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.

 

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.)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