Mixed Bag Monday

April 13, 2020
                                                     Mixed Bag Monday

            On our main project here. . . on Friday and part of Saturday I was working an idea to perhaps re-do some of what we have done and get better results.   We base the "floor"—the zero-competence line—on the number that is four standard deviations below the norm FOR THE DECADE; for teams in the 1950s, we use the 1950s to establish the zero-competence line.  

I thought perhaps I might get better results by doing something else, specifically this.  Suppose that, rather than placing each team into one of twelve decades, I placed each team into one of 24 "peer groups".   First I divided baseball history into six twenty-year periods, 1900-1919, 1920-1939, 1940-1959, 1960-1979, 1980-1999, or 2000-2019.   Each of those six groups I divided into four "run levels", based on the runs scored/game in the league—high scoring, above average scoring, below average scoring level, low scoring.  In that way, all 241 leagues were placed into groups of leagues from (a) the same period, and (b) with a reasonably similar runs scored level. 

I thought that that might make the zero-competence level more predictable, more standard, thus stabilize the data, thus reduce the prediction error at the outcome.

I worked on it probably 15-20 hours, but it just didn’t work.  At all.   The prediction error was not only larger, it was MUCH larger; twice as large.  Some of that I could have gotten rid of by re-doing OTHER parts of the system, no doubt, but it was clear that I wasn’t going to gain anything without re-doing hundreds of hours of work, so I gave it up.  

Happens all the time.  It’s just research; anybody who does research, any field, knows that that’s the way it goes.  You invest an immense percentage of your work time in approaches that ultimately don’t lead anywhere.   It’s common.  The only difference here is that I am doing in public here things that are usually done quietly, without public documentation, so I have to report that I don’t have anything to report.   Wasted days.

 

 

 

The Learning Curve Simulator

            Then I took the rest of the weekend off to work on a couple of little fun projects.   This is based on an idea that I had decades ago, but have never written about before, I don’t think.   I had played around with it before, but for some reason this time something clicked, and I got a little bit out of it. 

            I created what I called the Learning Curve Simulator.  Suppose that you have a player who enters major league baseball with a "known" set of skills, known to us, although presumably unknown to his team, his fans, and even the athlete himself.   The athlete in any given plate appearance has a given probability of hitting a single, a given probability of hitting a double, a triple, a home run, etc.  Seven outcomes:  Walk, Single, Double, Triple, Home Run, Strikeout, Undescribed Out.   The player is defined by those seven outcomes, and those seven outcomes occur at random. 

            The thing is, though, that as the player goes through plate appearances, his skills grow and change according to his previous at-random outcomes.  If a player happens to hit a home run, then that home run becomes a part of his established skill set, and the probability that he will hit a home run increases by some very small amount.  It is unclear whether we are modeling confidence of learning here; they’re indistinguishable in practice; you can’t develop confidence in your ability to do something unless you know how to do it, and you can’t learn how to do it well and predictably until you develop some confidence.   After a player hits a home run, he gains a little bit of confidence in his ability to hit home runs, and also he gains a little bit of knowledge about how to hit a home run; it becomes a part of his skill set.  When he strikes out, he loses confidence, and becomes more likely to strike out in the next plate appearance, and in all future plate appearances. 

            The player’s "skills" or his "starting set skills" are the same from one iteration of the study to the next.   The player’s career is different every time you hit the "go" button, however, because the random numbers in the system trigger random events, and each random event becomes a predictor for subsequent events.  His career is, in a sense, a Random Walk, and I think that I have been working out how to do this since I first heard of the concept of a Random Walk, which was sometime in the 1980s.   But the computers we had then did not have the space, the memory, to construct an experiment like this.   Probably didn’t have enough space to do it until maybe five years ago, and didn’t get around to it until now. 

            Anyway, the "starting point" for each iteration was a player who, per 1,000 at bats, would get

            70 walks

            230 hits (a .247 batting average)

            162 singles  

            40 Doubles

            10 Triples

            18 Homers

            200 strikeouts, and

            500 undescribed outs. 

