Well, I'm not the fartest smeller....er...smartest fellar in the world, but I kinda think this whole rigamoroe about x amount of kinetic energy or even the KO formula (something like ((velocity X bullet weight X bullet diameter)/(7000 -the number of grains in a lb of powder, whatever that has to do with it)) is stuff dreamed up by overzealous mathematicians.
Every action causes an equal and opposite reaction, right? That means that the rifle is going to hit your shoulder with the same energy that the bullet hits the animal with.
Hmm....are you going to die from the kick from even a very large, light rifle? No, animals die from organ/vascular damage, not how much energy they are hit with. You could hit a deer with 800 ft lbs of energy from a ball bat and it likely wouldn't kill it; slip a knife between it's ribs with minimal force and the deer's not going to live long.
When bullets are pushed faster than they are constructed for, they can fail to penetrate. When not pushed fast enough, small diameter bullets can fail to expand and can simply "pencil" an animal and they will run quite a ways. Considering this, I'd say matching your bullet velocity/construction/caliber has a lot more to do with it than how much energy it has.
A bullet with a wide meplat will cause more trauma than a pointed bullet, for another example of a variable.
So does energy have nothing to do with it? Not exactly. The bullet needs enough energy to penetrate the vitals, and if it's a small diameter bullet it will also need enough velocity and energy to make the bullet expand properly so that it leaves a large wound channel.
How much energy and velocity is needed is going to depend heavily on bullet weight, bullet construction, caliber, and what animal is being hunted. Just for fun, we might also need to add a standard of deviation; lets use the number of deer killed with a .22 LR in the last 50 years! That ought to do it.
~Rat