Deviants At Work

June 11, 2013

                The standard deviation of OPS for all players in baseball history with 300 plate appearances in a season is .111; the average is .743 with a standard deviation of .111.

                On that scale the highest OPS of all time (1.477 by Bonds in 2002) is 6.59 Standard Deviations above the norm. ..quite an astonishing figure, and a number that would probably never occur if OPS had a "normal" bell-shaped curve.   The lowest OPS ever (300 or more Plate Appearances) was .310 by Will White (primarily a pitcher) in 1879.   The lowest OPS ever by a non-pitcher was .319, by Bill Bergen in 1909.  White’s figure is 3.89 standard deviations below the norm; Bergen’s is 3.81.

                Of course, some of the "spread" or deviation is accounted for by fluctuations in year-to-year norms.    This chart gives the average OPS (for a player with 300 Plate Appearances) and the Standard Deviations of OPS for every year since 1876.  The normal standard deviation now is .094:

YEAR

Count

Avg OPS

St Dev

1876

15

.727

.120

1879

41

.645

.126

       

1880

44

.631

.100

1881

44

.675

.096

1882

75

.659

.106

1883

117

.655

.106

1884

167

.654

.123

1885

103

.658

.113

1886

124

.665

.124

1887

121

.740

.121

1888

119

.638

.103

1889

118

.722

.102

1890

185

.719

.115

       

1891

122

.700

.105

1892

106

.669

.097

1893

89

.766

.102

1894

93

.840

.123

1895

91

.789

.123

1896

90

.773

.107

1897

99

.764

.106

1898

102

.703

.095

1899

105

.736

.105

       

1900

62

.743

.096

1901

129

.717

.117

1902

122

.703

.107

1903

129

.693

.103

1904

141

.644

.099

1905

135

.659

.094

1906

134

.651

.095

1907

133

.647

.079

1908

135

.626

.088

1909

134

.650

.091

       

1910

133

.680

.092

1911

126

.728

.107

1912

123

.734

.095

1913

126

.706

.097

1914

196

.696

.099

1915

199

.683

.089

1916

126

.672

.085

1917

136

.663

.088

1918

111

.678

.100

1919

115

.706

.087

       

1920

135

.733

.121

1921

133

.780

.111

1922

134

.780

.114

1923

139

.769

.122

1924

141

.769

.110

1925

136

.803

.114

1926

134

.774

.105

1927

131

.773

.119

1928

130

.782

.120

1929

132

.810

.124

       

1930

135

.822

.142

1931

137

.768

.119

1932

139

.772

.112

1933

133

.742

.111

1934

140

.771

.112

1935

141

.770

.100

1936

140

.786

.120

1937

142

.772

.122

1938

132

.778

.112

1939

143

.784

.106

       

1940

138

.763

.115

1941

134

.750

.118

1942

134

.711

.102

1943

131

.701

.088

1944

135

.718

.110

1945

132

.721

.096

1946

137

.729

.103

1947

135

.749

.101

1948

136

.761

.104

1949

134

.766

.103

       

1950

135

.791

.103

1951

131

.766

.096

1952

136

.731

.093

1953

134

.771

.104

1954

134

.757

.112

1955

135

.770

.109

1956

132

.772

.110

1957

139

.754

.113

1958

131

.763

.105

1959

135

.760

.096

       

1960

135

.751

.097

1961

157

.773

.112

1962

173

.761

.093

1963

171

.719

.095

1964

184

.727

.105

1965

174

.723

.102

1966

173

.728

.097

1967

174

.707

.106

1968

167

.679

.099

1969

199

.735

.114

       

1970

212

.752

.118

1971

209

.722

.101

1972

200

.707

.102

1973

227

.729

.101

1974

218

.718

.092

1975

216

.727

.098

1976

221

.705

.089

1977

238

.752

.105

1978

229

.728

.095

1979

238

.753

.102

       

1980

240

.739

.097

1981

156

.730

.093

1982

230

.738

.094

1983

245

.740

.090

1984

237

.729

.092

1985

229

.742

.087

1986

242

.745

.087

1987

240

.774

.104

1988

237

.722

.089

1989

240

.721

.088

       

