In the modern era of baseball the homerun has become the object of the fan’s adoration. In 1998 the nation stood in awe as Mark McGwire and Sammy Sosa battled it out towards Roger Maris’ 62. America applauded as the St. Louis’ slugger rounded the bases for the 70th time of the season, late in September, yet the “untouchable” feat stood for a mere three years, until Barry Bonds blasted his way into the record books. In this age of offense, where steroids, small ballparks, and power swell statistics, the baseball fan is forced to ponder whether or not any sacred clubs still exist within the game. That being said, since1901 there has been one achievement more hallowed than fifty homeruns in a season, a perfect game, thirty wins, 160 runs batted in, or even the triple crown, and that is the .400 club.
the early days of baseball .400 was commonplace, a deed worth noting, but
nowhere near the legendary number that it has evolved into. In the nineteenth
century twenty different players hit .400 a combined twenty-three times.
However, prior to the turn of the century organized baseball was still in a
state of development. For instance in 1887, base on balls were counted as hits,
accounting for 13 players reaching the .400 mark, in only one season. Another
reason for high early membership to the .400 club was the lack of a foul-strike
rule. Prior to 1901 in the National League and 1903 in the American League foul
balls that were not caught did not count as strikes, giving the hitter a
profound advantage at the plate. This is the reason many baseball historians exclude
Nap Lajoie from the other players to hit .400 in the
20th century. By playing for an American League team in 1901 (
years passed after 1930, and many in the baseball community thought that the .400
hitter might be extinct. Then in 1941 the Boston Red Sox 23-year old cleanup
hitter came onto the scene and put together arguably the most impressive season
in baseball history.
now sixty-two springs have ushered in the hope of another .400 hitter, yet all
sixty-two seasons have ended lacking even one batter to surpass the illustrious
mark. In 1941 the
Optimism is not universal in the sporting world when it comes to the chances of surpassing the Splendid Splinter’s mark. Many say the disappearance of the .400 hitter is due to the fact that the level of hitting and a batters devotion to his craft has declined since the first half of the 20th century. Others assert that night games, relief pitching, and longer schedules have also factored into the fall of the phenomenon. However, the late Stephen Jay Gould, a world-renown Harvard biologist, said that these theories are largely unfounded and lack strong evidence. According to him the, “modern artists of hitting – the Boggses, Carews, Bretts, and Gwynns – play with as much intensity as the great .400 hitters of our past – the Cobbs, Hornsbys, and Sislers”. Rather than the explanation that players have gotten worse Gould suggested that in fact they have improved over time. With all of the new tools available to the 21st century athlete this would seem to make sense. The conditioning, weight training, technology, and increased talent pool (race barrier prior to Jackie Robinson) would seem to suggest that the Major League player today has far more opportunities to sharpen his skills than those in the past. Tony Gwynn himself attributed much of his success to watching video tapes of his swing, something a Babe Ruth could not easily do.
So why then is batting average the one statistic not swelled by these personal improvements? The answer lies within a statistical term called standard deviation. In the early 1900s Ty Cobb, Rogers Hornsby, and George Sisler were giants among dwarfs. They were near the physical limits that a human being can possess when hitting, due not only to their natural talent, but also their desire to improve their skill. The giants in baseball still exist in the persona of such stars as Albert Pujols and Barry Bonds. These hitters too are near the barrier that limits a human’s productivity in a sport. However, the difference between these two eras is that the common ballplayer has gotten closer and closer to this barrier of man’s possibility, while the stars have no place to go. As this standard deviation has shrunk the giants of baseball no longer have been able to tower over the ordinary individuals in the sport. This decreasing chasm between the best and the average players has led to the disappearance of the .400 hitter. The argument that hitting ability has decreased since the early 1900s has little merit, since the Major League average was .252 for 1901-1910 and .258 for 1911-1920, an era when .400 was reached four times. For comparison purposes the ML average was a similar .258 from 1951-1960 and .257 from 1971-1980, two decades when no batter came very close to the mark. In fact league averages have constantly stayed near the .260 mark for the past century, with slight exceptions in the ‘20s and ‘30s, making it evident that something deeper is repressing the league leading batting averages.
With this data in mind I took Gould’s hypothesis about the shrinking standard deviation and tested it against such years as 1921, 1941, 1961, 1982, 2000, 2001, 2002, and 2003. For the earlier years (prior to 2000) I only entered batting averages when the player had at least 400 AB. Any smaller number of at-bats would suggest the player was either a reserve or injured, in which case the feat of hitting .400 would be minimized. For the 2000-2003 data I only included qualified batters (based on 3.1 plate appearances/game) in my calculations. The goal of my statistical analysis of these years was to either support or refute the hypothesis of diminishing standard deviation, and find the exact probability of a batter hitting .400.
to the standard deviation, I found convincing data that in fact the .400 hitter
is heading towards extinction. In 1921 the Sx
(Standard Deviation) was an amazingly high 40.554 points. What this means is that 68% of the 98
qualified batters were within 40.6 points of the league mean batting average of
308.51, or in other words just over two-thirds of batting averages in 1921 were
between .268 and .349. This was by far the highest Sx
I observed, and just twenty years later in 1941 this number had shrunk to
32.478, meaning that 68% of the 101 qualified batters were hitting between .248
and .313. Over the past few years this decrease in standard deviation is
evident on an even smaller scale, as Sx
has gone from 30.029 to 28.424 to 26.893 to 26.051 from 2000 up until last
year. It is clear that while there is a downsloping
trend since 1921 for the standard deviation it has slowed from 1941 to the
present. One explanation for this is the numerous expansion franchises, which
have entered both leagues since 1941. What these extra teams have done is
spread the talent thinner than before and allowed the stars to shine a bit
brighter than they would have had the talent still been condensed on fewer
teams. However the fact still remains that as each October passes it becomes it
becomes increasingly more difficult to hit .400. As the standard deviation
declines and the “ordinary” major league ballplayer approaches the sport’s
physical limits, the window of opportunity to join the ranks of
statistical formula on my scientific calculator I was able to determine the
percentage chance of a batter reaching 400 in the various random seasons I
studied. Based on the 1921 batting average distribution I calculated that there
was a 72.694% chance that at least one batter from that season would hit .400
or better. While no hitter from that specific year actually reached the mark,
one could estimate that approximately seven hitters would reach .400 in the
‘20s if the ’21 data was representative of the decade (.7 x 10 = 7). This was
in fact the case, as there were seven seasons of .400+ averages from 1921 to
1930. In 1941, which was the year Ted hit .400, there was just a 1.94% chance
of at least one batter hitting .400 or more.
Gould states, “In this context,
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