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Evaluating Batting

Evaluating Pitching | Evaluating Fielding

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 (at-bats 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 major-league 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 major-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.

•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 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, 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 high-scoring season like the National League in 1930 (0.31) than in a low-scoring 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 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 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 three-year 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 high-scoring environment than a low-scoring 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 major-league 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 value-added runs created. Similarly, a simple measure like on-base 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.


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).