1990

236

.739

.089

1991

230

.735

.092

1992

245

.722

.091

1993

250

.765

.100

1994

209

.796

.115

1995

232

.790

.106

1996

258

.797

.112

1997

251

.784

.106

1998

272

.783

.105

1999

281

.804

.110

       

2000

274

.814

.118

2001

267

.786

.118

2002

271

.774

.112

2003

272

.785

.107

2004

276

.793

.101

2005

284

.774

.093

2006

271

.798

.098

2007

279

.784

.098

2008

281

.776

.092

2009

284

.776

.092

       

2010

270

.762

.094

2011

265

.749

.094

2012

265

.757

.094

 

                The highest-ever norm for OPS was .840, in 1894, and the highest standard deviation was .142, in 1930.  1894 and 1930 were both huge hitter’s seasons; 1930 also had the second-highest OPS norm of all time, .822.

                With this information we can easily state each player’s OPS in terms of standard deviations above or below the norm.    This makes surprisingly little difference at the extremes.     The average OPS in 2002 was .774, but the standard deviation was only .112—almost the same as the overall historical average--so Bonds was still 6.30 standard deviations above the norm that year, and 6.20 above the norm in 2004.     It is interesting to look at Bonds and the steroid era in this light.   In 1998, when McGwire hit 70 home runs, his OPS was 4.17 standard deviations above the norm for that season.   This made him the first player in 41 years to be four standard deviations above the norm, the last previous being Ted Williams in 1957.    At that time McGwire was only the 12th "player" in history to be four standard deviations above the norm.   The others were Babe Ruth (7 times) and Ted Williams (4 times).

                Then came Bonds; he was +5.02 in 2001, +6.30 in 2002, +4.62 in 2003, and +6.20 in 2004.   Do you know what it means to be six standard deviations above the norm?   In a normally distributed population, only one data point in 500 million would be six standard deviations above the norm.   There are only 22,500 player/seasons in baseball history with 300 plate appearances.    Even though OPS is not normally distributed—nothing in baseball is—it is extraordinary to have data points which are six standard deviations above the norm.   The public just revolted; they couldn’t deal with those kind of numbers, although, of course, they weren’t looking at the numbers in that form.

                On the other end of the scale Bergen is still the worst, even normalizing for the year, and his number doesn’t change very much, either.    With a .319 OPS in 1909, Bergen was 3.91 standard deviations below the norm.    The average OPS for 1909 was just .650, but the standard deviation was .091, so, even normalizing for the era, Bergen is still 3.63 standard deviations below the norm, still the worst ever, and not really much less bad in this form than in the other.

                The only seasons in history which are 3 standard deviations below the norm, year adjusted, are Bill Bergen in 1906 (-3.08) and Bill Bergen in 1908 (-3.63).

                Here’s an interesting note for a 1980s Royals fan.   In 1985 one of the Royals’ shortstops was Onix Concepcion, who had a .500 OPS, which was 2.76 standard deviations below the norm for 1985.  At that time that was the 10th-worst figure of all time.   It would now be the 12th-worst.  In 1986 the Royals replaced Concepcion with Angel Salazar.   In 1987 Salazar had an OPS of .465, which was 2.98 standard deviations below the norm—the third-worst figure of all time.

                Through 2012 there have been 10,656 player/seasons which were above the league norm, and 11,808 which were below the league norm.     3,424 seasons have been at least one standard deviation above the norm, and 3,377 at least 1.0000 standard deviations below the norm.    69.8% of all seasons have been within one standard deviation of the norm.

                In history (through 2011):

                2 seasons have been 6.00 standard deviations above the norm (both by Bonds),

                5 seasons have been 5.00 standard deviations above the norm (all by Bonds and Ruth),

                16 seasons have been 4.00 standard deviations above the norm,

                118 seasons have been 3.00 standard deviations above the norm,

                732 seasons have been 2.00 standard deviations above the norm,

                3424 seasons have been at least 1.00 standard deviation above the norm,

                3377 seasons have been at least 1.00 standard deviation below the norm,

                263 seasons have been 2.00 standard deviations below the norm,

                2 seasons (both by Bill Bergen) have been 3.00 standard deviations below the norm.

