According to the video I saw made by Tim McCarver and a physics professor the center of mass is about 1.5" to 2" from the end of a wood bat. This fluctuates depending on the shape (turning model) of the bat. It's nearly 3" from the endcap on a typical high end aluminum bat.
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The handle. A baseball bat is a third class lever. The resistance is the end, and the effort and fulcrum are the handle.
Draw a line through all the different verticals and horizontal balance points of the club then the intersection of all those lines is the centre of gravity