            Which gives him a .300 on base percentage, .370 slugging percentage, .670 OPS.   In other words, this is a marginal major leaguer, can probably have a career if he is a defensive wizard and figures it out a little at the plate.

            This player, then, is exposed a set of random numbers.  The first random number determines whether he gets the plate appearance or does not.   The formula for this is his OPS (starts out at .670), minus .550, divided by 200.  That works out to .600, so for his first plate appearance, there is a 60% probability that he will get the plate appearance, a 40% chance that he won’t.   He is not guaranteed playing time, in other words.  He gets playing time if he DESERVES playing time, doesn’t get it if he doesn’t deserve it.

            After the first plate appearance, and with each plate appearance, his OPS either goes up, or it goes down.   If his OPS goes up, his playing time increases; if his OPS goes down, his playing time decreases. 

            Then, if the player gets the at bat, another random number generates an outcome from the at bat.   That outcome then replaces one one-thousandth of his known skill set, creating a newly defined skill set. 

            The question which we are ultimately pursuing here, although we are miles away from any answers,  is "To what extent are a player’s skills malleable or plastic, and to what extent are they limited or determinate?"   Well. . .we know that player’s skills are infinitely malleable on the negative slope, because there is this thing called "death"; if you die, you lose all of your ability.  There are lots of things that can happen to you to make you a LESS GOOD player.  What we don’t really understand is to what extent you can get better. 

            So, in my first attempt to make this work, I assumed that the player’s "present skill level" was based on:

1)      His last 1,000 plate appearances, plus

2)     His last 500 plate appearances, plus

3)     His last 100 plate appearances, plus

4)     His last 10 plate appearances, and

5)     He comes to the majors with a "silent history" of 1,000 plate appearances, presumably in the minor leagues, which are now represented as identical to one another, the player getting .23 hits, .04 doubles, .01 triples, .018 homers, .07 walks, etc., in each of those plate appearances. 

In other words, when a player is new to the major leagues, he is not "new"; he has A history.   It is just not a major league history.

What we are assuming here is that what has happened to the player in the last year (500 PA) is more relevant to where he is now than what happened the previous year, and also that what has happened in the last month (100 PA) carries a little more relevance, and also that what is fresh in the player’s memory (10 PA) carries even more relevance. 

The player’s skills, then, are represented in 1,610 plate appearances, which are his last 1,000 plate appearances, but with the last 500 counted at 2, the last 100 counted at 3, and the last 10 counted at 4.  1000 + 500 + 100 + 10 = 1610.  In the player’s first major league plate appearance, his chance of hitting a home run is 18/1000, or 28.98/1610.   If he happens to hit a home run in his first PA, this increases to 32.098/1610, or 20.44/1000—but the increase is temporary.  If he doesn’t hit another home run in his next nine at bats, which he probably will not, then his production level starts to slide back to where it was. 

I don’t know to what extent you are following me here, but I’m doing the best I can to explain.   Anyway, simulating plate appearances with that set of assumptions, I generated 13-year "careers" for each player, with the last season being just a little more than a half-season.   Each 720 potential plate appearances was a season, remembering that the player doesn’t get ALL of those 720 plate appearances unless he drives his OPS over .750.   And if the player’s OPS for his last 1000 plate appearances drops below .550, then he drops out of the majors.

I was interested to see:  will some of these players, with this set of assumptions, become superstars, and post .900 career OPS?  Or will that not happen. 

What happened in the first set of test runs is that the careers quickly became unrealistic.  One thing that would happen a lot is that players would start to hit unrealistic numbers of triples—35, 40 triples in a season sometimes.  And there were other unrealistic patterns, players hitting 70 doubles in a season, but the triples one was the most notable because the expected number of triples is so low that that is the easiest one to wander outside of it’s normal bounds. 

