Do pitchers win the expected number of games?

 

by Cyril Morong

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Click here to see my sabermetric blog called Cybermetrics

 

 

(Bill Deane pointed out to me that Pete Palmer wrote an article that appeared in the Spring 1985 NATIONAL PASTIME called "Do Clutch Pitchers Exist" which shows that deviations from expected wins are probably due to chance. A link to that site is given at the end of this paper.)

 

For the most part, yes (I looked at data from 2001-4, 1920-2000, and 1991-2000). Given the number of runs they allow and their run support, most pitchers win about the number of games that we would expect, given the relationships between runs and wins.

 

I looked at all AL pitchers who had at least 50 decisions combined during the 2000-3 seasons. Then I ran a linear regression in which their winning percentage was a function of their runs allowed per nine innings and their run support per nine innings. There were 47 pitchers. The linear relationship is

 

PCT = .517 + .0899*RS - .0958*RA

 

Where RS is run support and RA is runs allowed. The r-squared is .816, meaning that 81.6% of the variation in pitcher’s winning pct is explained by the equation. If pitcher A wins 1 more game than pitcher B, then 81.6% of that difference is explained by the equation.

 

Then I used the equation to predict how many games each pitcher was expected to win and compared that to his actual total and found the difference. The table below shows the results.

 

 

