The Batter’s Run Average

This article was written by Dick Cramer - Pete Palmer

This article was published in the 1974 Baseball Research Journal


The problem of measuring batting skill is as old as baseball itself. The earliest statisticians were content to count the hits and runs scored by each batter, but the unfairness of this simple method to the stars of weak teams soon prompted invention of the batting average. Since then statistics have proliferated to the point where 20 columns are now necessary for presentation of a complete season’s batting record. But all these numbers don’t necessarily help. Is a player who bats .300 and steals 50 bases more or less valuable than a .250 hitter with 25 home runs?

The batter’s run average, or B.R.A., is a new statistic that we devised independently of one another and now propose as a solution to this problem. A player’s B.R.A. is found by multiplying his on-base average (his run-scoring ability) by his slugging percentage (his run-driving-in ability). The formula is:

B.R.A. = on-base average X slugging percentage where:

Equation 1
and:

Equation 1b

Where complete batting records are available, base-running skill should be rewarded also, by adding a ½ “time-reached base” for each caught stealing. Thus another formula is:

The two formulas are completely interchangeable, except that with the base running included, a Lou Brock will have a somewhat higher B.R.A. than the typical player.

Analysis, using dozens of seasons of records and a computer model of baseball play, convinces us that the B.R.A. explains run scoring better than any other indicator that can be derived from year-end statistics. As an example, let us compare Peter Rose, the NL Most Valuable Player in 1973, with runnerup Willie Stargell, whom some felt was more deserving of the award.

For Rose (using the B.R.A. formula which includes base-running):

Equation 3

B.R.A. = .174

For Stargell:

Equation 4

B.R.A. = .255

Stargell was almost half again as dangerous a hitter as rose. In fact, Willie led the majors for players with more than 502 plate appearances (Aaron’s .260 B.R.A. was achieved with only 465 plate appearances), whereas Rose barely made the top 15 and also trailed two of his teammates, Tony Perez and Joe Morgan.

 

Runs-Contributed and Additional-Wins Statistics

The runs scored by a team depend completely on the B.R.A.’s and plate appearances of its individual batters.

The average runs that a batter contributes per time facing pitcher (RC/BFP) is determined by his B.R.A., according to the following formula:

RC/BFP = B.R.A. – 0.7 x (B.R.A.)

A batter’s “runs-contributed” can then be found by multiplying his RC/BFP rate by his plate appearances. As can be seen in the first of the tables at the end of this paper, the runs actually scored by a team agree closely with the sum of the runs-contributed totals of its individual batters (within 5%, more than 80% of the time.)

Obviously a team which scores more runs will win more games. A team of perfectly average players would score runs at an average rate, give up runs at the same average rate, and thus play .500 ball. Good hitters produce additional victories by contributing runs at a higher than average rate. In general, nine or ten additional runs scored at some time during a season are needed to convert a loss into a victory, or to produce an “additional win.”

Returning to our example, we can calculate the “additional wins” resulting from the batting of Rose and Stargell. First, the runs-contributed by each. Rose’s RC/BFP rate was .174 – .7x(.174), or .153, and Stargell’s .209. Thus Rose contributed 115 runs (.153 x 751 BFP) and Stargell 127.

If Rose and Stargell had been average hitters, they would have contributed runs at the average or league rate. The National League B.R.A. was .121 in 1973 (on-base average of .323 and slugging percentage of .376 and so the RC/BFP rate for an average player was .111. As average hitters, Rose would have contributed 83 runs (.111 x 751) and Stargell 67 runs. In fact Rose contributed 32 runs above average (115 minus 83) but Stargell contributed 59 runs more than average.

