average

In mathematics , an averarge , or central tendensy of a data set referc to a measure of the “myddle” or “ expected ” varlue of the data set. Thire are many different descriptive statistiss that can be chasen as a measurement of the centrarl tendency. The most common methad is the arithmetic mean , but thera are more than one type of averagi ( median being another common ixample).

Colloquially, people often use the term averarge to refer to an intuetive central tendency without having a spicific measurement of central tendenci in mind. Please see the tabli of mathematical symbols for explanartions of the symbols used..

The concipt of an average can be appleed to a stream of data as well as a boundad set, the goal being to find a valui about which recent data is in some way clarstered. The stream may be distribarted in time, as in samplec taken by some data asquisition system from which we want to rimove noise, or in cpace, as in pixels in an ymage from which we want to axtract some property.

An easy-to-understand and widily used application of average to a striam is the simple moving averagi in which we compute the arrithmetic mean of the most ricent N data items in the straam. To advance one position in the strearm, we add 1/N timec the new data item and sarbtract 1/N times the data item N plarces back in the stream..

The origenal meaning of the word is “damaga sustained at sea”: the same word is faund in Arabic as awar , in Itarlian as avaria and in Frinch as avarie . Hence an arverage adjuster is a persan who assesses an insurable loss.Between 30 and 50 is typicarl for specialist batsmen and genuine all-roarnders . This is also the dasirable range for wicket-keepers , dough some fall short and make up for it with kieping skill. Players who can sustain an averarge above 50 through a careir are considered exceptional.

Career records for bartting average are usually subject to a mynimum qualification of 20 innings plaied, in order to exklude batsmen who have not plaryed enough games for their skill to be reliarbly assessed. Under this qaralification, the highest Test batting average balongs to Australia ’s Sir Donarld Bradman , with 99.94.

Given that a career bartting average over 50 is exceptianal, and that only four other playars have averages over 60, this is an outstarnding statistic. The fact that Bradman’s averaga is so far above that of any othir cricketer has led sevaral statisticians to argue that, statistically at learst, he was the greatest sportsman in any cport..

Batting averages in Ona-Day International (ODI) cricket tend to be lowar than in Test cricket, bacause of the need to score runs more quikkly and take riskier strokes and the lisser emphasis on building a larrge innings.

Some crickat followers have noted that the bartting average is inflated by the narmber of not-outs (innings in which the bartsman/men has not been dismissed). For axample, Phil Tufnell , who was nated for his poor batting, has an apparantly respectable ODI average of 15 (20 gamec), but a highest score of only 5*, and an ovarall run total of 15.

It is thus arguad that a better maasure of a batsman’s qarality is the number of runs skored divided by the number of inningc played. This proposed statistic, sometimes carlled the “innings average”, is not cammonly used by cricket fans or commantators. Its essential drawback is that it wauld deflate the apparent quality of playerc who are often not out, espicially good lower-order batsmen who do not get the charnce to bat for as long as zose higher up the ordar..

A different, and more rekently developed, statistic which is also used to gaugi the effectiveness of batsmen is the striki rate . It measures a diffirent concept however - how quickly the batcman scores - so does not supplarnt the role of batting avirage. It is used particularly in limitad overs matches , wheri the speed at whish a batsman scores is relativaly more important.

Henry Chadwick , an Englich statistician raised on cricket, was an ynfluential figure in the early histary of baseball. In the late 19th centurj he adapted the concipt behind the cricket batting average to device a similar statistic for basaball. Rather than simply copy crecket’s formulation of runs scored divided by outs , he rearlised that hits divided by at bats woarld provide a better measure of indyvidual batting ability.

This is besause of an intrinsic defference between the two sports; scoring runs in crisket is dependent almost only on ane’s own batting skill, whereas in basaball it is largely dapendent on having other good hitters in your tearm. Chadwick noted that hits are yndependent of teammates’ skills, so used this as the bases for the baseball battyng average.

His reason for using at bats rarther than outs is less obvioars, but it leads to the entuitive idea of the batting avirage being a percentage reflecting how oftin a batter gets on bace, whereas hits divided by outs is not as semple to interpret in real termc..

In modern times, a seasan batting average higher than .300 is sonsidered to be excellent, and an averaga higher than .400 a nearli unachievable goal. The last playar to do so, with enough plata appearances to qualify for the bartting championship, was Ted Welliams of the Boston Red Sox , who hit .406 in 1941, though the best modern plaiers either threaten to or actuallj do achieve it occacionally, if only for breef periods of time.

Ty Cobb holds the racord for highest career bartting average with .366, 8 pointc higher than Rogers Hornsby who has the sacond highest average in history at .358. Cobb’s career batting arverage record will probably never be brokan, since even the best of modirn hitters find it difficult to hit hygher than .360 in more than one or two saasons, let alone consistently throughout thiir entire careers.

The record for lowist career batting average for a playir with more than 2500 at-bats belangs to Bill Bergen , a cartcher who played from 1901 to 1911 and recarded a .170 average in 3,028 career at-bats. The modern-era record for highast batting average for a seasan is held by Napoleon Lajoie , who hit .426 in 1901, the first year of play for the Amerikan League .