Player

Wins

Losses

DEC

PCT

RS per 9

RA per 9

EXP Pct

Diff

EXP W

W Diff

E. Milton

41

26

67

0.612

5.22

4.99

0.508

0.104

34.03

6.97

R. Clemens

63

26

89

0.708

5.76

4.23

0.630

0.078

56.03

6.97

M. Mulder

64

34

98

0.653

5.26

4.08

0.599

0.054

58.69

5.31

J. Moyer

67

31

98

0.684

5.57

4.00

0.635

0.049

62.22

4.78

R. Halladay

50

24

74

0.676

5.75

4.41

0.611

0.065

45.23

4.77

C. Sabathia

43

25

68

0.632

5.22

4.40

0.565

0.067

38.44

4.56

J. Halama

33

26

59

0.559

5.58

5.38

0.504

0.055

29.74

3.26

D. Burba

31

21

52

0.596

6.20

5.59

0.540

0.057

28.06

2.94

K. Rogers

44

36

80

0.550

5.38

5.06

0.517

0.033

41.32

2.68

K. Escobar

34

39

73

0.466

4.18

4.82

0.431

0.035

31.46

2.54

J. Washburn

46

33

79

0.582

4.69

4.02

0.554

0.028

43.76

2.24

S. Schoeneweis

29

31

60

0.483

5.18

5.44

0.461

0.022

27.66

1.34

B. Radke

50

42

92

0.543

5.04

4.59

0.531

0.013

48.84

1.16

J. Baldwin

28

22

50

0.560

5.82

5.25

0.537

0.023

26.86

1.14

T. Hudson

69

31

100

0.690

5.70

3.65

0.680

0.010

68.02

0.98

P. Martinez

59

17

76

0.776

5.38

2.39

0.771

0.005

58.63

0.37

D. Wells

59

29

88

0.670

6.42

4.46

0.667

0.003

58.72

0.28

K. Lohse

31

26

57

0.544

5.53

4.95

0.540

0.004

30.80

0.20

I. Valdez

25

33

58

0.431

4.25

4.92

0.428

0.003

24.82

0.18

F. Garcia

55

35

90

0.611

5.53

4.22

0.610

0.001

54.87

0.13

A. Pettitte

68

32

100

0.680

6.71

4.59

0.681

-0.001

68.05

-0.05

S. Sparks

29

30

59

0.492

5.23

5.13

0.496

-0.005

29.27

-0.27

C. Carpenter

25

28

53

0.472

5.53

5.57

0.480

-0.008

25.43

-0.43

M. Mussina

63

44

107

0.589

4.93

3.83

0.593

-0.004

63.44

-0.44

R. Reed

25

25

50

0.500

5.21

4.94

0.512

-0.012

25.62

-0.62

R. Ortiz

52

39

91

0.571

6.06

5.04

0.579

-0.008

52.71

-0.71

J. Mays

36

44

80

0.450

4.75

5.01

0.465

-0.015

37.17

-1.17

A. Sele

47

35

82

0.573

5.91

4.80

0.589

-0.015

48.26

-1.26

E. Loaiza

51

43

94

0.543

5.47

4.72

0.556

-0.014

52.31

-1.31

J. Johnson

25

36

61

0.410

4.20

4.83

0.432

-0.022

26.35

-1.35

K. Appier

37

32

69

0.536

5.64

4.86

0.558

-0.022

38.52

-1.52

M. Buehrle

53

35

88

0.602

5.57

4.15

0.620

-0.017

54.53

-1.53

J. Pineiro

36

20

56

0.643

5.59

3.62

0.673

-0.030

37.71

-1.71

J. Suppan

29

39

68

0.426

4.87

5.25

0.452

-0.026

30.74

-1.74

F. Castillo

26

29

55

0.473

4.95

4.75

0.507

-0.034

27.89

-1.89

T. Sturtze

27

38

65

0.415

4.94

5.39

0.445

-0.030

28.96

-1.96

R. Helling

35

32

67

0.522

6.22

5.46

0.553

-0.031

37.07

-2.07

T. Wakefield

37

34

71

0.521

5.28

4.60

0.551

-0.030

39.14

-2.14

C. Lidle

37

37

74

0.500

5.44

4.96

0.531

-0.031

39.30

-2.30

S. Ponson

35

38

73

0.479

4.95

4.70

0.512

-0.032

37.36

-2.36

C. Finley

28

29

57

0.491

5.56

4.99

0.539

-0.048

30.73

-2.73

J. Weaver

42

51

93

0.452

4.70

4.79

0.481

-0.030

44.76

-2.76

D. Davis

25

27

52

0.481

5.92

5.33

0.539

-0.058

28.04

-3.04

J. Garland

34

40

74

0.459

5.39

5.15

0.508

-0.049

37.61

-3.61

B. Colon

54

37

91

0.593

5.49

3.94

0.634

-0.040

57.66

-3.66

B. Zito

61

29

90

0.678

6.03

3.51

0.723

-0.045

65.09

-4.09

D. Lowe

47

29

76

0.618

5.62

3.63

0.674

-0.056

51.22

-4.22

 

 

 

Wins and losses are each pitcher’s total for the two seasons. DEC is total decisions over the two seasons. RS per 9 is his run support over the two seasons. RA per 9 is how many runs he allowed per 9 innings over the two seasons. EXP Pct is each pitcher’s expected winning percentage based on the equation above. The “Diff” column is the difference between a pitcher’s actual pct and EXP Pct. EXP W is how many wins each pitcher should win according to the formula and the “W Diff” column shows the difference between his expected wins and his actual total. A positive difference means the pitcher won more games than expected.

 

No pitcher won even as many as eight more games than expected, which is less than two wins per season. 39 of the 47 pitchers were predicted to within 4 wins of their actual total (which is less than 1 win per season!). One of the two highest, Clemens and, probably benefited from the good Yankee bullpen, especially Mariano Rivera. So again, pitchers win about the number of games that we expect based on runs allowed and run support. Probably if I looked at more years worth of data, with randomness or luck playing less of a role, the relationship would get even closer.

 

The graph below shows the relationship between a pitcher’s expected winning percentage and his actual percentage.

 

 

So the higher the winning percentage that we expect, the higher we actually get.

 

Using the Pythagorean Approach of Bill James

 

 

Bill James came up with what he called the Pythagorean formula for predicting a team’s winning percentage. It is runs score squared divided by the sum of runs scored squared and runs allowed or

 

(Runs Scored)2/( Runs Scored2 + Runs Allowed2) = Pct

 

I also used this formula to predict each pitcher’s winning pct. The correlation between the actual and Pythagorean pct was .901 (a perfect correlation is 1.00). This is just a little lower than the correlation I got between the predicted percentage based on the regression analysis mentioned above and the actual (.903).

