wBABIP by COUNT

We are all aware that different counts offer different advantages and disadvantages in the pitcher-batter match-up. But just how much of an advantage is a 3-1 count compared to an 0-2 count? 

Obviously these two situations offer different odds of a walk or a strikeout occurring, but I wanted to concern myself exclusively with how the count affects the ball off the bat.

Adding linear weights to the traditional BABip formula is something I think could be useful for this. For instance, if we took the 'generic' wOBA weights for total bases used in The Book, and then borrowed the denominator from the traditional BABIP formula, but included homeruns:

(0.90*1B + 1.24*2B + 1.56*3B + 1.95*HR) / (AB - SO + SF)

This gives us a better estimate of not only if the ball was converted to an out or not, but perhaps how well the ball was hit, by adjusting for extra bases, as well. We can then apply the results to the average wBABIP in all counts for reference:

COUNT	wBABIP	+/- AVG	% of AVG
“3-0”	0.466	0.106	1.29
“3-1”	0.414	0.054	1.15
“2-0”	0.405	0.045	1.13
“1-0”	0.378	0.018	1.05
“3-2”	0.378	0.018	1.05
“2-1”	0.376	0.016	1.04
“0-0”	0.375	0.015	1.04
AVG	0.360	0	1.00
“1-1”	0.356	-0.004	0.99
“0-1”	0.342	-0.018	0.95
“2-2”	0.341	-0.019	0.95
“1-2”	0.328	-0.032	0.91
“0-2”	0.318	-0.042	0.88

... from 2002 - 2011, includes post-season, excludes all pitcher's PA.