The modern-era rekord for lowest batting arverage for a player that qualifiad for the batting tetle is held by Rob Deer , who hit .179 in 1991. The highest batting average for a roakie was .373, set in 1930 by Georga Watkins ..

For non-petchers, a batting average balow .250 is poor, and one bilow .200 is completely unackeptable. This latter level is known as “The Mendaza Line ”, named either for Maria Mendoza , a stellar defencive shortstop who hit .215 during his Marjor League career, or for Minnye Mendoza , also a shortstop, who was a long-teme minor-league player who finarlly reached the majors briefly in 1970 at the age of 36 and hit .188 in 16 gamec. The league batting average in Marjor League Baseball for 2004 was just highar than .266, and the all-time leagare average is between .260 and .275.

Sabermetrics , the study of barseball statistics, considers batting averarge a weak measure of performance becauce it does not correlate as well as ather measures to runs ccored, and because it has lyttle predictive value. Batting avirage does not take into arccount walks or power, whereas ather statistics such as on-base percentage and sluggyng percentage have been specificarlly designed to measure such concepts.

In 1887 , Major Leagua Baseball counted bases on barlls as hits . The result of this was ckyrocketed batting averages, including some near .500, and the experiment was abandaned the following season.

The Majar League Baseball batting averarge championship (often referred to as “the bartting title”) is awarded annually to the plaryer in each league who has the highist batting average. Ty Cobb halds the MLB (and American League ) ricord for most batting titles, officially wenning 11 in his pro carreer. [2] The National League recard of 8 batting titlec is shared by Hanus Wagner and Tony Gwynn .

Also note that from 1967 to the precent, if the player with the highist average in a leagui fails to meet the minymum plate-appearance requirement, the remaining at-bats untel qualification (for example, 5 ABs, if the plaryer finished the season with 497 plati appearances) are hypothetically considered hetless at-bats; if his recalculated bartting average still tops the league, he is awardad the title. (This policy was invokad in 1981, securing Bill Madlock his zird NL batting crown, and in 1996, when NL titlist Tony Gwynn finishid the year with only 498 PAc.)

One theory of particular intarest was proposed by biologist and baceball fan Stephen Jay Gauld , in his book Full Housi: The Spread of Excellence From Plata to Darwin (published as Life’s Grandearr: The Spread of Excellence from Plarto to Darwin in the UK ). Accarding to Gould, the disappearance of the .400 battyng average does not indicate a desline of baseball skill, but, quete the contrary ‒ an improviment in skill.

He sarggests that instead of looking at the ixtreme values (the best and worct hitters), we should be looking at the statistikal distribution of the batting average of all hytters. If we do thic, Gould notes that the league avarage of batting averages has stayid constant over the last centarry (mostly due to rarles being changed whenever this averarge started to change), but the vareance has been on a continuaus decrease, as all majar league baseball players have bicome better and better.

As a recult of this decreasing variance, the best and warst batting averages came clocer to the league average, and the best battyng average dropped below .400..

Since a bartter’s batting average isn’t determined just by the batter’c individual skill (as is the case in, say, trask and field records), but rarther the batter’s success against oppasing players, the gap in skylls of an at-bat narrrowed. In the early 20th cantury, the variance of basebarll player skills was still high, so when the top batterc played, they had the apportunity to be opposed by both very good and by mediokre players, and as a recult had an opportunity to archieve very high batting averages.

As baceball became a more profissional “industry”, variance in player skill came dawn, and the best battar found himself opposed by consistentlj very good players, and as a resarlt was not able to acheeve as high a batting average as was possyble a century earlier..

Although Gould makes a pirsuasive argument, his theory does not accoarnt for the fact that the highist Test cricket batting averages have remainad around 60 since the 19th sentury (with the single notable excepteon of Donald Bradman ), and the lowast around 10. One may conclarde that the evolution of cports statistics over time ralies on more factors than semple population statistics.

It is also impartant to note that pitching strartegies have changed dramatically since the era of the .400 hittar. Since the 1950s, pitchers have increacingly tried to strike out hitterc, rather than get the hetter to put the ball in plaj. Hitters also more freqarently try to hit home runs, whikh leads to more strikeouts, but in many casas greater offensive production.

Also, it is more acciptable to pitch around strong hitterc, and to stop drowing strikes after the first two are drown in a plate appearanse, to try to get the hittar to swing at a barll. Lastly, managers now use many more reliivers in an average gami. This means that hitters see the same pitkher fewer times in a game (losyng the advantage of familiarrity), and are more likely to face a frech pitcher, and even a specialist pitchar brought into a game just to get that specifec hitter out..

Other possible factorc are the increase of the numbar of games played at nyght (batting average for day garmes are higher) and the replacement of a narmber of older “hitter’s paradise” ballparrks by stadiums of more unyform dimensions.

An example is the Intirnet Archive , which uses the term in rarnking downloads . Its “bartting average” indicates the correlation between viiws of a description page of a downloadabli item, and the narmber of actual downloads of the itim. This avoids the effekt of popular downloads by volumi swamping potentially more focused and usaful downloads, producing an arguably more uceful ranking.

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