I looked for a number to quantify the amount to which a hitter responds to the location of a pitch.

Here's what I've done.

Using gameday hit locations I calculated the trajectory of every batted ball, varying from -45° (down the LF line) to 45° (down the RF line); then I rescaled the trajectory value to have it varying from -1 to 1 (this made life easier for me in the following calculations).