 

                The "elimination of the norms" discussed by the late, great Stephen Jay Gould is observable in the data, but not terribly significant.   From 1876 to 1919 the average OPS was .696, and the average standard deviation was .103, so the deviation was 15% of the norm.   From 1920 to 1968 the average OPS was .757 and the average standard deviation was .108, so the deviation was 14% of the norm.   From 1969 through 2012 the average OPS was .756, and the average standard deviation was .100, so the deviation was 13% of the norm.      In the 21st century the standard deviation has been 12% of the norm.

                Let’s look at the careers of twelve players, stating their OPS as standard deviations above and below the norm. ..I’ll do Cobb, Ruth, Bonds, Hornsby, Mantle, Musial, Miguel Cabrera, Mazeroski, Bergen, Hal Lanier, Tim Wallach and Steve Garvey, and I’ll put those in chronological order.    What the heck; I’ll do Norm Cash, too; I should always do Norm Cash.   And Bill Buckner.    And Bill Bruton.    OK, that’s 15.   These numbers are not park- or position-normalized, so whoever led the league in OPS would have the highest OPS in terms of standard deviations above the norm.    We’re not including any seasons with less than 300 plate appearances, since the study is of players with 300 or more plate appearances in a season.

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Bill

Bergen

1901

1

17

.179

.433

-2.42

Bill

Bergen

1902

0

36

.180

.438

-2.48

Bill

Bergen

1904

0

12

.182

.411

-2.37

               

Bill

Bergen

1906

0

19

.159

.359

-3.08

Bill

Bergen

1908

0

15

.175

.404

-2.52

Bill

Bergen

1909

1

15

.139

.319

-3.63

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Ty

Cobb

1906

1

34

.316

.749

+1.04

Ty

Cobb

1907

5

119

.350

.853

+2.59

Ty

Cobb

1908

4

108

.324

.842

+2.45

Ty

Cobb

1909

9

107

.377

.947

+3.25

               

Ty

Cobb

1910

8

91

.383

1.008

+3.56

Ty

Cobb

1911

8

127

.420

1.088

+3.35

Ty

Cobb

1912

7

83

.409

1.040

+3.22

Ty

Cobb

1913

4

67

.390

1.002

+3.06

Ty

Cobb

1914

2

57

.368

.979

+2.85

               

Ty

Cobb

1915

3

99

.369

.973

+3.25

Ty

Cobb

1916

5

68

.371

.944

+3.19

Ty

Cobb

1917

6

102

.383

1.014

+3.99

Ty

Cobb

1918

3

64

.382

.955

+2.78

Ty

Cobb

1919

1

70

.384

.944

+2.72

               

Ty

Cobb

1920

2

63

.334

.867

+1.11

Ty

Cobb

1921

12

101

.389

1.048

+2.42

Ty

Cobb

1922

4

99

.401

1.026

+2.16

Ty

Cobb

1923

6

88

.340

.882

+0.93

Ty

Cobb

1924

4

74

.338

.866

+0.88

               

Ty

Cobb

1925

12

102

.378

1.066

+2.29

Ty

Cobb

1927

5

93

.357

.912

+1.18

Ty

Cobb

1928

1

40

.323

.809

+0.23

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Rogers

Hornsby

1916

6

65

.313

.814

+1.66

Rogers

Hornsby

1917

8

66

.327

.868

+2.33

Rogers

Hornsby

1918

5

60

.281

.764

+0.86

Rogers

Hornsby

1919

8

71

.318

.814

+1.24

               

Rogers

Hornsby

1920

9

94

.370

.990

+2.13

Rogers

Hornsby

1921

21

126

.397

1.097

+2.86

Rogers

Hornsby

1922

42

152

.401

1.181

+3.53

Rogers

Hornsby

1923

17

83

.384

1.086

+2.59

Rogers

Hornsby

1924

25

94

.424

1.203

+3.95

               

Rogers

Hornsby

1925

39

143

.403

1.245

+3.86

Rogers

Hornsby

1926

11

93

.317

.851

+0.72

Rogers

Hornsby

1927

26

125

.361

1.035

+2.21

Rogers

Hornsby

1928

21

94

.387

1.130

+2.90

Rogers

Hornsby

1929

39

149

.380

1.139

+2.64

               

