That equation doesn't look to be written in a way that would exclude a case for Vbs being 0. That would yield an exit velocity in the direction that the pitch is traveling, right (the negative sign on Vps)? If you held the bat in a vice of some kind, wouldn't a pitched ball hitting the bat still see a change in direction (sign)?
Edit to add: Would the walls of the bat compressing and expanding back out be considered a component of Vbs, to account for the exit velocity being positive?
Edit to add: Would the walls of the bat compressing and expanding back out be considered a component of Vbs, to account for the exit velocity being positive?