Batting average
From Academic Kids

Batting average is a statistic in both baseball and cricket measuring the performance of baseball hitters and cricket batsmen, respectively. The two statistics are related, in that baseball averages are directly descended from the concept of cricket averages.
The term batting average is also used in nonsporting contexts to represent various statistical measures of performance.
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Batting average in cricket
In cricket, a player's batting average is the total number of runs he has scored divided by the number of times he has been out. Since the number of runs a player scores and how often he gets out are primarily measures of his own playing ability, and largely independent of his team mates, batting average is a good statistic for describing an individual player's skill as a batsman. Batting average has been used to gauge cricket players' relative skills since the 18th century.
Most players have batting averages in the range 1040: between 30 and 40 is typical for specialist batsmen and allrounders, while between 10 and 20 is typical for specialist bowlers.
Career records for batting average are usually subject to a minimum qualification of at least 20 innings played. This is because it is easy to sustain an artificially high average over a career spanning few matches. Under this qualification, the highest Test batting average belongs to Australia's Sir Donald Bradman, with 99.94. Given that a career batting average over 50 is exceptional, and that only four other players have averages (barely) over 60, this is an outstanding statistic. The fact that Bradman's average is so far above that of any other cricketer has led several statisticians to argue that, statistically at least, he was the greatest sportsman in any sport.
Batting averages in oneday international cricket tend to be lower than in Test cricket, because of the need to score runs more quickly and the lesser emphasis on building a large innings.
Some cricket followers have noted that the batting average is inflated by the number of notouts (innings in which the batsman has not been dismissed), and argue that a better measure of a batsman's quality is the number of runs scored divided by the number of innings played. This proposed statistic has never been given an accepted name and is not commonly used by cricket fans or commentators. It may have the disadvantage that it would deflate the apparent quality of lowerorder batsmen who are often not out but are rarely given the chance to bat for long.
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Batting average in baseball
In baseball, the batting average 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 team mates' 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 over .300 is considered to be good, and an average over .400 a nearly unachievable goal. The last player to do so, with enough at bats to qualify for the batting championship, was Ted Williams of the Boston Red Sox, who hit .406 in 1941.
Ty Cobb holds the record for highest career batting average. Some hold his lifetime average as .366 others as .367, 89 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 over .360 in more than one or two seasons, let alone consistently throughout their entire careers.
For nonpitchers, 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 over his Major League career, or for Minnie Mendoza, also a shortstop, who was a longtime minorleague 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  the most recent completed season  was just over .266, and the alltime league average is between .260 and .275.
The Major League Baseball batting average championship (often referred to as "the Batting Title") is awarded to the player in each league who has the highest batting average with at least 3.1 plate appearances per game that his team has played during a season.
Sabermetrics considers batting average a weak measure of performance because it does not correlate as well as other measures to runs scored. Batting average does not take into account walks or power, whereas newer statistics like slugging percentage have been specifically designed to measure such concepts. Others would say it 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 team mates have done. It is interesting to note that measuring individual performance rather than runs scored was precisely Chadwick's goal in devising the statistic.
The decline of the .400 hitter
A point of interest to baseball followers is that hitting .400 was not uncommon in the early 20th century, but has not occurred 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, who applied his knowledge of biological population statistics to the question. Many scientists believe that the range of a given species will tend to decrease over time. That is, the average difference between the tallest and shortest members of a species will tend to decline over time; the difference between the fastestrunning and the slowest members will tend to decline; and so on.
Gould argued 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.) that the evolution of baseball batting averages has mimicked this behaviour. In other words, the difference between the strongest hitters and the weakest hitters has declined as a natural consequence of the improvement of baseball skills over time. Not only has the .400 hitter disappeared; so has the .150 hitter. Thus the evolution of baseball players can be said to mimic other evolutionary groups.
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.
See also
Batting average in other contexts
Following from usage in cricket and baseball, batting average has come to be used for other statistical measures of performance.
An example is the Internet Archive, which uses the term in ranking downloads. Its "batting average" indicates the correlation between views of a description page of a downloadable item, and the number of actual downloads of the item. This avoids the effect of popular downloads by volume swamping potentially more focused and useful downloads, producing an arguably more useful ranking.