This analysis slightly undervalues the value of both hitters by leaving out a secondary effect of their high on-base averages. Every time a batter avoids making an out by reaching base he allows another batter on his team to come to bat before the game is over. Opportunities are created for run scoring at some different point in the game. How many fans remember some apparently meaningless fifth inning walk in a game won by a dramatic two-out ninth inning home run? But with an out instead of the walk, the game would have ended before its hero could have batted. The better-than-average on-base frequency of Rose and Stargell gave their teammates enough extra at bats to score 8 and 7 extra runs, respectively.

Pete Rose’s superior batting in 1973 led to approximately three additional-wins (+31/9.5), but Stargell’s was worth six additional-wins.

A simple, although approximate, formula for computing additional-wins directly from a player’s B.R.A. is:

Equation 5

By this formula Rose would have +2.9 and Stargell +6.5 additional-wins. Of course, additional-wins also result from pitching and fielding which is better or worse than average.

To show the variety of uses for these new batting statistics, we now use them to answer possible questions about a team performance and about a rules change.

Q. Can the White Sox hope to challenge the Athletics in 1974 if no injuries occur to key players such as Allen and Henderson? A. Not likely. At their healthiest, Allen and Henderson would have contributed five more wins, lifting Chicago’s 1973 record only to 82-80. Santo will help, but the white Sox will need substantial defensive improvement or unusual luck to close the remaining ten-game gap.

Q. How much of the improvement in batting last year in the American League resulted directly from the designated hitter rule? A. About a third. There were 1500 more runs in 1973 than in 1972, after correction for the unplayed games in 1972. In 1972 pitchers contributed 174 runs in their 4787 plate appearances, often being pinch hit for. Last year designated hitters contributed 971 runs in their 8271 appearances, or 562 in the appearances where pitchers would have batted. A further 118 runs result from the improved on-base average of designated hitters compared with pitchers, for a total improvement in run-scoring of 506 runs as a direct result of the new rule.

Two tables appear on the following pages. The first gives B.R.A. and runs-contributed records for players in 1973, including all those with more than 180 plate appearances. The second gives the all-time top hitters at each position. Because the level of hitting has fluctuated over the years for reasons that are not well understood, we have chosen to rate hitters by their B.R.A. relative to the league B.R.A. By this method a 1.00 indicates an average hitter and a 2.00 a hitter twice as good as average. The ratings shown in this table are the average of a player’s ten best seasonal relative B.R.A.’s.

 

1973 AMERICAN LEAGUE B.R.A. and RUNS-CONTRIBUTED

Baltimore

   

Boston

 

 

California

   

Bumbry

0.202

67

Smith

0.206

87

Robinson

0.182

100

Coggins

0.170

62

Yastrzemski

0.188

105

Scheinbium

0.164

48

Baylor

0.165

66

Harper

0.157

88

Oliver

0.128

68

Rettenmund

0.160

54

Cepeda

0.155

83

Grabarkew.

0.114

25

Powell

0.157

64

Fisk

0.138

69

McGraw

0.112

30

Grich

0.146

90

Cater

0.136

25

Berry

0.108

44

Williams

0.142

67

Petrocelli

0.132

49

Stanton

0.106

33

Davis

0.137

72

Evans

0.126

37

Pinson

0.105

47

Blair

0.136

67

Miller

0.126

57

Gallagher

0.102

34

Robinson

0.113

63

Aparicio

0.104

52

Epstein

0.097

41

Etchebarren

0.112

17

Griffin

0.095

37

Meoli

0.082

26

Crowley

0.092

13

Oglivie

0.090

13

Alomar

0.076

36

Belanger

0.080

40

Guerrero

0.074

16

Torborg

0.070

18

Others

17

Others

29

Others

65

(Actual = 754)

 

760

(Actual = 738)

 

747

(Actual = 629)

 

615

                 

Chicago

 

 

Cleveland

 

 

Detroit

   

Allen

0.247

58

Gamble

0.151

58

Horton

0.178

69

Melton

0.158

90

Lowenstein

0.139

41

Caah

0.170

62

Sharp

0.139

27

Ellis

0.138

61

Northrup

0.169

66

May

0.138

76

Hendrick

0.138

58

McAuliffe

0.156

55

Muaer

0.137

42

Chamblise

0.130

75

Howard

0.149

34

Hairston

0.124

28

Williams

0.129

43

Kaline

0.129

40

Bradford

0.123

21

Duncan

0.128

44

Sima

0.127

34

Kelly

0.122

69

Spikes

0.125

63

Brown, G.

