There have been numerous studies in the past that have evaluated the much-maligned and often misquoted "200+ ranking factors" that Google use to evaluate a website's organic value and subsequent ability to rank for searches, but the latest from Stone Temple Consulting confirms that Links are the alpha and omega when it comes to rankings.
What this demonstrates is that, despite an ever-increasingly complex algorithm that's now evolving through machine learning more than human engineering, the quality and volume of Links (that's quality AND volume) has a direct correlation with a site's ability to rank.
The only things that come anywhere near that level of importance to organic positioning are Content (fantastic, authoritative, original content, which naturally attracts a lot of these quality links that a site needs), and RankBrain, the machine learning part of the Google search algorithm that helps the algorithm improve with every search.
Without Links, your Content may stand on its own two feet and perform well. In a competitive SERPs, Links will make the difference between the first page and the purgatory of page 2 and onwards.
The new study says there is a “near-perfect correlation” between ranking highly in Google and the links pointing to that page. This study aggregated the count of links by ranking position for the top 50 results across 6,000 search results pages, and it showed a near-perfect correlation between links and ranking. They used three different statistical models when analyzing the results.