So my first thought was, "Well, the player doesn’t really "learn" to hit triples in the same way that he learns to hit home runs or learns to take a walk.  The triple is just something that happens sometimes; it is not a predictable outcome of a given swing path."  So my first effort to fix that problem was to divert half of the "learned triples" into doubles; in other words, when a player happened to hit a triple, that increased his chance of hitting a double or a triple by a little bit, but had less impact on the triple itself.

That didn’t really do any good; that just caused some players to hit unrealistic numbers of doubles AND triples, and made those effects a little bit more muted so that the OTHER anomalies in the system would become more noticeable.   What I learned from this is:  player’s skills are not THAT malleable.  My initial set of assumptions had overstated the extent to which a player might reasonably learn from his major league experience. 

I started adding "shaping" to the player’s history; in other words, I started adding into the 1,610-plate-appearance image of the player’s current and evolving skills a small number of plate appearances that don’t change no matter what the player has done.   The game has a normal shape that no player can escape.  Adding to each plate appearance a little bit of "normal shape" reduced the likelihood that the player’s career would wander outside of those normal parameters. 

The shaping was based on the player’s starting point—that is, per 1,000 plate appearances, he would have 230 hits, 40 doubles, 10 triples, etc.   I first put into the system 100 plate appearances of "normal shaping", thus increasing the base sample for each plate appearance to 1,710 plate appearances—1,000, plus 500, plus 100, plus 10, plus 100 plate appearances of immutable shaping. 

This proved to be inadequate.  Player’s careers still wandered outside of normal parameters.  I increased the shaping to 200 PA; still not enough.  I increased it to 400 PA; still not enough.   I increase it to 600 PA; that seemed to work.   That was enough to keep the player’s skills within normal ranges.

So now the player’s skill set was defined by 2,210 plate appearances—1,000, plus 500, plus 100, plus 10, plus 600.    That is as far as the experiment went, and all of the "imaginary careers" that I will show you at the end of this article were generated using this hypothesis.  This premise, this approach; whatever you want to call it. 

These studies, primitive as they were, produced reasonably realistic-looking careers, not truly realistic, and I did learn something from doing them.   I got a sort of "first look" at the extent to which a player can adapt and re-shape his talents on the upside, and some understanding of the role.

At this point, our failures and limitations are more significant than our successes—which, again, is common in research; the most common thing you learn from doing research is why your research failed.  Anyway, the most obvious false assumption of this research is that the player’s skills remain "plastic" or "adaptable" throughout his career at the same level they are when he enters the majors.   This causes the "projected careers" of these players to very often take unprecedented and frankly improbable twists six, eight, ten years into the career.  Those same changes-of-direction might not be improbable early in the players career; they are later.  My model doesn’t build that in. 

I ran several hundred "test career projections" with this model, and captured a few of them to share with you.   The display models are not fully representative; I tented to save the ones in which the player did better.  There are a lot of very short and unsuccessful career, and there are a lot of tests in which the "player" has the full 13-year career but winds up with a career OPS in the mid-.600s.  There are not many "good" careers that develop out of this premise, and there are no great ones.  One player, whose career I failed to capture, hit 200-some home runs and wound up with a career OPS in the .770-.780 range.  But no player wound up with a career .300 average or 500 homers or anything remotely like that; I think just the one player with over 200.   The model suggests, although it certainly does not prove, that the extent to which a player may improve his skills at the major league level is limited. 

Of course, in real life, the "starting point" is a variable, not a constant.   I was attempting here to look at the question of variability FROM A CONSTANT STARTING POINT.  Among real players, the starting point is not a constant. 

I also have another little study ready to write up here, but it is getting late enough in the day that I’m not sure I will have it ready by 5 o’clock.  I’ll go ahead and post this one, and then work on the other one.   Thanks for reading.