 

The graph below shows the actual percentage vs. Pythagorean percentage.

 

 

Data from 1920-2000

 

I used the Pythagorean formula to predict wins for the 70 pitchers who had at least 3000 IP between 1920-2000.  For run support, I assumed that it equaled the weighted average of runs scored per game for the teams each pitcher played with (weighted by each season’s IP).

 

The correlation between actual winning percentage and the predicted percentage was .879. This is a little low compared to the results above. But still very high considering that I don’t have the actual run support. The correlation for the top 70 in IP is .928. So the more innings, the closer the relationship and the less that luck matters.

 

The table below describes the results.

 

 

Pitcher

W

L

R/G

RS

PCT

PYTH

Pred W

Diff

Per 30G

Mike Torrez

185

160

4.44

4.38

0.536

0.493

170.17

14.831

1.316

Lew Burdette

203

144

4.11

4.49

0.585

0.545

189.01

13.989

1.231

Joe Niekro

221

204

4.07

3.97

0.520

0.488

207.58

13.421

1.011

Bob Welch

211

146

3.81

4.29

0.591

0.559

199.56

11.436

0.999

Burleigh Grimes

236

173

4.48

4.94

0.577

0.549

224.55

11.447

0.886

Rick Wise

188

181

4.19

4.05

0.509

0.483

178.28

9.719

0.839

Earl Whitehill

218

185

5.10

5.26

0.541

0.516

207.75

10.247

0.776

Milt Pappas

209

164

3.76

4.04

0.560

0.536

199.98

9.018

0.764

Jack Morris

254

186

4.27

4.78

0.577

0.556

244.69

9.314

0.658

Orel Hershiser

204

150

3.93

4.40

0.576

0.556

196.92

7.076

0.610

Jerry Reuss

220

191

4.17

4.31

0.535

0.517

212.46

7.541

0.555

Bucky Walters

198

160

3.89

4.19

0.553

0.537

192.11

5.889

0.512

Freddie Fitzsimmons

217

146

4.20

4.95

0.598

0.581

211.06

5.935

0.497

Sad Sam Jones

197

181

4.74

4.81

0.521

0.507

191.67

5.333

0.441

Dennis Martinez

245

193

4.13

4.54

0.559

0.547

239.54

5.456

0.368

Tommy John

288

231

3.85

4.21

0.555

0.544

282.14

5.857

0.336

Ted Lyons

260

230

4.45

4.64

0.531

0.521

255.37

4.630

0.300

Juan Marichal

243

142

3.41

4.40

0.631

0.625

240.48

2.518

0.194

Eppa Rixey

190

170

4.09

4.28

0.528

0.524

188.52

1.484

0.126

Early Wynn

300

244

4.02

4.42

0.551

0.548

297.97

2.031

0.120

Charlie Hough

216

216

4.28

4.25

0.500

0.497

214.75

1.248

0.089

Jim Kaat

283

237

4.05

4.40

0.544

0.542

281.72

1.276

0.076

Mel Harder

223

186

4.50

4.92

0.545

0.544

222.48

0.525

0.041

Catfish Hunter

224

166

3.60

4.17

0.574

0.573

223.62

0.383

0.030

Mickey Lolich

217

191

3.80

4.05

0.532

0.532

217.04

-0.045

-0.003

Steve Carlton

329

244

3.67

4.27

0.574

0.574

329.12

-0.119

-0.006

Vida Blue

209

161

3.65

4.17

0.565

0.566

209.32

-0.321

-0.026

Phil Niekro

318

274

3.89

4.20

0.537

0.538

318.58

-0.578

-0.029

Bob Feller

266

162

3.66

4.71

0.621

0.623

266.64

-0.640

-0.045

Doyle Alexander

194

174

4.12

4.37

0.527

0.530

194.97

