THE BATTER’S RUN AVERAGE (B.R.A.) |

By Richard D. Cramer and Pete Palmer
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: On-base average = plate appearances Abs + walks + HBP and: slugging percentage = at bats 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: B.R.A. = at bats + walks + HBP 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. = 680 AB + 65W + 6HBP B.R.A. = .174 For Stargell: B.R.A. = 522 AB + 80W + 3 HBP 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.) 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: additional-wins = League B.R.A. 2.5 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. 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
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
ALL-TIME B.R.A. LEADERS BY POSITION
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
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
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
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
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
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
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
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 |