Imagine Moons being distributed every day [Chart]

Thanks to u/meeleen223 for inspiration.

The idea of this post is to try to estimate how Moons to Karma ratio would look like, were we to distribute the Moons on a day-to-day basis.

Methods and results

To estimate daily karma earned, I simply used one of my more pessimistic ensemble models (described in more detail in my prior post [1]), but this time I applied it to every individual Daily rather than to whole Moon Round of Dailies.

[c01] This chart shows estimated amounts of Karma earned by sub on a daily basis. Round 10 had 7 missing Dailies for some reason.

To simulate the daily Moons distribution I run a few simulations and discovered that:

• initial Day 1 Round 1 distribution to contributors would be equal to 9.038e+04 Moons
• daily % decrease in Moons distributed would be equal to 9.038e-04 %

[c02] This chart was actually quite difficult to calculate. If you sum up distributed amount of Moons for each day, you'd come up with the same numbers as if Moons were distributed quad-weekly.

Daily Moons to Karma ratio estimate is then easy: Daily Moons distribution / Daily Karma earned estimate.

[c03] And here they are - daily Moons to Karma ratios. I wonder what happened before Moon Round 10 started.

Discussion

I have to clarify that Daily Moons to Karma ratio is not the same metric as Round Moons to Karma ratio. You can calculate Round ratio by averaging all Daily ratios for a particular Moon Round from chart [c03]. This is also the reason, why we don't yet know the true Round 16 Moons to Karma ratio.

I now like the number 9.038 for some reason.

Bonus charts

Let's make sure that charts [c01, c03] are at least approximately believable.

[c04] To calculate this chart, I summed up earned Karma estimates from [c01] for each Moon Round and plotted them against true known earned Karma values for every Moon Round from distribution CSV files. To me, correlation is obvious, therefore we can assume that [c01, c03] should be believable. If sum of parts is approximately correct, then individual parts should also be approximately correct.

Finally, let's plot [c03] using logarithmic scaling for vertical axis.

[c05] Yes, now we can see the obvious downwards trend. But it's good, since scarce and pricy Moons could actually improve the quality in the sub (see my post [2] on this subject).

References

[1] My prior post about predictive model test https://www.reddit.com/r/CryptoCurrency/comments/oghi7f/a_machine_learning_model_which_predicts_moons_to/

[2] My prior post about how Moon Round 16 seems to prefer Quality over Quantity https://www.reddit.com/r/CryptoCurrency/comments/ouxvri/what_makes_this_moon_round_different_chart/