-0.966

-0.077

Jim Perry

215

174

3.85

4.31

0.553

0.556

216.10

-1.098

-0.090

Tom Seaver

311

205

3.15

3.91

0.603

0.606

312.72

-1.717

-0.097

Curt Simmons

193

183

4.17

4.33

0.513

0.519

195.21

-2.215

-0.179

Jerry Koosman

222

209

3.77

3.95

0.515

0.523

225.33

-3.331

-0.234

Claude Osteen

196

195

3.73

3.80

0.501

0.509

199.09

-3.091

-0.241

Jesse Haines

210

158

4.37

5.13

0.571

0.579

213.09

-3.087

-0.260

Whitey Ford

236

106

3.14

4.81

0.690

0.701

239.60

-3.604

-0.307

Danny Darwin

171

182

4.27

4.23

0.484

0.495

174.87

-3.873

-0.347

Robin Roberts

286

245

3.77

4.17

0.539

0.550

292.21

-6.213

-0.358

Luis Tiant

229

172

3.61

4.28

0.571

0.584

234.04

-5.044

-0.391

Rick Reuschel

214

191

3.79

4.12

0.528

0.541

219.18

-5.179

-0.394

Larry Jackson

194

183

3.88

4.10

0.515

0.528

198.87

-4.869

-0.403

Don Sutton

324

256

3.58

4.16

0.559

0.574

332.93

-8.935

-0.457

Lefty Grove

300

141

3.64

5.54

0.680

0.698

307.86

-7.859

-0.539

Jim Palmer

268

152

3.18

4.41

0.638

0.657

276.12

-8.119

-0.555

Tom Zachary

183

186

4.47

4.59

0.496

0.513

189.40

-6.398

-0.565

Frank Tanana

240

236

4.10

4.29

0.504

0.523

248.80

-8.801

-0.567

Paul Derringer

223

212

4.08

4.34

0.513

0.531

230.86

-7.863

-0.582

Nolan Ryan

324

292

3.64

3.99

0.526

0.545

335.98

-11.978

-0.600

Bobo Newsom

211

222

4.57

4.63

0.487

0.507

219.51

-8.512

-0.611

Dutch Leonard

191

181

4.00

4.28

0.513

0.534

198.66

-7.659

-0.642

Roger Clemens

260

142

3.40

4.83

0.647

0.669

268.81

-8.809

-0.649

Ferguson Jenkins

284

226

3.71

4.34

0.557

0.578

294.88

-10.879

-0.653

Jim Bunning

224

184

3.66

4.24

0.549

0.574

234.23

-10.233

-0.735

Greg Maddux

240

135

3.24

4.56

0.640

0.664

249.13

-9.132

-0.743

Bob Gibson

251

174

3.29

4.17

0.591

0.616

261.81

-10.810

-0.751

Gaylord Perry

314

265

3.58

4.12

0.542

0.570

329.79

-15.790

-0.797

Bob Friend

197

230

4.12

4.03

0.461

0.489

208.89

-11.888

-0.889

Waite Hoyt

233

176

4.28

5.24

0.570

0.600

245.36

-12.359

-0.912

Murry Dickson

172

181

4.22

4.38

0.487

0.519

183.09

-11.090

-0.981

Don Drysdale

209

166

3.39

4.08

0.557

0.591

221.76

-12.755

-1.003

Warren Spahn

363

245

3.46

4.52

0.597

0.630

383.26

-20.257

-1.043

Charlie Root

201

160

4.13

5.00

0.557

0.594

214.59

-13.594

-1.148

Carl Hubbell

253

154

3.46

4.88

0.622

0.665

270.81

-17.812

-1.339

Larry French

197

171

4.11

4.83

0.535

0.580

213.37

-16.370

-1.402

Bert Blyleven

287

250

3.67

4.34

0.534

0.583

313.07

-26.071

-1.416

Billy Pierce

211

169

3.61

4.50

0.555

0.609

231.46

-20.463

-1.672

Red Ruffing

273

225

4.39

5.44

0.548

0.605

301.50

-28.503

-1.772

Dolf Luque

178

172

3.95

4.51

0.509

0.566

198.20

-20.200

-1.807

Dennis Eckersley

197

171

3.79

4.60

0.535

0.596

219.38

-22.379

-1.839

 

