I just did the calculations on new block rewards from the Constantinople update – Check my math?

TL;DR: Here are my calculations for the new daily supply of ETH after the Constantinople changes. Check my math for anything wrong.

I’ve been reading about Constantinople and this “thirdening”, with block rewards reducing from 3 ETH to 2 ETH. I’ve seen a lot of numbers about inflation, supply, etc. floating around. I wasn’t 100% sure where those numbers came from, so I went to etherscan to try to figure out myself what post-Constantinople would look like. Did some basic calculations with the reward information I know…check it out and let me know where I probably messed up:

FYI: The etherscan information I have, I took as averages from January 1, 2018 – January 7, 2019.

**Without Uncles*\*

Pre-Constantinople [reward = 3 ETH/block]:

5902.37 regular blocks produced/day [etherscan]

5902.37 * 3 ETH = 17,707.10 new ETH/day

17707.10 * 365 = 6,463,091.5 new ETH/year

Post-Constantinople [reward = 2 ETH/block]:

5902.37 regular blocks produced/day [assumption based off last year’s block data]

5902.7 * 2 ETH = 11,805.4 new ETH/day

11805.4 * 365 = 4,308,971 new ETH/year

For new ETH/day and ETH/year, the new ETH issued due to regular block rewards reduces by 33%.

**Calculating Uncles*\*

Pre-Constantinople [reward based off 3/8]

20,320.66 = total daily new ETH supply (regular and uncle rewards) [etherscan]

17,707.10 = daily new ETH supply from regular blocks

20,320.66 – 17,707.10 = 2,613.55 (daily new ETH supply from uncle blocks)

There are, on average, 1089.28 uncle blocks created per day:

2,613.55 / 1089.23 = average reward per uncle block

2.40 ETH = average reward per uncle block

5902.37 regular blocks + 1089.28 uncle blocks = 6991.64 total new blocks/day

1089.28 / 6991.64 = 15.58% of total new blocks/day are uncle blocks

Post-Constantinople [reward based off 2/8]

Assuming 5902.37 regular blocks/day and 1089.28 uncle blocks/day in post-Constantinople.

The formula for uncle rewards is:

R = ((uncle number) + 8 – (block number)) * (ETH/8), where:

R = reward per uncle block

Uncle Number = the uncle block number

Block Number = the block number

ETH = ETH rewards per block

So to plug it in with block number 7,080,001, the reward for uncle #1 is:

R1 = ((7,080,000) + 8 – (7,080,001)) * (2/8)

R1 = (7) * (1/4)

R1 = 1.75 ETH

The reward for uncle #2 is:

R2 = ((7,079,999) + 8 – (7,080,001)) * (2/8)

R2 = (6) * (1/4)

R2 = 1.5 ETH

The reward for uncle #3 is:

R3 = ((7,079,998) + 8 – (7,080,001)) * (2/8)

R2 = (5) * (1/4)

R2 = 1.25 ETH

In other words, the uncle rewards post-Constantinople reduce by .25 ETH every additional uncle block. There is, however, no way to predict how many uncle blocks will be sustained per regular block. The max is 7, but from what I’ve read, rarely are more than 2 sustained. In that case, if only 2 are usually sustained, we can average the ETH rewards per uncle block:

((1.75) + (1.5)) / 2 = Average ETH reward per uncle block

1.625 ETH = Average ETH reward per uncle block

Now, from our pre-Constantinople data, we understand that 5902.37 regular blocks and 1089.28 uncle blocks were created per day. It is my understanding overall uncle blocks will reduce post-Constantinople, but if we consider that negligible and look at pre-Constantinople numbers, that means:

1089.28 * 1.625 = 1,770.08 ETH/day in uncle rewards post-Constantinople

Final Calculations:

Pre-Constantinople:

17,707.10 new ETH/day from regular blocks

2,613.55 new ETH/day from uncle blocks

20,320.66 total new ETH/day

7,417,040.9 total new ETH/year

Post-Constantinople:

11,805.4 new ETH/day from regular blocks

1,770.08 new ETH/day from uncle blocks

13,575.48 total new ETH/day

4,955,050.2 total new ETH/year

Supply Reduction

((13,575.48 – 20,320.66) / 20,320.66) * 100 = % decrease in total new ETH supply/day

-33.19% = % decrease in total new ETH supply/day

And after all that…it was still just 33%…

Ether Inflation Calculation

I took these more specific numbers for post-Constantinople ETH issuance and looked at what inflation would be like (not taking into account any potential future reward reductions). And yes, I took into account the first ~2 weeks of 2019 with 3 ETH rewards:

Ether Inflation Chart

Date ETH Supply Inflation Inflation Change
Jan 2016 76166284
Jan 2017 87493855 14.87%
Jan 2018 96712864 10.54% -4.34%
Jan 2019 104142773 7.68% -2.85%
Jan 2020 109199001 4.86% -2.83%
Jan 2021 114154051 4.54% -0.32%
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