The core idea is to define your annual expenditures (let’s say $50k), a long term investment strategy you personally feel comfortable with (say 5% ROI), and from there you can deduce the amount you need to save to be financially independent (in this case, $1M).
Could you elaborate? Why would you need a level of comfort with an ROI? Or is the thing you need to be comfortable with actual the risk involved in getting that target ROI? Is that what you mean?
Also is the "million" you mention just a hypothetical? Although a million is a lot of money I don't thinks it's enough it's large enough to to qualify as being financially independent no? At least not in the US or EU. You would still need to work full time as it's not enough to retire on.
if you'Re thinking of a McMansion with several cars which you exchange every so often and constantly buy new gadgets etc then no, its not gonna be enough.
You sure as hell do need more than that if you want to retire in your early 50s and you plan on living another 30 years. At least if you want to live somewhere remotely interesting. $1 million divided by 30 would mean you need to live on 33K a year. Which is about $2,750 a month without accounting for future inflation which would erode this figure substantially over those 30 years. An average inflation rate of 2.50% would be a cumulative inflation of 109.76%. Your $2750 would trend towards half that during that time[1]
A common thread that these people tend to find though is that once you've saved up that much money, what you have actually learned is how to efficiently grow wealth, and I have seen very few examples of people actually just stopping there and coasting. Usually they just keep on trucking, maybe shifting into a different field.