Qualifying for Batting Average makes no sense. It doesn't use the denominator.

Denominator. You know. The bottom of an equation.

http://mlb.mlb.com/mlb/downloads/y2015/official_baseball_rules.pdf

9.20 Statistics
The League President shall appoint an official statistician...

9.22 Minimum Standards for Individual Championships
To assure uniformity ...

(a) The individual batting, slugging or on-base percentage champion ... provided
the player is credited with as many or more total appearances ... at the plate in league championship games as the number of games scheduled for each club in his club’s league that season,
multiplied by 3.1 ... Total appearances at the plate shall include official times at bat, plus
bases on balls, times hit by pitcher, sacrifice hits, sacrifice flies
and times awarded first base because of interference or obstruction...

Rule 9.22(a) Comment: For example, if a Major League schedules
162 games for each club, 502 plate appearances qualify
(162 times 3.1 equals 502) a player for a batting, slugging or
on-base percentage championship.... Fractions of a
plate appearance are to be rounded up or down to the closest
whole number.
______________________________________

The same problem exists for slugging average. Both have at bats (AB) as the denominator, NOT plate appearances (PA). It's pretty basic.

There are other problems, which will be addressed in another post. They include whether the qualification should be based on opportunities (AB) or accomplishments (Hits, Total Bases, etc.) or some combination. However, opportunity qualification should NOT be based on PA.