That ~$250M/year is spending on both homeless and homelessness prevention, only about $100 million of that is actual services for the homeless, of whom there are ~7000, so about $14,000/homeless person.
http://sfist.com/2016/04/12/no_san_francisco_does_not_spend_...
I think there's a strong argument for changing tactics, but if one of my friends anywhere in the bay area told me they were living on $14,000/yr I would ask if they have enough food, so it doesn't surprise me that this isn't really working.