Bracer goes on the arm you use to hold the stave. It protects you from the string snapping. Considering that a bowstring's got 50+ lbs. of force, it can be significant. There's no reason to put a bracer on the arm pulling the string back.
That is true, but in Kyuudou (traditional Japanese archery), you use a special glove on your drawing hand to hold the bowstring closer to the palm. The covered fingers are used to hold the arrow straight, since in Kyuudou, you nock the arrow on the outside of the stave, rather than the inside (inside being the common way Western archery is done).
Bracer, not glove. And leather gloves were used by Europeans and Arabs, if not damn near everyone. It gives you some protection from your fingers bleeding from pulling the string.