 

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

278

52

10

1

3

13

71

.187

.223

.263

.486

 

138

32

5

0

0

7

42

.232

.269

.268

.537

 

24

4

1

0

0

1

9

.167

.200

.208

.408

 

440

88

16

1

3

21

122

.200

.236

.261

.498

 
                       
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

495

133

20

1

17

38

104

.269

.321

.416

.737

 

330

72

9

0

7

23

65

.218

.269

.309

.578

 

407

104

9

5

17

34

77

.256

.313

.428

.740

 

403

101

16

5

5

21

83

.251

.288

.352

.640

 

503

140

28

4

19

31

83

.278

.320

.463

.783

 

482

112

13

1

10

31

83

.232

.279

.326

.604

 

349

94

22

3

6

34

75

.269

.334

.401

.735

 

317

65

12

4

2

26

70

.205

.265

.287

.552

 

298

85

14

0

6

14

54

.285

.317

.393

.710

 

444

118

30

8

2

34

98

.266

.318

.383

.701

 

377

79

18

7

4

18

82

.210

.246

.326

.572

 

193

37

5

3

3

22

46

.192

.274

.295

.570

 

200

50

7

9

3

11

52

.250

.289

.420

.709

 

4798

1190

203

50

101

337

972

.248

.297

.374

.672

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

385

98

7

4

11

36

78

.255

.318

.379

.698

 

351

81

9

2

5

10

70

.231

.252

.311

.563

 

181

35

5

2

1

11

37

.193

.240

.260

.499

 

245

58

14

1

5

23

45

.237

.302

.363

.666

 

456

121

34

2

7

33

110

.265

.315

.395

.710

 

438

116

23

1

8

16

98

.265

.291

.377

.667

 

431

120

24

3

4

16

93

.278

.304

.376

.680

 

417

118

25

5

3

19

78

.283

.314

.388

.703

 

260

55

13

1

3

11

65

.212

.244

.304

.547

 

428

107

21

1

22

21

100

.250

.285

.458

.743

 

401

90

11

0

10

34

98

.224

.285

.327

.612

 

525

163

31

2

16

38

115

.310

.357

.469

.826

 

326

92

27

2

5

15

81

.282

.314

.423

.737

 

4844

1254

244

26

100

283

1068

.259

.300

.382

.682

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

444

120

20

5

7

38

101

.270

.328

.385

.713

 

548

165

28

3

6

41

107

.301

.350

.396

.746

 

355

82

12

6

0

29

79

.231

.289

.299

.588

 

208

40

5

1

4

12

56

.192

.236

.284

.520

 

205

43

7

3

4

12

54

.210

.253

.332

.585

 

220

39

8

6

2

14

66

.177

.226

.295

.522

 

261

55

15

4

5

11

54

.211

.243

.356

.599

 

198

40

13

0

1

14

36

.202

.255

.283

.538

 

162

35

6

3

0

8

44

.216

.253

.290

.543

 

305

76

17

2

6

19

70

.249

.293

.377

.670

 

273

67

13

1

2

14

79

.245

.282

.322

.605

 

326

86

25

3

2

23

88

.264

.312

.377

.690

 

298

101

20

6

2

21

54

.339

.382

.466

.849

 

3803

949

189

43

41

256

888

.250

.297

.354

.651

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

413

95

13

8

15

27

85

.230

.277

.409

.686

 

383

93

16

5

4

38

89

.243

.311

.342

.653

 

329

84

19

1

4

25

61

.255

.308

.356

.664

 

424

109

27

1

5

21

93

.257

.292

.361

.653

 

157

20

6

0

2

11

42

.127

.185

.204

.388

 

318

90

27

4

6

40

65

.283

.363

.450

.813

 

635

178

41

9

6

40

151

.280

.323

.402

.725

 

412

115

26

3

1

33

93

.279

.333

.364

.697

 

316

73

13

1

1

25

61

.231

.287

.288

.575

 

253

65

11

0

0

25

57

.257

.324

.300

.624

 

251

55

10

1

2

18

60

.219

.271

.291

.562

 

285

73

15

3

0

17

71

.256

.298

.330

.628

 

