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Yes, there is a direct correlation between the keyword difficulty and the time it takes to rank for it. There is also a concept/formula that can predict how difficult it would be to rank for a particular keyword. It is called Keyword Golden Ratio (KGR) and is developed by Doug Cunnington. KGR is calculated by dividing the number of allintitle Google results for a specific keyword by its search volume. If the KGR for a keyword is less than 0.25, it's a low-competitive keyword that you can rank for easily and quickly. Please note that 0.25 is just a rule of thumb and you can select any threshold you think is right for you.

There is also a nifty tool built for this, called Allintitle Bulk Search tool that calculates the KGR score for many keywords at once: https://allintitle.co
Hope this helps.

I think Yext is really worth the cost and has the most important local directories covered. One main advantage of services like Yext or Moz Local is the ease of making updates to the listings. With manual citations, if you need to make a small change to the hours or description of the business, you need to repeat the task for all the sites one by one. But with Yext or Moz Local, it can happen quickly by just updating the business under your Yext or Moz Local account while automation will take care of updating the rest of the listings in the background for you.
There is also this business listing scan tool out there that I thought might be relevant to this question, it covers the most sites and also tells you what's your completeness score and your accuracy score with a short link that you can use to share the web-based report with others. I hope you find my answer useful.

Hi Mark,

Yes, there is a tool that does this exact job: https://allintitle.co

You can search for multiple keywords at once (500 keywords for example) and then export results to a CSV file. It also gives search volume, Google trends info, Keyword Golden Ration score (KGR), SERP overview as well as  Cost Per Click info.

Hope it helps.