups Batters: All Good Average Poor Vs Pitcher Type Actual Formula Actual Formula Actual Formula Actual Formula AL All with 100+ BFP OAV .286 .315 .289 .255 Good .233 .250 .249 .276 .275 .251 .251 .223 .220 Ave .273 .290 .290 .317 .319 .292 .293 .262 .259 Poor .303 .317 .325 .340 .356 .323 .328 .287 .291 NL All with 100+ BFP OAV .283 .312 .283 .253 Good .228 .245 .247 .266 .274 .251 .247 .218 .219 Ave .263 .284 .283 .314 .313 .280 .283 .259 .253 Poor .299 .317 .321 .351 .353 .322 .321 .279 .289
Dan Levitt