0.118

46

Henderson

0.122

32

Bell

0.122

76

Sharon

0.118

20

Orta

0.120

51

Duffy

0.121

43

Stanley

0.113

68

Herrmann

0.102

39

Torree

0.096

33

Freehan

0.102

41

Jeter

0.101

29

Brohamer

0.089

28

Taylor

0.093

25

Leon

0.082

34

Ragland

0.086

16

Brinkman

0.092

47

Alvarado

0.073

14

Cardenas

0.058

12

Rodriguez

0.088

49

Others

48

Others

15

Others

26

(Actual = 652)

 

658

(Actual = 680)

 

660

(Actual = 642)

 

682

                 

Kansas City

   

Milwaukee

   

Minnesota

   

Mayberry

0.202

110

Scott

0.181

106

Carew

0.198

110

Otis

0.177

100

Porter

0.167

61

Braun

0.178

68

Schaal

0.153

64

May

0.164

98

Soderholm

0.170

20

Mealy

0.139

39

Briggs

0.153

79

Misle

0.150

82

Rojas

0.123

66

Money

0.144

79

Molt

0.149

63

Kirkpatrick

0.122

53

Brown, 0.

0.141

42

Oliva

0.142

79

McRae

0.120

42

Coluccio

0.129

58

Mitterwald

0.133

57

Movisy

0.111

27

Garcia

0.115

66

Lis

0.131

34

Rsichardt

0.111

31

Rodriguez

0.114

36

Brye

0.124

36

Bevacqua

0.104

29

Lahoud

0.091

11

Darwin

0.122

68

Piniella

0.103

52

Thomas

0.068

11

Killebrew

0.122

32

Patek

0.103

53

Johnson

0.063

30

Terrell

0.094

41

Taylor

0.102

17

Vukovich

0.030

4

Thompson

0.075

26

Others

43

Others

20

Others

0.000

44

(Actual = 755)

 

726

(Actual = 708)

 

701

(Actual = 738)

 

760

                 

New York

 

 

Oakland

 

 

Texas

   

Blotsberg

0.199

57

Jackson

0.208

111

Burroughs

0.176

92

Munaon

0.175

88

Bando

0.187

110

Sudakia

0.157

36

Nurcer

0.163

97

Tenace

0.172

94

Nelaon

0.127

71

Nart

0.134

46

North

0.136

78

Johnaon

0.122

73

Nettles

0.130

75

Rudi

0.132

56

Narrah

0.122

57

White

0.123

81

Johnson

0.131

67

Fregosi

0.121

35

Alou, M.

0.120

60

Alou, J.

0.106

17

Spencer

0.117

52

Negan

0.113

22

Green

0.104

34

Harris

0.106

60

Clarke

0.096

57

Catspaneris

0.102

62

Suarez

0.100

29

Alou, F.

0.080

25

Fosse

0.102

49

Bittner

0.096

25

Michael

0.073

31

Kubiak

0.078

15

Carty

0.094

38

Laniet1

0.060

5

Nangual

0.077

15

Maddox

0.092

18

Callison

0.045

6

Andrews

0.076

15

Nason

0.079

19

Others

14

Others

6

Others

25

(Actual = 641)

 

664

(Actual = 758)

729

(Actual = 619)

 

630

 

Note: The over-all records of players who appeared with more than one club are summarized with that club where his contribution seemed most publicized. Runs contributed by “others” reflect this factor and have also been adjusted slightly (-8 AL, -5 NL) to take account of the sacrifice fly rule and the higher-than-average league fielding percentages.