154

43

12

0

0

9

28

.279

.319

.357

.676

 

4330

1093

236

36

46

329

956

.252

.305

.355

.661

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

431

115

29

3

5

27

84

.267

.310

.383

.693

 

256

55

7

1

2

14

51

.215

.256

.273

.529

 

222

47

7

0

1

18

49

.212

.271

.257

.528

 

144

31

5

3

1

16

28

.215

.294

.312

.606

 

506

147

25

6

13

34

104

.291

.335

.441

.776

 

570

166

37

6

5

38

109

.291

.336

.404

.739

 

395

95

21

1

2

39

58

.241

.309

.314

.623

 

408

103

19

1

9

50

67

.252

.334

.370

.704

 

493

131

20

1

23

44

78

.266

.326

.450

.776

 

618

166

24

8

21

73

107

.269

.346

.435

.781

 

428

93

14

0

7

45

85

.217

.292

.299

.591

 

224

48

5

1

3

18

44

.214

.273

.286

.558

 

156

44

7

2

2

12

26

.282

.333

.391

.724

 

4851

1241

220

33

94

428

890

.256

.316

.373

.689

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

455

122

19

3

11

38

84

.268

.325

.396

.720

 

444

101

11

3

12

38

72

.227

.288

.347

.635

 

219

49

10

1

3

21

42

.224

.292

.320

.611

 

175

33

2

1

3

11

29

.189

.237

.263

.499

 

382

110

25

1

14

37

48

.288

.351

.469

.819

 

608

168

28

7

11

32

103

.276

.312

.400

.712

 

440

106

13

11

9

17

103

.241

.269

.382

.651

 

331

78

16

3

8

21

89

.236

.281

.375

.656

 

462

134

14

3

19

31

91

.290

.335

.457

.791

 

360

72

3

3

7

21

82

.200

.244

.283

.527

 

378

96

9

2

17

30

90

.254

.309

.423

.732

 

395

88

17

1

5

36

96

.223

.288

.309

.597

 

127

31

1

0

3

16

28

.244

.329

.323

.652

 

4776

1188

168

39

122

349

957

.249

.300

.377

.677

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

404

95

17

2

8

30

91

.235

.288

.347

.635

 

397

108

20

2

4

41

101

.272

.340

.363

.703

 

439

124

30

2

8

33

103

.282

.333

.415

.747

 

539

169

26

2

7

43

114

.314

.364

.408

.772

 

649

199

37

7

0

48

171

.307

.354

.385

.740

 

366

92

14

6

2

20

91

.251

.290

.339

.629

 

294

71

21

1

3

29

68

.241

.310

.350

.660

 

359

82

14

1

6

34

84

.228

.295

.323

.618

 

406

107

19

3

7

30

98

.264

.314

.377

.691

 

615

184

24

17

11

65

123

.299

.366

.447

.813

 

522

116

22

12

12

44

109

.222

.283

.379

.662

 

307

55

15

3

6

17

70

.179

.222

.306

.528

 

111

30

7

2

3

8

32

.270

.319

.450

.770

 

5408

1432

266

60

77

442

1255

.265

.320

.379

.699

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

415

113

16

7

8

18

80

.272

.303

.402

.705

 

536

159

26

11

9

31

120

.297

.335

.437

.772

 

497

117

19

5

15

27

130

.235

.275

.384

.659

 

413

102

16

8

9

35

92

.247

.306

.390

.696

 

327

72

13

2

5

18

82

.220

.261

.318

.579

 

246

48

10

4

4

11

62

.195

.230

.317

.547

 

162

31

6

2

2

13

51

.191

.251

.290

.542

 

425

135

24

5

15

25

71

.318

.356

.504

.859

 

656

183

27

7

14

53

125

.279

.333

.405

.738

 

521

135

33

4

9

38

95

.259

.309

.390

.699

 

379

88

16

3

6

30

80

.232

.289

.338

.626

 

