The use of comma in written English

The main reason to leave off/on commas in this kind of sentence is to make clear whether the "which" clause is a specifier or not. When I say

The horse, which won the last race, still seems winded.

I am simply supplying additional information about the horse. On the other hand,

The horse which won the last race still seems winded.

Means that I want to be specific about which horse I am speaking.