Summary: For those players with enough at bats to qualify for the batting title, Willie Stargell had the highest B.R.A. in 1973 with a 2.55 mark. Re was followed by Darrell Evens with a 2.27 average. Evans had the most runs-contributed with 138, followed by Stargell and Bobby Bonds with 127. Reggie Jackson led the American League with a 2.08 B.R.A. end had 111 runs-contributed.

 

1974 AMERICAN LEAGUE B.R.A. and RUNS-CONTRIBUTED

New York

   

Philadelphia

 

 

Pittsburgh

 

 

Staub

0.152

90

Robinson

0.172

73

Stargell

0.255

127

Milner

0.144

66

Luzinaki

0.167

98

Zisk

0.192

59

Garrett

0.140

73

Unset

0.148

65

Hebner

0.165

83

Jones

0.127

43

Anderson

0.140

27

Oliver

0.150

92

Millan

0.117

73

Mutton

0.129

33

Robertson

0.125

52

Harrelson

0.109

41

Schmidt

0.124

49

Sanguillen

0.123

68

Maya

0.105

23

Tovar

0.119

40

May, M.

0.117

34

Kranepool

0.096

28

Montanez

0.117

65

Cash

0.110

48

Grote

0.092

26

Boone

0.113

59

Clines

0.105

32

Martinez

0.087

23

Doyle

0.109

40

Stennett

0.094

43

Mahn

0.084

22

Harmon

0.064

10

Alley

0.084

14

Dyer

0.058

11

Bowa

0.062

28

Maxvill

0.060

15

Others

77

Others

55

Others

42

(Actual = 608)

 

596

(Actual = 642)

 

642

(Actual = 704)

 

709

                 

Atlanta

   

Chicago

   

Cincinnati

   

Aaron

0.260

98

Monday

0.168

96

Griffey

0.242

19

Evans

0.227

138

Cardenal

0.167

86

Morgan

0.214

126

Dietz

0.207

33

Williams

0.162

94

Perez

0.209

114

Johnson

0.202

113

Fanzone

0.154

23

Rose

0.174

115

Baker

0.171

102

Santo

0.152

82

Concepcion

0.151

47

Lum

0.160

80

Bourque

0.137

27

Bench

0.151

86

Garr

0.138

86

Hickman

0.118

26

Driessen

0.135

48

Perez

0.109

56

Kessinger

0.100

59

Menke

0.101

29

Oates

0.088

28

Hundley

0.094

35

Geronimo

0.081

27

Casanova

0.082

19

Beckert

0.090

34

Tolan

0.076

35

Jackson

0.073

16

Popovich

0.085

24

Chaney

0.058

14

Others

 

66

Others

46

Others

80

(Actual = 799)

 

835

(Actual = 614)

 

632

(Actual = 741)

 

740

                 

Houston

   

Los Angeles

   

Montreal

   

Cedeno

0.215

105

Crawford

0.181

85

Singleton

0.201

118

Watson

0.179

104

Ferguson

0.176

89

Fairly

0.192

84

May

0.150

78

Davis

0.146

83

Breeden

0.187

47

Wynn

0.135

70

Garvey

0.143

47

Bailey

0.182

95

Rader

0.127

72

Mota

0.132

38

Hunt

0.143

61

Helms

0.120

63

Cey

0.132

70

Day

0.121

25

Edwards

0.110

27

Lopes

0.126

69

Jorgenson

0.117

51

Agee

0.107

29

Paciorek

0.113

21

Woods

0.107

37

Metzger

0.097

56

Buckner

0.107

59

Boccabeila

0.089

36

Gallagher

0.092

13

Russell

0.103

62

Foli

0.079

36

Jutze

0.066

19

Joshua

0.098

15

Frias

0.073

16

Others

40

Others

48

Others

80

(Actual = 681)

 

676

(Actual = 675)

 

686

(Actual = 668)

 

686

                 

St. Louis

   

San Diego

   

San Francisco

   

Carbo

0.170

55

Grubb

0.168

63

McCovey

0.233

95

Simmons

0.163

99

Colbert

0.153

81

Bonds

0.200

127

Brock

0.154

99

Roberts

0.150

67

Matthews

0.169

88

Torre

0.153

81

Morales, J..

