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 aboveaverage performance, while a negative
number is a belowaverage 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 (ABH+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 onbase 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 majorleague 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 bigleague
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 playbyplay 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
earnedrun 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 earnedrun
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
highscoring season like the National League in 1930 (.31)
than in a lowscoring 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 designatedhitter 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 runscoring.
In 1998, Coors Field in Colorado had a park
factor of 1.19, an aboveaverage park for
hitters. Meanwhile, Qualcomm Park in San Diego had a park
factor of .91, a belowaverage 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.
Conclusion
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.
