This is something that we were thinking about and couldn't really find a solution yet, so appealing to the smart people here.
we all know that social media is good, we believe that, we encourage our users to use our lovely social media links... well, it's a social media world. Problem is: depending on many variables, including page, type of pages, hierarchies, goals, site owner's technology, human resources and so on, it's difficult to find a formula for a cost/benefit radio that we can apply to any situation with some kind of reasonable expectation in terms of return, where return could be measured by money, bounce rate, fidelity or any other metric as long as it works.
Right now, we've done some (quite extensive) Multivariate Tests and I'm observing the traffic leaks and disruption of user's attention isn't worth the benefits. The more action oriented the page is, the worse the results are. This is quite obvious, of course, and quite expected, so I'm taking this as an extreme of the range. Say "do not use Social Media at all", or 0 (zero) in an equation. This doesn't represent a problem in itself, because we have clearly identified user's behaviors with this kind of pages
However, in informative pages such as a corporate website, or an artist's site, or any kind of "brochure" site, I think that social media is needed and may prove useful, despite the eventual immediate monetary costs, like when using paid campaigns. Here, I can measure the return in terms of fidelity, so no problem either.
Then I have "mid way" sites: sites that may have call to actions, but they're not a meaningful part of the site. Take the artist's site again, and a link to buy tickets for a performance. In terms of analytics, this is the more complicated case, because it doesn't "fall" on any side.
My question/s is/are: is there some kind of CURRENT study/research (I have several 3-4 years old) or ux.stackexchange user's observations supporting or contradicting these observations and not coming from social media sites themselves? I'm not talking about traffic from social media to my site, but links to social media in my page. Even better, is there some kind of equation relating to the influence of social media placement (or lack of) and its costs, whether they're monetary, SEO or other?
EDIT BASED ON COMMENTS Just to narrow and focus, I have data with very definitive results, so outstanding I'm wondering if they're correct. I might share them at a later time, but not at the beginning because I would like non influenced answers. I admit the title is a bit broad, but I think the text of the question is as explanatory as possible and it focuses on 3 main cases (not saying that there are not more than this, just delimiting 3 big groups) and the effects of traffic leaks and technical issues (like site slowness) and its return in terms of benefits.
Just in case a more technical redaction helps understanding the question, I'm looking for more research I can compare with ours, and if possible, how to extract an algorithm that serves as much cases as possible based on the data I have