Baseball Bat and Moment of Inertia

In the midst of the World Series, I thought it would be interesting to examine some aspects of physics in the sport.  Many baseball players (including most of those on the Indians and Cubs I would assume) work hard in practice to improve their swing speed in order to hit the ball a greater distance.  These players lift weights to strengthen their muscles in order to exert greater forces.  Bats of different weights are also known to help players improve their swing speeds.  I thought it would be interesting to see how the concentration of weight within the bat could contribute to swing speed.  If a player has two bats, that are equal in size and weight, but differ in where the mass is concentrated, which bat can be swung the fastest when the same force is exerted?

"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.