Nathan - the truth is that simply having more social media signals, more links and more indexed pages doesnt mean you will outrank a competitor. Although theses statistics may give you a better DA than your competitors, that metric is used more as a general reference. What you should be doing is breaking down the three signals above as follows:
1. Social Media: OK so you have a lot of 'likes' - are people tweeting, posting on your fb page? Bookmarking? Social activity is the big signal.
2. You have more links - are they relevant? Are they from separate relevant domains? I've had instances where clients come on board and say "I have 5000 links and my competitor has 200 and they outrank me". Further investigation shows that the '5000' links were from only 58 domains, most of which were spammy blog links that were not directly relevant in content (paid blog networks). The competitor however, had 200 links from about 150 domains, and many of those domains were specifically about the vertical. In other words, they were natural relevant links.
3. A lot more indexed pages. Again this means nothing - what matters is that each page has value, is unique and informative according to Google. In fact, if the pages aren't deemed informative and unique, having more indexed pages can be harmful. Just because Google hasn't dropped duplicate/spammy pages from their index doesn't mean that they are 'helping' you rank. In this case you are blogging so as long as the blog posts are unique then you should be ok, but always remember quality not quantity.