Yes all those factors are part of it. Defeating armor is not a question of if, but a question of how much. How much force needs to be imparted to X projectile to penetrate Y armor, conversely what kind of armor do I need to wear to protect me from X projectile? No one will wear armor if it doesn’t protect you from the most common damage you will take, if a man in armor easily went down to an arrow without fail, he would drop the armor and pick up a bow without hesitation. Thus will armor protect you from arrows, given a good set of armor and facing the common type of projectile for its time, yes.
The energy a projectile carries will depend on what point in its flight it is in. The energy at release is not the same as the energy it carries in a long arch as gravity brings the arrow back down to earth. The weight of the shaft shape of arrowhead, caliber of bullet etc all are factors in figuring this questions out. Over history bows have been of many different draw weights, the arrows have been of many different weights, the arrowheads have been of different shapes, and armor has been of many different qualities. A bow used from horseback will be different from that used by a footman and an arrow meant to fly 500 yards will not be the same as an arrow meant to hunt deer with or the arrow meant to be used against a man in armor. So any time you ask this question you need to be specific, what bow, what arrow, what armor, etc. comparing the wrong types will lead to false understandings of armor and arrows. If you take a 120 lb longbow with hardened steel bodkin arrowheads and put it up against naked chainmail you will shred the maile like Swiss cheese, but this is a poor comparison, wrong bow, wrong arrowhead to use against that armor, and you would usually have another type of armor to help diffuse the energy of the arrow.
The one constant you can see through history is that armored men have stood in a hailstorm of arrows, survived and it took melee weapons to move in and kill them after. From Carrhae to Agincort and many more, the armored men were not killed in droves by arrows. They were annoyed, pestered and exhausted by arrows, some did die, but most fought hand to hand and when killed it was by other weapons.
Now you have brought up a point I think is very important to any discussion of Arrows vs Armor, that being damage. Perhaps the armor did hold to one arrow or ten arrows, but did it damage the armor? How many arrows will it take to damage the armor to the point is will give? This seems to be the more important question to me.
This is a flawed test as all are, too close range, too light of armor but it demonstrates the point of damage. -
http://www.youtube.com/watch?v=q-Xp56uVyxs
I’m with Stacy more realistic tests should be done, but frankly it’s also a stupid thing to do. A skilled archer if he can aim will not aim dead center, the variable is can he aim.