There have been many mathematical formulas put forward over the years which attempt to reduce life to an equation. It doesn't work. What does work is choosing a round that provides a trajectory suitable for the range over which you intend to shoot, with a bullet that will function as it was designed, within an impact velocity window defined by the muzzle velocity at the high side and the velocity at your furthest intended range at the low side. A bullet that does not exit on a broadside shot may possibly fail on a frontal or quartering shot. An animal dies from a bullet wound when its brain cannot get enough oxygen to sustain life. The life support system of the animal is compromised with damage to the lungs or other major organs, by massive bleeding as oxygen to the brain is provided by the blood supply, or when the central nervous system itself is directly damaged resulting in a stoppage of heart or lung action or brain function. Sometimes game goes down as if the rug was pulled out from under it. Other times, game of a similar size can run long distances with a similar wound. The bullet path and performance are important considerations, but so is the condition of the animal, whether or not it is alert to danger, whether or not the lungs were expanded or deflated at the moment of bullet impact, and whether or not the heart was punctured or if the major blood vessels were cut off the top of it.
Ultimately someone asks the question, that given a certain set of circumstances which is better, the light and fast small bore bullet or the slower heavier big bore bullet. There are certain rules that must be adhered to if this question is to be answered in a realistic fashion. First is that for the purposes of the comparison the optimum bullets in each case are chosen. The light fast bullet is better at compensating for errors in range estimation. It can produce a wound out of scale in soft tissue due to the supersonic shock-wave that is created. On the negative side, much of the velocity can be used up quickly attempting to overcome the resistance of thick skin and fat and large bones. The short length for caliber of a light bullet can result in over expansion at high velocity and when the bullet no longer has a linear axis to rotate around, stability and straight line penetration are lost. A very fast bullet is likely to loose a larger percentage of its mass than is a slower heavier bullet. A loss of mass will cause the bullet to loose velocity more rapidly, resulting in a narrower, shallower wound. Whether or not this is enough to matter depends on the original weight on the bullet and the velocity of the impact.
The heavy slow hunting bullet seldom is made with a ballistically inefficient shape, and is therefore most useful at short to moderate ranges. Bullet drop over these short distances is unimportant so a bullet can be chosen which produces an optimum wound volume. The weight of the bullet is sufficient that little velocity is lost in the penetration of the skin, fat or even when a large bone is hit. The bullet is still super sonic, so there is a shock wave that disrupts soft tissue, but it will not cause as wide a wound compared as a ratio to the original diameter of the bullet, but it could be very well as wide or wider than the soft tissue damage of the small bore. Little percentage of the original bullet weight is lost due to the lower impact velocity, and for that reason there is not loss of penetration potential. Because expansion is more moderate, the bullet becomes nose heavy but the linear axis remains intact so straight line penetration is optimal for the impact velocity.
