According to the initial report from the archaeologists excavating Greyfriars Church in Leicester, the skeleton that they suspect is that of King Richard III has:
A barbed metal arrowhead {was} found between vertebrae of the skeleton’s upper back.
It seems quite unlikely that the arrow entered the body after death. We know that Tudor paid scant regard to the rights due to a dead King. But if the body had been used for target practice after death, there should be more evidence in the form of nicks to ribs and other bones and possibly more arrowheads at the site where the skeleton was found.
According to Charles H. Ashdown, Medieval archers had 2 types of arrow in their bag. "The flight-arrow was lightly feathered, had a short head (or pile), was a yard in length and with proper elevation could kill at 240 yards or more." (Armour and Weapons in the Middle Ages, page 156f) This type of arrowhead was termed a "bodkin", was square or triangular in cross-section and proved very effective in piercing plate armour. This would be the arrow of choice in the opening rounds of a battle, as at Towton.
The other kind of weapon was called a SHEAF-ARROW which "had heavier piles, required but slight elevation, was often shot at point blank range and was essentially for close fighting." (opsit, page 157) The heavier arrowhead was frequently barbed. This made it more damaging to withdraw from a wound. It was also flat and roughly triangular in shape, designed to slice through flesh and blood vessels, causing major internal bleeding. As such, the barbed arrowhead was, and still is, popular among hunters of game (see page 176 - 181 of Longbowby Robert Hardy).
Such arrows could and did penetrate plate armour. This is clearly shown by an illustration from Froissart, showing the terrible injuries inflicted at Poitiers by English bowman to men and horses. Two French knights are shown with arrows piercing their back at the right of the image. The strikes are similar to that described on the remains at Leicester. At left of the picture we see English bowmen about to release arrows with clearly barbed heads. The artist gives the impression that these were indeed fired at very short range.
From the information so far released it is impossible to say whether the victim was shot in the back or through the chest. When the full report is issued this should be made clear. However, it seems unlikely that an arrow would have penetrated from chest to spine. Certainly Richard would have worn state-of-the-art Gothic armour, designed to deflect just such an injury. Such a blow would also have left damage to ribs and sternum, which would be easy to verify.
I surmise that the victim was shot in the back at close range. An archer would have most likelihood of striking the back plate at right angles, penetrating the armour and so wounding his target. The back plate would have impeded penetration but clearly couldn't stop.
When the exact site of the arrow is revealed it should become clear whether it damaged the spinal cord or merely the muscles overlaying the vertebrae. If the former, the result would have led to paralysis and collapse; the latter would cause blood loss, weakness and eventual inability to protect himself.
Our most sympathetic authors, such as Sharon Penman and Paul Murray Kendall, have depicted the King's violent death as being smashed to the ground by overwhelming numbers and then hacked to death. The arrow injury suggests a different scenario.
King Richard is on foot, protecting his dying standard-bearer who had suffered the loss of both legs. The King is "fighting manfully" to borrow Polydore Vergil's phrase (Polydore Vergil, page 224). Instead of rushing him, his assailants encircle him until one of the Cheshire bowmen puts an arrow in his spine. This would lead to the King's inability to hold his weapon and he would fall to the ground. Then a killing blow would be administered consonant with the reported head injury to the skull, probably by a pole-axe.
It is ironic that the Cheshire bowmen who prided themselves as the Royal bodyguard for Richard II should be implicated in the death of Richard III. It is also ironic that Richard, whose sigil was a boar, should have been brought to his knees by a hunting arrow.