By "metric", I assume you're talking about statistics, in which case I would measure the success of my social media marketing by, well, it depends on what platform I'm aiming for. On Facebook, I measure the effectiveness based on how many discussions I've sparked on my website page, how much traffic streamed in as a result of my latest article, and at the end, how much money was made. On Twitter, I base it on the number of retweets, and on Pinterest, the number of pins.
I don't use any specific tools other than the analytics suites on my site, there really is no need for anything more in my opinion.
Traffic and income are the two bottom lines for me. Success and failure for any marketing campaign is measured by the increase in traffic & income -- the higher the better, of course. . Anything over 10% is a win in my opinion.
I would look at the time spent against profits gained. If I see that I am doing well in relation to how much time I spend on social media marketing, then I'd say it's worth it. Afterwards, making it more efficient in a way that I can spend less time to get more income, but that part is easier said than done.