If peak batting averages vary over time across unstable means, and there is no systematic change in variances, then the wall needs to be based on a standardized performance that controls for variation in raw batting averages season by season.
If the distance between the wall of human performance and standardized batting averages is relatively constant overtime, then a player is prevented from climbing to .
In his 1986 piece, he described his data as including all batting averages of players who averaged at least two at bats per game in order "to gauge trends of regular players" (Gould, 1986, p.
On the whole, left-handed batting averages are higher than righty averages, meaning it should be more difficult for a right-hander to rise to .
2] For example, how could batting averages before 1893 be compared equally to batting averages since 1893, when the pitcher's mound was moved from 50 feet to 60 feet 6 inches from home plate?
Second, a five-year moving average of batting averages at one and two standard deviations from their season means will give a preliminary look at whether or not there is shrinkage in the left and right tails of the distributions of batting averages over time.
Declining variance in batting averages around relatively stable season means is critical to Gould's improvement hypothesis, but he never rigorously tests the stability of the means over time (Gould, 1996, p.
As Figure 1 shows, the mean league batting averages for righties and lefties over time are not stable.
There is no evidence at all that mean batting averages are anything close to constant overtime.
A key assumption about the dynamics of batting averages over time is that the distribution of batting averages in any given season, or aggregation of seasons, is approximately normal.
If the left and right hand tails of the distributions of batting averages over time have been shrinking, then the shrinkage should be apparent in the progression of points defining the tails.
The improvement hypothesis cannot be rejected just from this descriptive look at the data, but t he figures create skepticism about declining variance in batting averages over time explaining the demise of the .