While I do agree with the above comments, Backlinks aren't the only factors that determine rankings.
I have to respectfully interject that Backlinks while not the only factor, is a HUGE factor, and becomes even more so it seems when all other factors are met with quality.
Now also remember, RANKBRAIN DOESN'T TREAT ALL NICHES EQUALLY, it will decide on rankings for each niche by using different percentages of algorithms. So what works for one niche, isn't going to work for another always.
A quote from the link below: " Within Google, there are a number of core algorithms that exist. It is RankBrain’s job to learn what mixture of these core algorithms is best applied to each type of search results. For instance, in certain search results, RankBrain might learn that the most important signal is the META Title. "
Read this and have your mind blown: http://techcrunch.com/2016/06/04/artificial-intelligence-is-changing-seo-faster-than-you-think/
Now in my niche, if you're 95% sure the rest of your SEO is on point, backlinks can alter serps ranking more directly than I've seen almost any other factor so far. I say this because I've been disavowing backlinks for one client for the past 5 months now, I see direct correlations between me removing bad backlinks and seeing keyword rankings improve. I have also seen than when one of our EPA backlinks were redirected ( while they did a redesign on the directory we were in ) our Domain Authority plummeted and our keywords took a bit of a tumble.
I've also seen competitors climb to page 1, using black hat backlink tactics, such as sitewides, article spinning and just using keyword rich anchor texts in articles for sites with DA of 20 - 40. They have a site that is a shell compared to others in the industry, really don't have anything else besides these backlinks that could be helping them, and that they do until penguin is re-released.
I understand many claim that I shouldn't be able to know this because there are just too many factors, but after a year analyzing my competition, backlinks are what gets them visible in our niche at least.
Top 3 factors for Keyword Ranking has been said to be:
- Rankbrain
- Backlinks
- Quality Content