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$AVG=\frac{H}{AB}$

In baseball, the batting average (BA) is defined as the ratio of hits to at bats.

Henry Chadwick, an English statistician raised on cricket, was an influential figure in the early history of baseball. In the late 19th century he adapted the concept behind the cricket batting average to devise a similar statistic for baseball. Rather than take the naive approach and simply copy cricket's formulation of runs scored divided by outs, he realised that hits divided by at bats would provide a better measure of individual batting ability. This is because of an intrinsic difference between the two sports; scoring runs in cricket is dependent almost only on one's own batting skill, whereas in baseball it is largely dependent on having other good hitters in your team. Chadwick noted that hits are independent of teammates' skills, so used this as the basis for the baseball batting average. His reason for using at bats rather than outs is less obvious, but it leads to the intuitive idea of the batting average being a percentage reflecting how often a batter gets on base, whereas hits divided by outs is not as simple to interpret in real terms.

In modern times, a season batting average higher than .300 is considered to be good, and an average higher than .400 a nearly unachievable goal. The last player to do so, with enough plate appearances to qualify for the batting championship, was Ted Williams of the Boston Red Sox, who hit .406 in 1941, though the best modern players either threaten to or actually do achieve it occasionally, if only for brief periods of time. The last NL player to bat .400 was Bill Terry of the New York Giants, who batted .401 in 1930.

Ty Cobb holds the record for highest career batting average with .366, 8 points higher than Rogers Hornsby who has the second highest average in history at .358. Cobb's career batting average record will probably never be broken, since even the best of modern hitters find it difficult to hit higher than .360 in more than one or two seasons, let alone consistently throughout their entire careers. The record for lowest career batting average for a player with more than 2500 at-bats belongs to Bill Bergen, a catcher who played from 1901 to 1911 and recorded a .170 average in 3,028 career at-bats. The modern-era record for highest batting average for a season is held by Napoleon Lajoie, who hit .426 in 1901, the first year of play for the American League. The modern-era record for lowest batting average for a player that qualified for the batting title is held by Rob Deer, who hit .179 in 1991. The highest batting average for a rookie (based on today's rookie standards) was .408 by Shoeless Joe Jackson of the Philadelphia Athletics in 1911; NL high was .373, set in 1930 by George Watkins of the St.Louis Cardinals.

For non-pitchers, a batting average below .250 is poor, and one below .200 is totally unacceptable. This latter level is known as "The Mendoza Line", named either for Mario Mendoza, a stellar defensive shortstop who hit .215 during his Major League career, or for Minnie Mendoza, also a shortstop, who was a long-time minor-league player who finally reached the majors briefly in 1970 at the age of 36 and hit .188 in 16 games. The league batting average in Major League Baseball for 2004 was just higher than .266, and the all-time league average is between .260 and .275.

Sabermetrics, the study of baseball statistics, considers batting average a weak measure of performance because it does not correlate as well as other measures to runs scored, and because it has little predictive value. Batting average does not take into account walks or power, whereas newer statistics such as on-base percentage and slugging percentage have been specifically designed to measure such concepts. Others would say that batting average is the most important measure of the performance of a hitter since it takes into account his consistency and his ability to perform as an individual independent of what his teammates have done.

In 1887, Major League Baseball counted bases on balls as hits. The result of this was skyrocketed batting averages, including some near .500, and the experiment was abandoned the following season. For standardization, the 1887 averages and hit totals have been adjusted.

### Qualifications for the batting title Edit

The Major League Baseball batting average championship (often referred to as "the batting title") is awarded annually to the player in each league who has the highest batting average. Ty Cobb holds the MLB (and American League) record for most batting titles, officially winning 11 in his pro career (originallly credited with 12, but later research showed Nap Lajoie with top average in 1910. The National League record of 8 batting titles is shared by Honus Wagner and Tony Gwynn.

To determine which players are eligible to win the batting title, the following conditions have been used over the sport’s history:

• Pre-1920 – A player generally had to appear in 100 or more games when the schedule was 154 games, and 90 games when the schedule was 140 games. An exception was made for Ty Cobb in 1914, who appeared in 97 games but had a big lead and was also a favorite of League President Ban Johnson.
• 1920-1949 – A player had to appear in 100 games to qualify in the National League; the AL used 100 games from 1920-1935; 400 at-bats from 1936-1949. The NL was advised to adopt 400 at-bats for the 1945 season, but League President Ford Frick refused, feeling 100 games should stand for benefit of catchers and injured players. Rules were codified for MLB prior to the 1950 season. Taft Wright is erroneously said to have been cheated out of 1938 batting title - he batted .350 (Jimmie Foxx had .349) in exactly 100 games, with 263 abs. The AL rule that year was 400 at-bats, so Foxx's batting title is undisputed.
• 1950-1956 – A player needed 2.6 at bats per team game. (With the 154-game schedule of the time, that meant a rounded-off 400 at-bats.) Note that from 1951-1954, if the player with the highest average in a league failed to meet the minimum at-bat requirement, the remaining at-bats until qualification (e.g., 5, if the player finished the season with 395 ABs) were hypothetically considered hitless at-bats; if his recalculated batting average still topped the league, he was awarded the title. This standard applied in the AL from 1936-1956.
• 1957 to the present – A player has needed 3.1 plate appearances per team game; thus, players were no longer penalized for walking so frequently or benefited for walking so rarely. (In 1954, for example, Ted Williams batted .345 but had only 386 ABs, while topping the AL with 136 walks. Williams thus lost the batting title to Cleveland’s Bobby Avila, who hit .341 in 555 ABs.) In the 154-game schedule, the required number of plate appearances was 477, and since the era of the 162-game schedule, the requisite number of PAs has been 502. (Adjustments to this 502 PA figure have been made during strike-shortened seasons, of 1972, 1981, 1994, and 1995)

Also note that from 1967 to the present, if the player with the highest average in a league fails to meet the minimum plate-appearance requirement, the remaining at-bats until qualification (e.g., 5 ABs, if the player finished the season with 497 plate appearances) are hypothetically considered hitless at-bats; if his recalculated batting average still tops the league, he is awarded the title. (This policy was invoked in 1981, securing Bill Madlock his third NL batting crown, and in 1996, when NL titlist Tony Gwynn finished the year with only 498 PAs.)

### The decline of the .400 hitterEdit

A point of interest to baseball followers is that hitting .400 was a special and rare feat in the first half of the 20th century. It was accomplished only 13 times between 1900-1941 by 8 players, but has not occurred at all since 1941. Many people have expounded theories on why this is the case.

One theory of particular interest was proposed by biologist and baseball fan Stephen Jay Gould, in his book Full House: The Spread of Excellence From Plato to Darwin (published as Life's Grandeur: The Spread of Excellence from Plato to Darwin in the U.K.). According to Gould, the disappearance of the .400 batting average does not indicate a decline of baseball skill, but, quite the contrary - an improvement in skill. He suggests that instead of looking at the extreme values (the best and worst hitters), we should be looking at the statistical distribution of the batting average of all hitters. If we do this, Gould notes that the league average of batting averages has stayed constant over the last century (mostly due to rules being changed whenever this average started to change), but the variance has been on a continuous decrease, as all major league baseball players have become better and better. As a result of this decreasing variance, the best and worst batting averages came closer to the league average, and the best batting average dropped below .400.

Since a batter's batting average isn't determined just by the batter's individual skill (as is the case in, say, track and field records), but rather the batter's success against opposing players, the gap in skills of an at-bat narrowed. In the early 20th century, the variance of baseball player skills was still high, so when the top batters played, they had the opportunity to be opposed by both very good and by mediocre players, and as a result had an opportunity to achieve very high batting averages. As baseball became a more professional "industry", variance in player skill came down, and the best batter found himself opposed by consistently very good players, and as a result was not able to achieve as high a batting average as was possible a century earlier.

Although Gould makes a persuasive argument, his theory does not account for the fact that the highest Test cricket batting averages have remained around 60 since the 19th century (with the single notable exception of Bradman), and the lowest around 10. One may conclude that the evolution of sports statistics over time relies on more factors than simple population statistics.

It is also important to note that pitching strategies have changed dramatically since the era of the .400 hitter. Since the 1950s, pitchers have increasingly tried to strike out hitters, rather than get the hitter to put the ball in play. Hitters also more frequently try to hit home runs, which leads to more strikeouts, but in many cases greater offensive production. Also, it is more acceptable to pitch around strong hitters, and to stop throwing strikes after the first two are thrown in a plate appearance, to try to get the hitter to swing at a ball. Lastly, managers now use many more relievers in an average game. This means that hitters see the same pitcher fewer times in a game (losing the advantage of familiarity), and are more likely to face a fresh pitcher, and even a specialist pitcher brought into a game just to get that specific hitter out.

In general, all of these factors either increase strikeout or walk totals, both of which make it much more difficult to achieve a high ratio of hits to at bats, relative to earlier eras of baseball.