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About Batting Runs
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About Batting Runs

Batting runs are an estimate of a player's total individual offensive contribution to his team. Batting runs are scaled according to the league average and the player's home ballpark so that they estimate how many runs the player contributed above or below the league average. A positive number is an above-average performance, while a negative number is a below-average performance. In 1998, for example, Mark McGwire of the Cardinals was +98, while Neifi Perez of the Rockies was -39. Simply put, the batting runs formula estimates that the Cardinals would have scored 98 fewer runs had they replaced McGwire with an average hitter, while the Rockies would have scored 39 more runs had they replaced Perez with an average hitter.

The batting runs formula is, more or less:

(.47 * 1B) + (.78 * 2B) + (1.09 * 3B) + (1.40 * HR) + (.31 * (BB + HBP + SB - CS)) - (.28 * (AB - H + CS))

These numbers are based on the relative value of each event in producing runs. While the value of a single, double, triple, home run, walk, hit by pitch, and stolen base remains constant, the cost of an out (AB-H+CS) varies in the formula from season to season. In 1998 an out was worth about .28 of a run in each league. Batting runs are also adjusted to reflect the presence of the designated hitter in the American League since 1973 as well as the influence of the player's home park on offense. This method is based on Pete Palmer's The Hidden Game of Baseball and his encyclopedia, Total Baseball. Palmer devised a simulation of thousands of Major League games since 1900 in order to derive these values. For a more detailed discussion, keep reading.

Advantages of Batting Runs
There are lots of methods for evaluating overall offensive performance, including Bill James' runs created, Tom Boswell's total average, Paul Johnson's estimated runs produced, and on-base percentage plus slugging average. In 1984 Pete Palmer published The Hidden Game of Baseball, which introduced his batting runs formula. In 1989 he published the first edition of Total Baseball, an encyclopedia with batting runs estimates for every season for every player in major-league history. Five advantages of the batting runs formula are:

  • The formula is highly accurate. When applied to a team's offensive statistics, the batting runs estimated by the equation correlate highly with the number of runs actually scored by the team. Applied to every big-league team since 1901, the batting runs estimates diverge from actual runs scored by an average of only about 2.9 percent.
  • The formula uses statistics that are commonly available. While even more accurate measures of offensive performance exist, they often rely on situational statistics or even play-by-play data not readily accessible to the average fan. Anyone could take the formula above, find the basic statistics in his local newspaper or on the Internet, and figure batting runs estimates for his favorite players.
  • The formula's result is expressed in an easily understood unit, i.e., runs. Unlike formulas that express their outcome in bases gained, ratios, or percentages, batting runs estimate what the player produced in terms of the most important element of offense.
  • The formula reveals whether the player performed above or below the league average, putting the player in the context of the season in which he played. Whereas a .300 batting average and 100 runs batted in was an average performance in the National League in 1930, when the league batting average was .303 and the league earned-run average was 4.97, the same performance was stellar in the American League in 1968, when the league batting average was .230 and the league earned-run average was 2.98. Because batting runs is always measured against the league average, it requires no additional adjustment for seasonal context.
  • The formula incorporates not just the player's positive contributions, like hits, home runs, and stolen bases, but his negative actions, too, i.e., his outs. A player who hits .300 with 30 home runs and makes 400 outs is likely not as valuable as a player who hits .300 with 30 home runs and makes 300 outs. Batting runs estimate a player's net value, not just his gross value.

Cost of an Out
The following is a more detailed explanation of how the batting runs estimates are devised. The values of a single (.47), double (.78), triple (1.09), home run (1.40), walk (.31), hit by pitch (.31), and stolen base (.31) are constant. The cost of an out, though, changes to reflect the offensive level of the season in which the statistics were compiled. For example, an out is more costly in a high-scoring season like the National League in 1930 (.31) than in a low-scoring season like the American League in 1968 (.22).

To determine the cost of an out, the value of all the offensive events produced by the league in a season is divided by the outs made by the league:

[(1B * .47) + (.78 * 2B) + (1.09 * 3B) + (1.40 * HR) + (.31 * (BB + HBP + SB - CS))] / (AB - H + CS)

In this way, the league average is set to zero, since the value of the league's positive events is set to equal the value of the league's negative events, i.e., its outs.

Pitchers and the Designated Hitter
Pete Palmer, in The Hidden Game of Baseball and Total Baseball, sets the value of an out each season according to the league's offensive events while excluding the offensive statistics of pitchers. Since removing pitchers from the league totals is a lot of work, the values here, unlike in Palmer's books, include the offensive statistics of pitchers.

This creates a disadvantage for players in the American League since 1973, when the designated-hitter rule was adopted. While a National Leaguer is compared to a league average that includes pitchers, an American Leaguer faces stiffer competition since designated hitters bat in place of pitchers.

The solution employed here is to adjust American League batting runs since 1973 appropriately. On average, pitchers deflate the value of an out in the National League by about four percent. Meanwhile, designated hitters, since they are generally above average, inflate the value of an out in the American League by about one percent. Consequently, American Leaguers are given a five percent bonus in their batting runs estimates. While this adjustment is not as precise as subtracting the offensive statistics of pitchers, it saves a lot of time. The value of an out for each league and season is included with the team statistics.

Stolen Bases and Caught Stealing
Unlike in Palmer's work, here stolen bases and caught stealing are included directly in a player's batting runs. Palmer uses a separate measure, stolen base runs, in which stolen bases are worth .30 of a run and caught stealing cost .60 of a run, to determine the value of baserunning. For the sake of simplicity, here stolen bases are counted with walks and hit by pitch as .31 of a run, while caught stealing are subtracted as .31 of a run, since they remove a baserunner, and are also counted against a player as an out according to the league value of an out. This comes very close to the values for a stolen base and caught stealing used by Palmer. Base running is included in the computation of batting runs only in the seasons for which stolen base and caught stealing data are both available.

Park Factor
Another adjustment made to batting runs is to account for the effect of the player's home park on offense. Just as a .300 batting average in the National League in 1930 is not the same as a .300 batting average in the American League in 1968, nor is a .300 batting average in Colorado the same as a .300 batting average in San Diego. Consequently, batting runs are adjusted for the extent to which a ballpark inflates or deflates run-scoring.

In 1998, Coors Field in Colorado had a park factor of 1.19, an above-average park for hitters. Meanwhile, Qualcomm Park in San Diego had a park factor of .91, a below-average park for hitters. The park factors used here are those provided by Total Baseball. They include not only the team's runs scored and allowed at home and on the road, but an adjustment for the fact that a player does not face his own team's pitching staff.

To get an idea of how a ballpark can affect a player's performance, Dante Bichette produced an estimated +29 runs unadjusted for park effect, but +5 when taking into account the light air at Coors Field. Conversely, Tony Gwynn contributed an estimated +21 batting runs unadjusted for park effect, but +29 considering the pitchers' haven that is Qualcomm Park. The park factors for every team and season are included with the team statistics.

There you have it. Batting runs are not necessarily a lot more accurate than other methods of player evaluation, like Bill James' runs created or Paul Johnson's estimated runs produced. Similarly, a simple measure like OPS, adjusted for league average and park effect, correlates almost as highly with team runs scored. But for the purposes here, to express a player's value above or below the league average in a unit easily understood, batting runs is the best choice.

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Updated March 10, 1999