# The Batter’s Run Average

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:

and:

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):

B.R.A. = .174

For Stargell:

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.

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.)2

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) squared, 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:

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