Rogers

Hornsby

1931

16

90

.331

.996

+1.92

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Babe

Ruth

1918

11

66

.300

.966

+2.89

Babe

Ruth

1918

29

114

.322

1.114

+4.37

               

Babe

Ruth

1920

54

137

.376

1.379

+5.36

Babe

Ruth

1921

59

171

.378

1.359

+5.22

Babe

Ruth

1922

35

96

.315

1.106

+2.87

Babe

Ruth

1923

41

131

.393

1.309

+4.42

Babe

Ruth

1924

46

121

.378

1.252

+4.39

               

Babe

Ruth

1925

25

66

.290

.936

+1.16

Babe

Ruth

1926

47

146

.372

1.253

+4.54

Babe

Ruth

1927

60

164

.356

1.258

+4.09

Babe

Ruth

1928

54

142

.323

1.172

+3.25

Babe

Ruth

1929

46

154

.345

1.128

+2.55

               

Babe

Ruth

1930

49

153

.359

1.225

+2.84

Babe

Ruth

1931

46

163

.373

1.194

+3.59

Babe

Ruth

1932

41

137

.341

1.146

+3.33

Babe

Ruth

1933

34

103

.301

1.023

+2.54

Babe

Ruth

1934

22

84

.288

.985

+1.90

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Stan

Musial

1942

10

72

.315

.888

+1.74

Stan

Musial

1943

13

81

.357

.988

+3.27

Stan

Musial

1944

12

94

.347

.990

+2.48

               

Stan

Musial

1946

16

103

.365

1.021

+2.84

Stan

Musial

1947

19

95

.312

.902

+1.51

Stan

Musial

1948

39

131

.376

1.152

+3.77

Stan

Musial

1949

36

123

.338

1.062

+2.88

               

Stan

Musial

1950

28

109

.346

1.034

+2.35

Stan

Musial

1951

32

108

.355

1.063

+3.09

Stan

Musial

1952

21

91

.336

.970

+2.57

Stan

Musial

1953

30

113

.337

1.046

+2.66

Stan

Musial

1954

35

126

.330

1.036

+2.49

               

Stan

Musial

1955

33

108

.319

.974

+1.88

Stan

Musial

1956

27

109

.310

.908

+1.23

Stan

Musial

1957

29

102

.351

1.034

+2.47

Stan

Musial

1958

17

62

.337

.996

+2.22

Stan

Musial

1959

14

44

.255

.792

+0.33

               

Stan

Musial

1960

17

63

.275

.841

+0.92

Stan

Musial

1961

15

70

.288

.898

+1.11

Stan

Musial

1962

19

82

.330

.926

+1.78

Stan

Musial

1963

12

58

.255

.747

+0.29

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Mickey

Mantle

1951

13

65

.267

.792

+0.27

 

Mickey

Mantle

1952

23

87

.311

.924

+2.08

 

Mickey

Mantle

1953

21

92

.295

.895

+1.20

 

Mickey

Mantle

1954

27

102

.300

.933

+1.57

 

               

 

Mickey

Mantle

1955

37

99

.306

1.042

+2.51

 

Mickey

Mantle

1956

52

130

.353

1.169

+3.62

 

Mickey

Mantle

1957

34

94

.365

1.177

+3.73

 

Mickey

Mantle

1958

42

97

.304

1.035

+2.59

 

Mickey

Mantle

1959

31

75

.285

.904

+1.50

 

               

 

Mickey

Mantle

1960

40

94

.275

.957

+2.12

 

Mickey

Mantle

1961

54

128

.317

1.135

+3.22

 

Mickey

Mantle

1962

30

89

.321

1.091

+3.57

 

Mickey

Mantle

1964

35

111

.303

1.015

+2.74

 

               

 

Mickey

Mantle

1965

19

46

.255

.831

+1.06

 

Mickey

Mantle

1966

23

56

.288

.927

+2.05

 

Mickey

Mantle

1967

22

55

.245

.825

+1.10

 

Mickey

Mantle

1968

18

54

.237

.782

+1.04

 

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Bill

Bruton

1953

1

41

.250

.636

-1.30

Bill

Bruton

1954

4

30

.284

.701

-0.50

               

