Benny Skogberg is spot on in saying that the more options you provide, the higher the chances of registration since users might opt for registration using the standard registration module or the social login options.
That said, studies have shown that having a social login option does increase your conversion rate. To quote this article
We wanted to test the increase in conversion that social sign on
creates. To do that, we looked at a series of campaigns that had
either just a regular old form, and compared those against similar
campaigns that had both a regular old form AND a Social Sign-On option
(in these tests, it was LinkedIn).
When both were present, 86% of submissions occurred through the
regular old form, and 14% occurred through the social option. The
Social Sign-On is cannibalizing the regular form submissions to some
extent (people switching from the regular old form to the social).
Where it gets interesting is when you compare the overall conversion
rates to the standard form only. A form with both options converts
8.5% MORE website visitors to form submitters!
Also a couple of responses from quora do confirm that social logins have increased conversions (Note : I am aware that it is not a written statistical study but anecdotal information can be useful too) To quote the quora post :
Full disclosure, I am a marketing manager at Gigya. We provides social
login for hundreds of heavily trafficked sites with millions of users
authenticating via social login. Typically, we see conversion rates
increase anywhere from 20-40% after social login implementation.
Keep in mind that conversion rate is highly dependent on the following
factors:
- Choice of social networks for login. It's suggested to offer at least three social identity providers to start with. Not all users
want to sign in with Facebook. In fact, our aggregate stats show that
about 60% of users authenticate with Facebook, 12% Google, 10%
Twitter, and a variety of other social networks make up the rest.
With regards to which social login option can greatly work for your demographic, I strongly recommend reading this excellent article which compares login and registration via social logins and their distributions. To quote an excerpt from the article
When it comes to social login, people want choice. Facebook currently
leads as the most popular identity provider for social login. During
Q3, Facebook lost a bit of ground with its share dropping slightly to
45%,
Google has gradually closed the gap on Facebook as the second most
popular choice, and its share increased a fraction of a percent during
Q2