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Your mention of Schilling made me curious -- is/was there any correlation between his K rate movement and his BABIP?
Well - his best BABIP of his career: 1992: .239 -- K/9 = 5.85 (worst of career)
His other good BABIP years?
1995 - .283 -- (K/9 8.84)
1996 - .284 -- (K/9 8.93)
1999 - .273 -- (K/9 7.59)
The interesting part of this is that the '97/'98 seasons his K/9 spiked to double-digit (11.29 and 10.05), while his BABIP also ballooned to .315 and .318.
Now, this is not a scientific study - and I'm not normalizing for team BABIP, etc., etc., etc.  But, there DOES seem to be a connection (a loose one) between BABIP and K/9 --  As K-rate climbs, BABIP does, too.  (at least for Schilling). 
This, I believe, harkens back to what I witnessed with the Braves' big three for over a decade.  They pitched "consistently".  They threw THEIR best stuff - and executed at a level that thwarted most hitters.  The entire concept of "fooling" the hitters by mixing up pitches wasn't even discussed.  In most cases, the catcher, ump, hitter, pitcher, and 90% of Braves fans KNEW what the next pitch was going to be -- and the hitter would whiff, or hit it weakly.  There was about as much question about what was coming next as there is when Mariano takes the mound. 
But - if the pitcher and hitter KNOW what is coming - so does the defense.  And THAT is huge, (in a sport where 70% of BIPs turn into outs).  Atlanta dominated in pitcher (and defense) for a decade with "fooling hitters" being the lowest of priorities.
And in thinking about it -- if a pitcher gets ahead 0-2 or 1-2, the 'normal' reaction of hitters is to shorten their swings, "protect" the plate.  Here's some food for thought:  What is the BABIP for the AL with 2 strikes?  .287  -- with 3 balls?  .314.
0-2: .291 -- OPS .404
1-2: .272 -- OPS .400
2-2: .274 -- OPS .456
Definitely food for thought.

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