Bill

Bruton

1955

9

47

.275

.728

-0.39

Bill

Bruton

1956

8

56

.272

.723

-0.45

Bill

Bruton

1957

5

30

.278

.755

+0.01

Bill

Bruton

1958

3

28

.280

.696

-0.64

Bill

Bruton

1959

6

41

.289

.735

-0.25

               

Bill

Bruton

1960

12

54

.286

.758

+0.07

Bill

Bruton

1961

17

63

.257

.712

-0.54

Bill

Bruton

1962

16

74

.278

.776

+0.16

Bill

Bruton

1963

8

48

.256

.708

-0.11

Bill

Bruton

1964

5

33

.277

.745

+0.17

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Norm

Cash

1960

18

63

.286

.903

+1.57

 

Norm

Cash

1961

41

132

.361

1.148

+3.34

 

Norm

Cash

1962

39

89

.243

.894

+1.44

 

Norm

Cash

1963

26

79

.270

.856

+1.45

 

Norm

Cash

1964

23

83

.257

.804

+0.73

 

               

 

Norm

Cash

1965

30

82

.266

.883

+1.57

 

Norm

Cash

1966

32

93

.279

.829

+1.04

 

Norm

Cash

1967

22

72

.242

.783

+0.71

 

Norm

Cash

1968

25

63

.263

.816

+1.37

 

Norm

Cash

1969

22

74

.280

.831

+0.85

 

               

 

Norm

Cash

1970

15

53

.259

.823

+0.60

 

Norm

Cash

1971

32

91

.283

.903

+1.79

 

Norm

Cash

1972

22

61

.259

.802

+0.93

 

Norm

Cash

1973

19

40

.262

.828

+0.99

 

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Bill

Mazeroski

1957

8

54

.283

.725

-0.26

Bill

Mazeroski

1958

19

68

.275

.747

-0.15

Bill

Mazeroski

1959

7

59

.241

.621

-1.44

               

Bill

Mazeroski

1960

11

64

.273

.712

-0.40

Bill

Mazeroski

1961

13

59

.265

.678

-0.84

Bill

Mazeroski

1962

14

81

.271

.733

-0.30

Bill

Mazeroski

1963

8

52

.245

.629

-0.94

Bill

Mazeroski

1964

10

64

.268

.681

-0.45

               

Bill

Mazeroski

1965

6

54

.271

.641

-0.80

Bill

Mazeroski

1966

16

82

.262

.694

-0.34

Bill

Mazeroski

1967

9

77

.261

.644

-0.59

Bill

Mazeroski

1968

3

42

.251

.616

-0.63

               

Bill

Mazeroski

1970

7

39

.229

.607

-1.23

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Hal

Lanier

1964

2

28

.274

.630

-0.93

 

               

 

Hal

Lanier

1965

0

39

.226

.545

-1.74

 

Hal

Lanier

1966

3

37

.231

.546

-1.86

 

Hal

Lanier

1967

0

42

.213

.494

-2.00

 

Hal

Lanier

1968

0

27

.206

.461

-2.19

 

Hal

Lanier

1969

0

35

.228

.514

-1.95

 

               

 

Hal

Lanier

1970

2

41

.231

.543

-1.77

 

 

 

First

Last

Year

HR

RBI

Avg.

OPS

OPS Vs. League

Bill

Buckner

1971

5

41

.277

.672

-0.50

Bill

Buckner

1972

5

37

.319

.758

+0.50

Bill

Buckner

1973

8

46

.275

.648

-0.80

Bill

Buckner

1974

7

58

.314

.763

+0.49

               

Bill

Buckner

1975

6

31

.243

.644

-0.84

Bill

Buckner

1976

7

60

.301

.716

+0.12

Bill

Buckner

1977

11

60

.284

.739

-0.12

Bill

Buckner

1978

5

74

.323

.765

+0.39

Bill

Buckner

1979

14

66

.284

.756

+0.03

               

Bill

Buckner

1980

10

68

.324

.810

+0.74

Bill

Buckner

1981

10

75

.311

.829

+1.07

Bill

Buckner

1982

15

105

.306

.783

+0.48

Bill

Buckner

1983

16

66

.280

.746

+0.07

Bill

Buckner

1984

11

69

.272

.705

-0.26

               

Bill

Buckner

1985

16

110

.299

.773

+0.35

Bill