"Axis"= location of hand grip on bat
Bat 1 = long uniform rod
Bat 2= long rod with mass concentrated at the end away from the hand grip
deltaKE= -deltaPE + W(NC)
1/2Iw^2 + 1/2mv^2 = -(0J-mgh)
1/2I(v/r)^2 + 1/2mv^2 = mgh
1/2v^2(m+I/(r^2)) = mgh
If mgh is equal for the two bats, 1/2v^2(m+I/(r^2)) must be constant. The bat with the larger I (moment of inertia) will have the slower speed. Therefore, the player should choose Bat 1, with the smaller I, in order to swing faster.