The batting triple crown, bestowed on the hitter
who simultaneously leads his league in batting average,
home runs, and runs batted in, is among baseball's rarest
and most revered feats. While the triple crown statistics
measure three important things, they aren't the best
means to evaluate a hitter's overall value.
Looking solely at batting average, for example, ignores
the contribution of reaching base by drawing walks.
Giving a hitter credit only for his home runs ignores the
power inherent in hitting doubles and triples. If you're
looking at runs batted in, why not take into account runs
scored, too?
Runs batted in and runs scored, unless solely the product
of a hitter's own home runs, are dependent not only on
his own ability, but that of his teammates, too. A great
RBI man requires lots of runners to reach base ahead of
him. A prolific table setter needs the help of the
hitters behind him to score many runs. Runs batted in and
runs scored are a product of opportunities as much as
ability.
Instead of measuring how many times he drives in his
teammates who succeed in reaching base, or how many times
his teammates succeed in driving him in when he reaches
base, it's possible to isolate the value of the things a
hitter does himself. Each offensive event, singles,
doubles, triples, home runs, bases on balls, hit by
pitch, stolen bases, caught stealing, and outs, has an
approximate value that can be measured in runs. Batting
runs uses these values to estimate a hitter's total
individual contribution to his team above or below the
league average. Here is the batting runs formula:
(0.47 * 1B) + (0.78 * 2B) + (1.09 * 3B) +
(1.40 * HR) + (0.31 * (BB + HBP + SB  CS))  (0.276 *
(AB  H + CS))
While the value of a single, double, triple, home run,
walk, hit by pitch, and stolen base remains constant, the
cost of an out (atbats minus hits plus caught stealing)
varies in the formula from season to season depending on
the league's offensive levels. In 1998 an out was worth
about 0.276 runs 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 hitter's home ballpark on
offense. This formula is based on the method presented by
Pete Palmer in The Hidden Game of Baseball and
Total
Baseball. Palmer devised a simulation of
thousands of majorleague games since 1900 in order to
derive these values, but similar values have been
discovered by other researchers using different
approaches.
Five advantages of the batting runs formula are:
• The formula is of proven accuracy.
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 majorleague 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.
•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 basic and 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, walks, 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 value of a single (0.47),
double (0.78), triple (1.09), home run (1.40), walk
(0.31), hit by pitch (0.31), and stolen base (0.31) is
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
(0.31) than in a lowscoring season like the American
League in 1968 (0.22). A caught stealing also fluctuates
with the cost of an out, since it costs a team both a
baserunner and an out.
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:
[(0.47 * 1B) + (0.78 * 2B) + (1.09 * 3B)
+ (1.40 * HR) + (0.31 * (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 equal to
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 great deal
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 4 percent. Meanwhile, designated hitters,
since they are generally above average, inflate the value
of an out in the American League by about 1 percent.
Consequently, American Leaguers are given a 5 percent
adjustment in their batting runs estimates. While this
modification is not as precise as subtracting the
offensive statistics of pitchers, it saves a great deal
of time.
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 0.30 runs and caught stealing cost 0.60
runs, to determine the value of baserunning. For the sake
of simplicity, here stolen bases are counted with walks
and hit by pitch as 0.31 runs, while caught stealing are
subtracted as 0.31 runs, 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. Baserunning 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 has to be made to
a hitter's batting runs: the effect of ballparks. A
hitter who plays his home games in Coors Field will
benefit over a hitter who plays his home games in Dodger
Stadium. Consequently, batting runs are adjusted for
batters' park factor. Batters' park factor not only
accounts for the hitter's home ballpark, but also for all
the ballparks where the hitter's team played, and
includes an adjustment for the fact that the hitter does
not face his own team's pitching staff.
Batters' park factor is expressed so that 1.00 is
average, above 1.00 represents a hitters' park, and below
1.00 represents a pitchers' park. For example, in 1998
Coors Field had a batters' park factor of 1.19, while
Dodger Stadium had a batters' park factor of 0.93. The
park factors used here are based on threeyear averages
provided by Total
Baseball. To read more about park factor, consult
the Glossary. Annual park
factors are listed in the Standings
and Team Batting
sections.
Park factor is applied to the batting runs formula by
adjusting the value of an out, because an out is more
costly in a highscoring environment than a lowscoring
environment. Thus, the batting runs formula, adjusted for
ballpark effect, is:
(0.47 * 1B) + (0.78 * 2B) + (1.09 * 3B) +
(1.40 * HR) + (0.31 times (BB + HBP + SB  CS)) 
(0.276 * BPF * (AB  H + CS))
Thus, an out costs 0.33 runs in Coors Field but only
0.26 runs in Dodger Stadium. This makes sense, since a
team would expect to score more runs with its outs in
Colorado than in Los Angeles.
Caveats. Batting runs has its limitations. The
values assigned to each offensive event are based on
averages. Yet clearly a single with a runner on third
base is worth more than a single with a runner on first
base, just as an out with the bases loaded is usually
more costly than an out with no one on base. While
statistics exist that reveal how well a batter hits in
particular base and out situations, such detailed
information would make batting runs much more complicated
in order to achieve greater accuracy.
Moreover, batting runs is limited by the data available.
It would be useful to know how often a batter advances a
runner with outs, how frequently a faster player takes
extra bases on hits and outs than a slower player, and
how often a batter reaches base or advances on errors.
Such statistics are not readily available to most fans.
Indeed, even more common statistics, like stolen bases
and caught stealing, are unavailable for many players in
majorleague history.
In any event, batting runs is an estimate, not a
definitive value. The ability of his teammates to reap
the value of a batter's contribution is a huge factor in
determining whether real runs, not just batting runs, are
gained. Batting runs proceeds on the assumption that the
batter's actions take place within an average context.
Obviously this is not always the case.
Conclusion. Batting runs are not necessarily more
accurate than other methods of hitter evaluation, like
Bill James' runs
created, Paul Johnson's estimated
runs produced, Jim Furtado's extrapolated
runs, or Tom Ruane's valueadded
runs created. Similarly, a simple measure like
onbase percentage plus slugging average also correlates
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. To read a comparison of hitter evaluation
methods, check out Furtado's
article in the latest edition of the Big
Bad Baseball Annual.
Sources:
Glossary,
Total
Baseball, edited by John Thorn, Pete Palmer,
Michael Gershman, and David Pietrusza (Sixth Edition,
1999).
The Hidden Game of Baseball, by John Thorn and
Pete Palmer (1984).
