Calculation Example

Let's break down the calculation of the Return Coefficient (M) over 15 days, if count increases 50 every day, referrals increases 20 every day, staking 1m DP on day1.

Formulas Recap:

• Initial M Decay: Initial_M_decayed = 0.52 * (1 - 0.0155 * (Day - 1)) (Applied only to the initial M, not the incremental factors. For Day 1, (Day-1) is 0, so no decay.)

• Participation Factor: Participation_Factor = (Count / (144 + Count)) / 3

• Staking Factor: Staking_Factor = 0.25 * ln(P/10,000 + 1) * (0.25 + t/30) / 4.5

  • P = 1,000,000 (Staked amount)

  • t = Day (Days locked, which increases daily)

• Referral Factor: Referral_Factor = (Referrals / (20 + Referrals)) / 5

• Total M: M = Initial_M_decayed + Participation_Factor + Staking_Factor + Referral_Factor

Assumptions:

• Count: Starts at 0, increases by 50 every day. So on Day N, Count = (N-1) * 50.

• Referrals: Starts at 0, increases by 20 every day. So on Day N, Referrals = (N-1) * 20.

• Staking (P): Fixed at 1,000,000.

• Days Locked (t): t = Day.

Now, let's calculate the values for each day:

Day	Initial M (Decayed)	Count	Participation Factor Calculation	Participation Factor	Referrals	Referral Factor Calculation	Referral Factor	Staking (P)	Staking (t)	Staking Factor Calculation	Staking Factor	Total M
1	0.52	0	(0 / (144 + 0)) / 3	0	0	(0 / (20 + 0)) / 5	0	1,000,000	1	0.25 * ln(100+1) * (0.25+1/30)/4.5	0.0709	0.5909
2	0.5119	50	(50 / (144 + 50)) / 3	0.0854	20	(20 / (20 + 20)) / 5	0.1	1,000,000	2	0.25 * ln(100+1) * (0.25+2/30)/4.5	0.0815	0.7788
3	0.5038	100	(100 / (144 + 100)) / 3	0.1366	40	(40 / (20 + 40)) / 5	0.1333	1,000,000	3	0.25 * ln(100+1) * (0.25+3/30)/4.5	0.0921	0.8658
4	0.4957	150	(150 / (144 + 150)) / 3	0.1709	60	(60 / (20 + 60)) / 5	0.15	1,000,000	4	0.25 * ln(100+1) * (0.25+4/30)/4.5	0.1027	0.9193
5	0.4876	200	(200 / (144 + 200)) / 3	0.1961	80	(80 / (20 + 80)) / 5	0.16	1,000,000	5	0.25 * ln(100+1) * (0.25+5/30)/4.5	0.1133	0.9570
6	0.4795	250	(250 / (144 + 250)) / 3	0.2166	100	(100 / (20 + 100)) / 5	0.1667	1,000,000	6	0.25 * ln(100+1) * (0.25+6/30)/4.5	0.1239	0.9867
7	0.4714	300	(300 / (144 + 300)) / 3	0.2335	120	(120 / (20 + 120)) / 5	0.1714	1,000,000	7	0.25 * ln(100+1) * (0.25+7/30)/4.5	0.1345	1.0108
8	0.4633	350	(350 / (144 + 350)) / 3	0.2479	140	(140 / (20 + 140)) / 5	0.175	1,000,000	8	0.25 * ln(100+1) * (0.25+8/30)/4.5	0.1451	1.0313
9	0.4552	400	(400 / (144 + 400)) / 3	0.2602	160	(160 / (20 + 160)) / 5	0.1778	1,000,000	9	0.25 * ln(100+1) * (0.25+9/30)/4.5	0.1557	1.0489
10	0.4471	450	(450 / (144 + 450)) / 3	0.2709	180	(180 / (20 + 180)) / 5	0.18	1,000,000	10	0.25 * ln(100+1) * (0.25+10/30)/4.5	0.1663	1.0643
11	0.4390	500	(500 / (144 + 500)) / 3	0.2804	200	(200 / (20 + 200)) / 5	0.1818	1,000,000	11	0.25 * ln(100+1) * (0.25+11/30)/4.5	0.1769	1.0781
12	0.4309	550	(550 / (144 + 550)) / 3	0.2889	220	(220 / (20 + 220)) / 5	0.1833	1,000,000	12	0.25 * ln(100+1) * (0.25+12/30)/4.5	0.1875	1.0906
13	0.4228	600	(600 / (144 + 600)) / 3	0.2965	240	(240 / (20 + 240)) / 5	0.1846	1,000,000	13	0.25 * ln(100+1) * (0.25+13/30)/4.5	0.1981	1.1020
14	0.4147	650	(650 / (144 + 650)) / 3	0.3034	260	(260 / (20 + 260)) / 5	0.1857	1,000,000	14	0.25 * ln(100+1) * (0.25+14/30)/4.5	0.2087	1.1125
15	0.4066	700	(700 / (144 + 700)) / 3	0.3097	280	(280 / (20 + 280)) / 5	0.1867	1,000,000	15	0.25 * ln(100+1) * (0.25+15/30)/4.5	0.2193	1.1223

Here's a chart illustrating the change in the Return Coefficient (M) over the 15 days: