My background is in coding actually, and I have some data scientist friends, so while I'm no data scientist myself, that's where I put my faith. If you want to know what works, anecdotes are fine, I like hearing what experts think works, but nothing beats some proper data analysis done on the right data set.
Not a lot of people do that work in local unfortunately... I need to get off my butt and get into that myself one of these days, but for now, Dan Leibson's the guy to pay attention to. He's working right now I guess on the 2017 local ranking factor study, but his
2016 study is still great, even if it was done pre-possum.
For my two cents, you're basically looking at two classes of factors. You've got 'the price of entry' factors first up. Those are the things everyone needs to do to have even a shot... you can do everything else perfect and still shoot yourself in the foot if you mess this stuff up. It's stuff like site load speed, NAP consistency and citation work, onsite UX (bounce rate and CTR from the SERPs are both known to affect ranking) building solid reviews on the right sites, and so on. Then you've got your competitive difference makers... if you do everything else right, this is what decides who 'wins'. So if I was to pick one factor that I'd say is most important for local pros to focus on, it'd be getting your backlink game up to speed... though obviously you still need to hit everything else too if you want it to actually work.
Moz also posted their 2017 expert survey last month, so if you'd like to see what all the experts think to go along with the data study I posted above,
you should check it out. That'll give you a great sense of what's happened post Possum too, Darren Shaw made a point of organizing things around that topic for this survey.