There is a lot of things unclear about if bows can pierce through plate.
Adding some empirical data by Alan Williams. He studied armour more than anyone else and produced a book of almost 1000 pages about it. (The Knight and the Blast Furnace)
Lets take a look at the data. I will take it straight from the conclusion. The necessary kinetic energy (in joules) needed to defeat armour setups (Cause penetration past the armour of 40 MM actual penetration into flesh is excluded) These tests are done using the pyrimidial bodkin point.
Knight (C13) in mail and padding: 120 J.
Knight (C13) in mail, padding, and 2 mm coat of iron plates: 220 J.
Knight (C15 with Milanese armour) curved plate of 2 mm, medium-carbon, air-cooled, striking angle of 30°, no padding: 230 J.
Landsknecht/Swiss Pikeman (C16 Nürnberg infantry armour) keeled armour, 2.5 mm, at 45°, no padding: 260 J.
How much force does an arrow have? Williams cites quite low values (The tested longbow was quite weak with only 80lbs draw weight)
The normal english warbow suggests an average draw weight of 140lbs, A bow like that would generate around 120 J at point blank
The average English longbow generated kinetic energy of 120 Joules which is just enough to penetrate the armour of a knight who is wearing nothing but chain mail and padding. 50-100 Joules more would be needed to cause enough tissue damage to incapacitate him!
How about crossbows? Taken the measurements of Payne-Gallwey one can arrive at 140 J for a heavy siege crossbow of 1200lbs. As you can see, plate armor is more than sufficient.
But, this is tested against the strongest part of the armour, arrows can still be deadly by hitting weak points, or damage joints and immobilize people in armour.
And before you recite armour test videos:
A lot of armour testing videos neglect quite some factors. For one it is stationary armour with nothing inside, usually a mere 1 MM and without a gambeson, together with the fact that most modern repro armour is mild steel - period armours were generally hardened; this makes a pretty significant difference to penetration.