Just as a side note, i think my explanation is a bit easier to understand... and more accurate, as its not rooted in money supply theory, which is basically silly anyway.
The second one is actually the better of the two, IMO, but ive been told the first one is easier
In my opinion, frankly the second blog is so convoluted and inundated with a overly verbose explanation of the unnecessary complexity of vests, that I just gave up reading it about halfway through. Sorry but IMO it is really bad. That is not the way to simplify explanations. I don't intend to offend you, and I just want to be honest with my reply. I am not downvoting you. No animosity is intended. We are trying to help each other and the community understand.
In my opinion, the first blog is better organized and has more concision making it easier to follow, yet still you introduce this afaics mathematically unnecessary complication of vests. Afaics, the understanding of vests is a programming issue on the backend and it is mathematically irrelevant w.r.t. to understanding the economic structure of Steem, which is why I never mention it as it will only make the explanation of the economic structure of the Steem system more obtuse.
Afaics, there appears to be a mathematical equivalence between my way of conceptualizing (and the UI's way of presenting) SP as units of restricted STEEM coupled with the STEEM being separate units of the money supply where the supply of STEEM is increased ~100% yearly, versus your explanation of SP as vests converted to STEEM units by a ratio which changes as supply of vests increases. Frankly I've never found yet a complete explanation of the way vests are accounted and programmed on the backend, which is another reason I don't discuss them. And I haven't studied the code to figure it out. And I didn't find your explanation of them to be complete and unambiguous. If you'd like to cite a more canonical resource on vests, I'd appreciate that.
I don't know of a more cannonical source, unless the founders would care to comment. I figured out the way it works by looking at the numbers on steemd from day to day.
You cant get the numbers right without understanding vests.... i kind of see what youre trying to do, and tbh youre not far off but youre either double counting something or not counting it enough. Youre missing a key division that happens with the steem power value.
You're basically leaving two things out that almost (but not quite) cancel each other out.
1: the creation of additional vests to pay bloggers, etc devides the vesting fund, and decreases the Steem value of SP. In fact, if you @lukestokes (i think) has a pretty cool blog where you can actually see this effect happening with liquidity rewards (which are awarded the same way) as hourly pulses on a graph of a sharp decrease in SP growth rate. its visible here because althou gh the steem to fund them is created constantly, theyre actually awarded in big hourly lumps.
ALL new steem is created as steem power. not 90%, 100%. There is no such thing as newly created free steem.
The two things above almost cancel each other out, which is how you got fairly close with your numbers. But all youre doing is making an approximation based on an incorrect understanding of the proccess.
this is why your numbers are closest to accurate at a 0% growth rate of 81.8%.... , because thats the point where the two factors above cancel out perfectly. Its also why youre way off on the outlying numbers.
for example 5:95 SP ratio would create a huge gain for the 5%... they would start off with like 5% of the money supply and end up with a hair less than 50%, for a net gain of around 1000%.
the above should even be clear intuitively. If 90% of the new money being created serves to increase the value of the initial 5% holdings, the effect should be far greater than what youre talking about.
So for example, these 5 steem in SP. In the yearly doubling you create 100 steem. 90 of those steem are for SP incentives, and they get added on to those 5.
So those 5 steem in SP would now be worth about 95 (out of a 200 steem money supply)