407

113

26

2

12

43

85

.278

.347

.440

.786

 

239

49

11

0

4

20

39

.205

.266

.301

.568

 

5223

1345

243

60

112

362

1112

.258

.306

.391

.697

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

282

53

10

0

3

31

65

.188

.268

.255

.524

 

276

73

10

4

6

24

52

.264

.323

.395

.718

 

505

139

27

12

7

28

93

.275

.313

.418

.731

 

554

153

34

19

12

21

108

.276

.303

.471

.774

 

653

186

39

21

20

35

121

.285

.321

.501

.822

 

512

123

16

2

4

26

110

.240

.277

.303

.580

 

225

47

6

1

5

9

39

.209

.239

.311

.550

 

344

94

6

6

11

24

73

.273

.321

.422

.742

 

442

115

21

6

6

34

84

.260

.313

.376

.689

 

507

126

30

3

13

39

103

.249

.302

.396

.699

 

358

82

17

0

5

26

82

.229

.281

.318

.600

 

430

115

20

5

13

37

80

.267

.325

.428

.753

 

280

82

21

0

8

57

58

.293

.412

.454

.866

 

5368

1388

257

79

113

391

1068

.259

.309

.399

.708

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

329

74

16

5

1

24

60

.225

.278

.313

.591

 

217

46

10

0

4

12

44

.212

.253

.313

.567

 

244

51

18

2

0

12

55

.209

.246

.299

.545

 

171

41

9

0

1

11

25

.240

.286

.310

.596

 

235

58

8

1

0

14

39

.247

.289

.289

.579

 

349

98

17

4

2

19

71

.281

.318

.370

.688

 

243

48

9

2

2

11

61

.198

.232

.276

.508

 

394

120

30

2

10

35

78

.305

.361

.467

.828

 

646

188

52

7

9

74

119

.291

.364

.435

.799

 

672

212

61

7

21

48

121

.315

.361

.521

.882

 

669

196

32

12

14

48

145

.293

.340

.439

.780

 

566

143

22

11

8

51

105

.253

.314

.373

.687

 

167

36

5

1

4

11

31

.216

.264

.329

.593

 

4902

1311

289

54

76

370

954

.267

.319

.395

.714

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

495

132

25

4

20

32

99

.267

.311

.455

.766

 

574

152

17

1

31

46

120

.265

.319

.460

.779

 

502

121

11

0

17

43

109

.241

.301

.365

.665

 

368

90

13

2

5

37

69

.245

.314

.332

.645

 

401

103

16

1

9

41

78

.257

.326

.369

.695

 

382

87

20

1

11

21

88

.228

.268

.372

.640

 

243

49

8

1

3

8

51

.202

.227

.280

.507

 

142

28

3

1

3

14

27

.197

.269

.296

.565

 

307

74

6

6

10

23

52

.241

.294

.397

.691

 

519

145

17

0

18

54

94

.279

.347

.416

.763

 

540

135

17

2

14

58

94

.250

.323

.367

.689

 

541

163

19

3

19

44

96

.301

.354

.453

.807

 

320

87

11

2

1

28

64

.272

.330

.328

.659

 

5334

1366

183

24

161

449

1041

.256

.314

.390

.704

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

402

97

14

6

5

31

87

.241

.296

.343

.639

 

234

51

10

3

0

22

52

.218

.285

.286

.571

 

449

134

21

2

7

27

76

.298

.338

.401

.739

 

438

111

22

1

5

26

100

.253

.295

.342

.638

 

352

96

27

3

3

24

72

.273

.319

.392

.711

 

448

113

31

2

5

28

113

.252

.296

.364

.660

 

433

139

22

4

6

34

87

.321

.370

.432

.802

 

635

190

34

4

16

71

127

.299

.370

.441

.811

 

681

208

32

9

21

39

125

.305

.343

.471

.814

 

674

217

30

15

8

44

125

.322

.364

.447

.810

 

