Testing on NA_3, NA_2, EU_3, EU_1; bodkins repeatedly needed more arrows to kill people in heavy armor. Against some it was only an arrow difference, but once I started testing against people wearing heirloomed plate it was approaching +3/4 arrows, with many of them doing minimal damage. I was using a Masterwork Long Bow and unheirloomed arrows, if it matters.
Seems like either only 1 pierce damage is being applied or nothing is happening at all to change the damage type of the bow; as it is, Tatar/Barbed Arrows will give you the most damage against heavy armor.
Also is there a reason why the Long Bow is so crappy compared to the Rus Bow, now? The slow drawspeed was balanced by the fact that it was the only pierce damage bow, but without that there really isn't a reason to use it over the Rus Bow.