Computer analysis by Warsaw University of Technology in 2017 demonstrated that heavy bodkin-point arrows could penetrate typical plate armour of the time at 225 metres (738 ft).

Can bows penetrate plate armor?

Even at extreme close-range with high-poundage war-bows, penetrating plate armor is almost impossible. Very powerful crossbows at very close range might do it, especially against low quality armor, but even then, the odds are in favor of the armored man.

Can arrows penetrate chainmail?

Bodkin arrow - probably yes. It depends on many factors like distance between archer and his target, angle of impact, draw of bow, etc. But even if an arrows penetrates the mail, it will not kill the soldier wearing it.