The key thing with any model of advanced stat breakdown is to compare players of similar usage, quality of linemates, and quality of competition. A lot of the advanced stat truthers will ignore all that on HF. I still remember all the discussions I'd have on here with Rangers posters that were big on advanced stats that would try and convince me that while both were in St. Louis, Shattenkirk was better than Pietrangelo. They simply couldn't understand how usage would impact corsi.
Control variables are fairly straightforward, but it's important to not attempt to control too many variables. Instead, what they'll do is set up alternate hypotheses and see if they can knock them out.
Besides that, defining the variables (similar usage, quality of linemates, quality of competition etc) is going to be the most difficult part of this. Operationalizing the variables is not impossible, but it's like a new field of study that hasn't accumulated enough literature for anyone to believe that the definitions are reliable and valid.
The best hockey advanced stats models are, imo, the simplest.
EXAMPLE:
Q1: similar usage vs quality of linemates = Q1A
Q2: quality of linemates vs quality of competition = Q2A
Q3: quality of competition vs similar usage = Q3A
Q4: etc
And then check for interactions between the results of each Q.
Advanced stats models that try to explain a lot in one or two graphs are probably missing the mark. Much better to break it all down into small studies and then measure for interactions.
So, without EVER having visited a website for advanced stats, I already know going into it that the good ones will keep it simple and present lots of data in simple but multiple formats, which can provide the context of dynamism in hockey. They are also going to provide definitions of the variables.
The bad advanced stats sites will try to capture the dynamism in a simple model and in as few graphics as possible. It won't work. Our perception is limited. Better said, our ability to present our fluid perceptions and make it understandable is limited.