588

163

22

14

2

31

122

.277

.313

.372

.686

 

385

107

18

15

2

21

82

.278

.315

.418

.733

 

271

81

10

7

1

16

61

.299

.338

.399

.737

 

5990

1707

293

85

81

414

1229

.285

.331

.403

.734

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

426

120

35

2

8

33

78

.282

.333

.430

.763

 

650

204

41

4

17

52

114

.314

.365

.468

.832

 

651

196

24

4

14

62

134

.301

.362

.415

.777

 

555

150

17

5

7

42

101

.270

.322

.357

.678

 

251

55

7

4

2

16

54

.219

.266

.303

.569

 

280

67

10

7

4

20

71

.239

.290

.368

.658

 

469

131

30

8

10

13

96

.279

.299

.441

.740

 

645

198

45

13

17

39

129

.307

.346

.496

.843

 

683

202

50

11

21

37

143

.296

.332

.493

.825

 

549

123

32

4

13

36

112

.224

.272

.368

.640

 

375

94

30

0

7

27

100

.251

.301

.387

.688

 

367

83

19

0

5

20

68

.226

.266

.319

.585

 

135

35

6

1

3

12

22

.259

.320

.385

.705

 

6036

1658

346

63

128

409

1222

.275

.321

.417

.737

 
                       
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

456

123

27

2

14

24

92

.270

.306

.430

.736

 

630

200

38

9

15

44

129

.317

.362

.478

.840

 

645

174

30

12

17

72

144

.270

.343

.433

.776

 

433

95

18

6

5

38

94

.219

.282

.323

.606

 

487

148

38

6

7

35

116

.304

.351

.450

.800

 

563

150

32

2

6

37

164

.266

.312

.362

.674

 

518

160

34

6

7

47

149

.309

.366

.438

.805

 

525

135

36

8

2

35

122

.257

.304

.368

.671

 

408

98

25

11

4

36

117

.240

.302

.385

.687

 

519

146

29

7

7

44

130

.281

.337

.405

.742

 

457

118

25

4

3

34

116

.258

.310

.350

.660

 

481

130

38

6

4

33

114

.270

.317

.399

.716

 

263

73

10

5

2

11

52

.278

.307

.376

.683

 

6385

1750

380

84

93

490

1539

.274

.326

.404

.729

 
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

411

106

16

4

5

33

86

.258

.313

.353

.666

 

226

39

3

2

1

19

53

.173

.237

.217

.454

 

188

52

5

4

3

8

30

.277

.306

.394

.700

 

502

141

23

10

16

28

110

.281

.319

.462

.781

 

669

188

23

17

19

41

159

.281

.323

.451

.774

 

635

163

25

16

23

44

126

.257

.305

.455

.760

 

504

131

19

14

11

37

104

.260

.311

.419

.729

 

576

159

21

13

13

37

112

.276

.320

.425

.745

 

657

195

27

15

18

48

134

.297

.345

.466

.810

 

566

154

19

8

12

38

127

.272

.318

.398

.715

 

372

95

19

1

4

18

73

.255

.290

.344

.634

 

297

68

18

2

4

23

73

.229

.284

.343

.628

 

178

46

14

0

2

22

40

.258

.340

.371

.711

 

5781

1537

232

106

131

396

1227

.266

.313

.411

.724

 
                       
                       

AB

H

2B

3B

HR

BB

SO

Avg

OBA

Slug

OPS

 

313

67

13

0

4

18

78

.214

.257

.294

.551

 

167

37

6

1

1

17

30

.222

.293

.287

.581

 

214

43

13

2

0

13

56

.201

.247

.280

.527

 

153

30

6

0

1

10

42

.196

.245

.255

.500

 

143

21

3

0

2

15

42

.147

.228

.210

.438

 

35

5

0

0

0

3

9

.143

.211

.143

.353

 

1025

203

41

3

8

76

257

.198

.253

.267

.521

 
                       
                       

AB

H

2B