Unfortunately, there is a lot of misunderstanding around how Google's search algorithm works.
Some of it is mysterious. Although I do not have a clear picture myself, there are a few things to note:
1. Google does show preferential treatment to its entities.
[URLnofo]http://blogs.wsj.com/law/2016/05/17/federal-lawsuit-alleging-google-improperly-censored-search-results-clears-hurdle/[/URLnofo]
2. Manual review.
Manual review means, a human reviewer looked at your site and decided it should not be ranked well. Google has published an example of their guidebook used for training manual reviewers of websites. The guidelines are detailed and worth reading.
It is unknown to me how many sites get manually reviewed, but I imagine it would not be possible to review every new website - only a small portion of search results.
A manual review could result in your site being ranked a "low effort site" - a low quality search result.
3. Engagement: Do your visitors leave after 3 minutes or 2 seconds? Google algorithms take this into account.
4. Your Money or Your Life Sites
Google has a criteria for sites that give financial, personal and other types of advice that can seriously influence the well being of a search user : their health, financials or personal life.
These Your Money or Your Life sites must have information verifying their legitimacy: a banking site must have a way to contact the bank - by phone, email, etc. These sites should be secured (HTTPS). These are examples of criteria that may be used for these more serious sites.
These criteria may be applied to manual reviews of some sites. It is unclear how many sites undergo this scrutiny.
5. Site load speed. The current generation of online users are extremely impatient and will abandon a site beyond 3 seconds (40% of traffic). This is a whopping percentage and an issue worth resolving before applying any other steps for ranking your site's pages.
6. HTTPS - now more important to ranking a site and considered
[URLnofo]https://en.wikipedia.org/wiki/HTTPS[/URLnofo]
7. Time.
These are just a few points to consider.