A couple of points that I would like to throw in to the discussion
I don't think that the majority of people would have been wearing plate even in the 15th/16th century. Some plate over a jack or just a jack would be much more common. Needle point bodkins can work against a cloth jack (they push the weave apart) but should cause less bad injuries than broadheads (I'm sure someone who hunts could comment). Broadheads bounce off against thick cloth armour if it is made right. Mail plus cloth armour is much better than it's component parts.
Before the English war bow appeared, bows were smaller, weaker and were drawn to the front of the face/chest. They were used by pretty much everyone except late Saxon armies. They are different weapons. There are accounts of crusader armies standing until Islamic armies ran out of arrows using similarly powered bows.
Andy
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