Why are 2 pheasants called a brace?

Pheasants are game birds that are hunted for food. In hunting, a "brace" is a term that refers to a pair of birds. One possible reason for using this term is that it was traditionally considered a suitable amount of game for a single hunter to carry. Another possibility is that gamekeepers would keep track of the number of pheasants killed by hunters by using braces, which would be easy to count and keep organized.