A 50% reduction in the kinetic energy of the payload does not necessarily give a 50% reduction in the kinetic energy of the firearm, which is free recoil energy.

For instance, cutting the payload by half while keeping the velocity constant gives a 2/3 reduction in free recoil energy.

The longhand formulae are available in a SAAMI file and elsewhere, but I find a recoil calculator like the one I posted in the link is a lot handier.