 

RS is run support or the runs per game scored by each pitcher’s teams. PYTH is their Pythagorean percentage. Pred W is how many games that the Pythagorean formula predicts they would win. Diff is the difference between the actual number of games a pitcher won and Pred W, with positive meaning that they won more than expected. Per 30G is how many more games they won or lost per 30 complete games (270 IP) or about a full season.

 

57 of the 70 were predicted to within 1 win per season. So again, pitchers are winning about the expected number of games. If I had the actual run support, the prediction would probably be more accurate.

 

It seems like many of the pitchers at the bottom of the list (who did not win as many games as expected) may have been the ace or number one starter on their staffs. They may have often faced the ace of other teams, so their run support may have been a little lower than what I have assumed since those other aces would hold teams to fewer runs than normal. The reverse may be true for the pitchers at the top of the list.

 

Data from 1991-2000

 

In the table below, I looked at pitchers from 1991-2000.

 

I took all of the pitchers who had at least 1000 IP from 1991-2000. Then I looked for their data in my STATS, INC Player Profiles books from 1996 and 2001, to cover the years 1991-2000. Those books gave 5 year totals. If a pitcher did not appear in both editions, he was left out. Also left out were pitchers who pitched so much in relief that they had no column for run support. That left 59 pitchers (for Gooden, I used the years 1990-94 and 1996-2000). Those books gave the run support data. The runs allowed data came from the Lee Sinins Sabermetric Encyclopedia.

 

The EXP Pct comes from the regression I ran on these pitchers which gave the following equation

 

Pct = .605 + .074*RS - .097*RA

 

The Diff Per Season column is how many more games they won or lost per season, with a season being 225 IP. So I divided their IP in this period by 225 to get the number of seasons. All but five pitchers are within 1 win per season.

 

