Comparing your Google Analytics data side by side with the dates of official algorithm updates is useful in diagnosing a site health issue or traffic drop. In the above example, a new client thought it was a switch to HTTPS and server downtime that caused the drop when it was actually the May 6, 2015, Google Quality Algorithm (originally called Phantom 2 in some circles) that caused the sudden drop in organic traffic – and the problem was probably compounded by unnatural linking practices. (This client did eventually receive a penalty for unnatural links when they ignored our advice to clean up).
Advertising with Google won't have any effect on your site's presence in our search results. Google never accepts money to include or rank sites in our search results, and it costs nothing to appear in our organic search results. Free resources such as Search Console, the official Webmaster Central blog, and our discussion forum can provide you with a great deal of information about how to optimize your site for organic search.