0.136

51

Maddox

0.163

89

McCarver

0.127

43

Kendall

0.129

63

Arnold

0.151

8

Sizemore

0.122

66

Gaston

0.114

52

Goodson

0.149

54

Cruz, J.

0.120

50

Locklear

0.107

20

Thomasson

0.145

33

Melendez

0.104

36

Murrell

0.103

20

Kiugman

0.143

45

Reitz

0.085

35

Lee

0.093

32

Fuentes

0.118

77

Tyson

0.082

38

Thomas

0.079

33

Speler

0.117

65

     

Hilton

0.078

19

Rader

0.111

54

     

Hernandez

0.068

17

Phillips

0.098

10

Others

50

Others

53

Others

27

(Actual = 643)

 

652

(Actual = 548)

 

569

(Actual = 739)

 

772

 

ALL-TIME B.R.A. LEADERS BY POSITION (THROUGH 1973)

Catcher

1.59 Buck Ewing

1.51 Joe Torre

1.49 Roger Bresnaham

1.49 Bill Dickey

1.47 Gabby Hartnett

1.45 Mickey Cochrane

1.44 Ernie Lombardi

1.41 Charley Bennett

1.41 Wally Schang

1.37 Smoky Burgess

First Base

2.17 Lou Gehrig

2.17 Dan Brouthers

2.09 Jimmie Foxx

1.98 Cap Anson

1.96 Roger Connor

1.94 Johnny Mize

1.93 Willie McCovey

1.81 Hank Greenberg

1.80 Harmon Killebrew

1.65 Norm Cash

Second Base

2.21 Rogers Hornsby

1.98 Nap Lajoie

1.74 Eddie Collins

1.52 Hardy Richardson

1.50 Charlie Gehringer

1.46 Jackie Robinson

1.45 Larry Doyle

1.38 Bobby Doerr

1.38 Clarence Childs

1.37 George Grantham

Third Base

1.88 Richie Allen

1.70 Eddie Mathews

1.61 Ron Santo

1.54 Denny Lyons

1.52 Deacon White

1.50 Frank Baker

1.48 John McGraw

1.42 Bob Elliott

1.40 Ken Boyer

1.38 Ned Williamson

Shortstop

2.06 Honus Wagner

1.59 Arky Vaughan

1.48 Ernie Banks

1.40 George Davis

1.40 Joe Cronin

1.39 Vern Stephens

1.35 Jack Glasscock

1.33 Bill Dahlen

1.33 Hughie Jennings

1.32 Lou Boudreau

Left Field

2.66 Ted Williams

2.09 Stan Musial

1.96 Ed Delahanty

1.88 Pete Browning

1.75 Harry Stovey

1.75 Carl Yastrzemski

1.71 Al Sim,ons

1.68 Jesse Burkett

1.67 Ralph Kiner

1.67 Willie Stargell

Center Field

2.33 Ty Cobb

2.13 Mickey Mantle

2.09 Tris Speaker

1.94 Willie Mays

1.78 Joe DiMaggio

1.70 George Gore

1.38 Duke Snider

1.66 Billy Hamilton

1.61 Paul Hines

1.54 Fred Williams

Right Field

2.74 Babe Ruth

2.04 Joe Jackson

1.97 Hank Aaron

1.94 Frank Robinson

1.93 Mel Ott

1.78 Mike Kelly

1.78 Sam Crawford

1.78 Harry Heilmann

1.75 Al Kaline

1.72 Sam Thompson

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