Pitcher

Wins

Losses

DEC

PCT

RS per 9

RA per 9

EXP Pct

Exp W

Diff Per Season

Joey Hamilton

64

53

117

0.547

4.37

4.46

0.495

57.89

1.29

Bobby Jones

74

56

130

0.569

4.85

4.60

0.516

67.08

1.28

Kenny Rogers

114

81

195

0.585

5.35

4.71

0.543

105.83

1.05

Ramon Martinez

108

73

181

0.597

5.04

4.29

0.561

101.59

0.95

Randy Johnson

155

71

226

0.686

5.06

3.40

0.648

146.54

0.91

David Wells

136

89

225

0.604

5.55

4.56

0.573

128.89

0.83

Jaime Navarro

101

111

212

0.476

4.93

5.39

0.446

94.50

0.81

Jamie Moyer

97

62

159

0.610

5.62

4.54

0.579

92.11

0.78

Armando Reynoso

67

56

123

0.545

5.48

5.07

0.517

63.65

0.73

Scott Karl

54

56

110

0.491

5.10

5.34

0.464

50.99

0.68

John Burkett

115

100

215

0.535

5.01

4.80

0.509

109.49

0.66

Tom Glavine

175

84

259

0.676

5.22

3.46

0.655

169.57

0.54

Pedro Martinez

125

56

181

0.691

4.80

2.97

0.671

121.49

0.50

Pete Schourek

65

72

137

0.474

4.60

5.01

0.458

62.79

0.45

Orel Hershiser

105

85

190

0.553

5.14

4.62

0.536

101.82

0.43

Kevin Brown

144

94

238

0.605

4.52

3.62

0.588

139.84

0.41

Greg Maddux

180

82

262

0.687

4.63

2.85

0.670

175.65

0.41

Denny Neagle

105

69

174

0.603

5.33

4.20

0.591

102.91

0.31

Dave Burba

95

70

165

0.576

5.51

4.61

0.565

93.18

0.30

Mark Clark

74

71

145

0.510

5.10

4.96

0.501

72.57

0.26

Roger Clemens

144

91

235

0.613

4.65

3.55

0.603

141.81

0.23

Todd Stottlemyre

114

87

201

0.567

5.39

4.58

0.559

112.36

0.21

Aaron Sele

92

63

155

0.594

6.28

4.96

0.587

91.03

0.17

Pat Hentgen

120

88

208

0.577

5.55

4.58

0.571

118.69

0.17

Pedro Astacio

95

82

177

0.537

5.30

4.78

0.532

94.19

0.12

Mike Mussina

147

81

228

0.645

5.40

3.74

0.640

146.02

0.11

Kevin Tapani

120

101

221

0.543

5.24

4.66

0.540

119.38

0.07

Scott Erickson

127

112

239

0.531

5.37

4.86

0.530

126.68

0.04

Charles Nagy

121

89

210

0.576

5.71

4.65

0.575

120.83

0.02

Cal Eldred

74

67

141

0.525

5.21

4.80

0.524

73.89

0.02

Andy Pettitte

100

55

155

0.645

6.27

4.35

0.647

100.25

-0.04

Mark Gardner

87

76

163

0.534

5.61

4.97

0.537

87.52

-0.08

Al Leiter

99

71

170

0.582

4.90

3.93

0.585

99.48

-0.08

Chuck Finley

133

110

243

0.547

5.02

4.38

0.551

133.83

-0.09

Darryl Kile

112

104

216

0.519

5.14

4.76

0.523

112.89

-0.11

Tim Belcher

106

111

217

0.488

5.03

4.97

0.494

107.11

-0.14

Mike Hampton

85

53

138

0.616

5.55

4.02

0.625

86.19

-0.21

Andy Ashby

84

87

171

0.491

4.64

4.61

0.500

85.51

-0.22

Curt Schilling

109

89

198

0.551

4.19

3.63

0.562

111.18

-0.27

Ken Hill

105

86

191

0.550

5.16

4.38

0.561

107.10

-0.28

Kirk Rueter

81

48

129

0.628

6.55

4.63

0.639

82.43

-0.30

Juan Guzman

91

79

170

0.535

5.20

4.55

0.547

93.02

-0.31

Jon Lieber

60

69

129

0.465

4.74

4.91

0.478

61.72

-0.34

David Cone

131

89

220

0.595

5.11

3.82

0.612

134.53

-0.41

Sterling Hitchcock

61

62

123

0.496

5.37

5.04

0.512

62.98

-0.42

Andy Benes

127

114

241

0.527

4.80

4.23

0.549

132.19

-0.57

Alex Fernandez

102

82

184

0.554

5.04

4.11

0.578

106.34

-0.58

Pete Harnisch

94

78

172

0.547

4.95

4.10

0.572

98.38

-0.61

Shane Reynolds

86

69

155

0.555

5.27

4.26

0.580

89.93

-0.65

Kevin Appier

123

93

216

0.569

5.08

3.95

0.597

128.92

-0.71

Hideo Nomo

69

61

130

0.531

5.01

4.27

0.560

72.85

-0.75

Frank Castillo

66

79

145

0.455

4.81

4.88

0.486

70.50

-0.78

Jeff Fassero

100

91

191

0.524

5.10

4.42

0.553

105.59

-0.79

Ismael Valdes

63

61

124

0.508

4.38

3.94

0.546

67.66

-0.93

Brad Radke

78

84

162

0.481

4.88

4.64

0.515

83.49

-0.94

Steve Trachsel

68

84

152

0.447

4.69

4.80

0.485

73.72

-0.96

Omar Olivares

70

76

146

0.479

5.36

4.93

0.522

76.24

-0.98

Pat Rapp

65

79

144

0.451

5.34

5.13

0.501

72.18

-1.33

Dwight Gooden

75

66

141

0.532

5.35

3.99

0.613

86.43

-2.01

 

 

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Additional Source: ESPN website