Standard life-ring stations normally come with 200 feet of line; for high bridges, the line is often increased to 400 feet. The best option is to throw it in up-current of the person in the water, though there are times when that won't work because you can't get to a good point to throw from. Obviously, the line also needs to be securely tied off to a solid object ASAP. People very seldom actually get pulled in with one of these; the idea is to allow them to hold on, stay afloat, and resist the current long enough to wait for skilled rescuers to arrive.
The thing is, even if the person in the water still drowns, the ring has done some good, because it allows LEOs and bystanders to TRY to effect a rescue without delay and without major danger to themselves, and that matters, too, for less obvious reasons. If you have tied off and thrown a life ring, you can tell yourself that you at least tried, even if the try did not have the desired result. It reduces mental anguish for survivors, and yes, takes away the stigma of standing on the bank apparently doing nothing. Most of all, it makes it far less likely that a well-meaning second person will jump into the water to try to effect a rescue and end up also needing help.