Quote from: PressF1 on July 20, 2014, 03:59:01 PM

The effect of 100% POS on the monthly inflation of Hobonickels

One of the reasons I like HBN is the fact that you can mint the coin without using mining rigs. Mining rigs consume a lot of energy, need a lot of attention, need to be bought and usually generate less coins every month where as minting hardly uses any energy and doesn't need much attention. Ok, you also need to invest but your investment generates more coins every month in stead of less.

But what about inflation? Granting 100% yearly interest on POS surely will sent the inflation through the roof, rendering your HBN-stash worthless over time. Or doesn't it?
Being almost a year into the HBN adventure I decided to do some math on the matter. To see what actually happens, what inflation is to be expected and how it's affected by the 100% POS rate.

First, I would like to know what inflation would be if there was no POS at all. Just the regular POW. Since the block chain tries to aim for a 30 second block interval, this isn't too hard to work out. 1 block every 30 seconds equals 2880 blocks a day. Since a POW block contains 5 HBN, the HBN money supply rises every day with 2880 * 5 = 14400 HBN. Let's put this together using excel:

Theoretical growth of supply without POS

    block     supply infl/mth
24-7-2013   0     0
1-8-2013    22646     113230
1-9-2013    111926   559630   394,2%
1-10-2013   198326   991630   77,2%
1-11-2013   287606   1438030   45,0%
1-12-2013   374006   1870030   30,0%
1-1-2014    463286   2316430   23,9%
1-2-2014    552566   2762830   19,3%
1-3-2014    633206   3166030   14,6%
1-4-2014    722486   3612430   14,1%
1-5-2014    808886   4044430   12,0%
1-6-2014    898166   4490830   11,0%
1-7-2014    984566   4922830   9,6%

So this is what we could expect without POS. 14400 HBN daily added to the supply. As you can see, the monthly inflation is decreasing. It makes sense when you think of it. For example in Oct. 2013 the supply goes in 31 days from 991630 to 1438030. An inflation (= increase of the supply) of 45%. A month later the same daily amount is added but since the supply is bigger than before, it's a smaller percentage. So in time the inflation will automatically decrease. Bear in mind: this is to be expected without POS!

Now it gets interesting. The theory is clear about inflation without POS but HBN has POS. a nice 100% of it. How did the supply evolve in reality? Did POS sent inflation through the roof? Let's see what happened. What's actually in the block chain. Check the above data to see the differences.

Observed growth of supply with POS

    block     supply infl/mth
24-7-2013    0     0
1-8-2013    24075   120372
1-9-2013    113060   541767   369,6%
1-10-2013   199014   960995   76,0%
1-11-2013   286219   1385908   43,8%
1-12-2013   372264   1849933   30,1%
1-1-2014    461136   2330766   23,9%
1-2-2014    550116   2778403   19,3%
1-3-2014    630790   3206341   14,7%
1-4-2014    719789   3671800   14,1%
1-5-2014    806508   4106540   12,0%
1-6-2014    898413   4629448   11,4%
1-7-2014    988559   5068546   10,0%

Indeed. What differences? In the first year of HBN, the 100% POS rate hasn't hardly changed the monthly inflation of HBN. On the first of July, the non-POS prediction of monthly inflation is 9,6%, the actual inflation with POS is only 0,4pp higher. That's hardly any effect at all! How is that possible?

I think the 30 second block time is key in understanding this. Whatever block is generated, the block chain will try to keep the block time at 30 sec, and thereby the amount of POS and POW blocks together as close as possible to 2880 a day.

So the possible difference in monthly inflation comes down to the difference in yield of POW and POS blocks. POW is fixed at 5 HBN. POS is not, so a high yield POS block (>5) raises inflation a bit but, and this is important, a low yield POS block (<5) lowers inflation as compared to POW only supply growth.

So if the mean POS yield is close to the fixed POW yield, POS adds no extra inflation. And this is the case with Hobonickels when considering the last year: 100% POS adds hardly any extra inflation. Funny isn't it? And the proposed max POS yield of 500 will drive it even further back.

Just let me know if you agree with my line of reasoning.

I generally agree with your reasoning, but just wanted to add another layer to your numbers.

If we look at the actual supply as of 1 July, we can see that a large part of the additional inflation is actually due to almost 4,000 extra blocks being generated compared to the theoretical growth.

Average block value as of 1 July is 5.127 HBN, which equates to 2.5% additional inflation, over pure POW.

If we correct the numbers for 1 July, so that the number of blocks generated are in line with expectations, the money supply would only have grown by 9.1%, and thus be below the theoretical target. (We can also see that the average block size of blocks from 1 June to 1 July is only 4.871 HBN, and POS is actually lowering inflation)

All in all I think we can conclude that for HBN POS does not appear to have a significant impact on supply, while still handsomely rewarding users who hold on to their coins. I believe that we can call this a win-win

Disclaimer: I have used PressF1's numbers as-is, so any errors in his numbers will have carried over.

scryptographer

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