wiki article about the subject for those interested.
http://en.wikipedia.org/wiki/Bodkin_point
'In a modern test, a direct hit from a steel bodkin point penetrated Damascus chain armour, although at point blank range.[2] However, the test was conducted without a padded jack or gambeson, which was layered cloth armor worn over heavier armor for protection against projectiles, as it was known to stop even heavy arrows.'
'Armour of the Medieval eras was not completely proof against arrows until the specialized armour of the Italian city-state mercenary companies.'
'Some recent tests have demonstrated that needle bodkins could penetrate all but heavy steel plate armour; one test used padded "jack" armour, coat of plates, iron and steel mail and steel plate. A needle bodkin penetrated every type, but may not have been able to inflict a lethal injury behind plate.'
That's my point. ( Pun intended.) Horses and everyone except plate wearers should be vulnerable to (1 or 2) arrow shots to the body in game. X-bows could penetrate plate, therefore even plate wearers in game should suffer from 1 to 2 x bow shots.
Are you sure you read your own wikipedia page, the information I got from it suggests that the armour penetrating abilities of the bodkin arrow are hugely overrated ingame, let alone the actual stopping power.