We need a metric to compare our specific level of authority (and likelihood of ranking) to other websites. Google’s own metric is called PageRank, named after Google founder Larry Page. Way back in the day, you could look up the PageRank for any website. It was shown on a scale of one-to-ten right there in a Google toolbar that many of us added to our browsers.
1) SEMrush - I believe that among all the 3rd party software, SEMrush has the largest keyword database. Their search volume data is pretty accurate and aligns with the Google keyword planner. Also, based on the type of content that needs to be produced (i.e. informational, transactional, etc.), one can utilize different filtering options available in it.

You can improve your site speed by a ton of methods, but the overall goal should be to test your site from different geo-locations using a tool like pingdom and then attend to issues. You could go for a CDN provider like Cloudflare or install caching plugins that speed up your site by reducing database queries and therefore the server load. Choosing the right hosting company for you is a critical decision and is based on many factors including your CMS, expected site traffic, and what your goals are for the site amongst others.
However, this does not mean you cannot topple them. It just takes more of an effort in terms of content as your page has to build the trust. That is why you will see the "Google dance" happening for fresh content from a site that is not yet trusted or is not very authoritative. Google gives your page a chance and measures user click-throughs when it pushes you to certain spots in the SERPs and then measures user engagement levels when the traffic hit your site through those positions in the SERPs.
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