Powerplay 'Maintain rating 5' is going to be easier from now on!

[garlenife]

It's shocking me. I was gaining 5333 merit per cycle so as to keep my rating 5. For 3 week. Then, 1 month later, I see this.

You need at least 100 merit to be rating 2. But my current merit is 83. ?! Still rating 2.

You can type&search; 'elite merit fall off' on google. 'at 26/05/2017' every guide from each forum were wrong about keeping rating 5. I remember finding 1 discussion said "we need around 3,400 merit". Too bad, I lost the URL.

Every of us (me included), shared the same common misconception. To maintain 'rating 5', your merit must be at least 10,000 before each cycle end. When the cycle end, your merit will fall off between 5,000 - 8,750, but you will stay rating 5.
Just forget about all the table and calculation, you might have seen before. They all true about 'How merit fall off', only make us think we need 5333 merit per cycle to stay rating 5. Your merit that exceeded 10,000, are wasted.
Make this simple; Every time you see your merit lower than 10,000 (still at ratings 5), just top it up to 10,000. No more overflow merit.

Spoiler

Algorithm for efficiently maintain ratings 5 (For some proving only, remember the word "Just forget about all the table and calculation"?)

c(0) = 0 {You're starting with 0 merit.}

n	{Power Play Cycle}	1	2	3	4	5	6	7	8	9	10
r	{merit Achieving before the cycle end}	10000	10000	10000	10000	10000	10000	10000	10000	10000	10000
c	{merit at first minute of current cycle}	0	5000	7500	7500	6875	6250	6249	6529	6623	6570
m	{merit Gaining at current cycle}	10000	5000	2500	2500	3125	3750	3751	3471	3377	3430
c(n-1)	{merit fall off from last cycle}	0	5000	2500	1250	1250	1562	1875	1875	1735	1688
c(n-2)		0	0	2500	1250	625	625	871	937	937	867
c(n-3)		0	0	0	1250	625	312	312	435	468	468

r = c+m
"c = [c(n-1) + m(n-1) + c(n-2) + c(n-3) + c(n-4)] / 2" only true if "r >= 10000"

Your target Merit for each cycle is m.
RESULT: (counting from Cycle 1 to 8)

earn ratings 5 at	cycle 2 (7 days)
earn ratings 5 for	7 cycles (49 days)
total merit Gaining needed between cycle 2 to 8	24097
total overflow merit between cycle 4 to 10	0

 

[SHEPR0N]

I think you have a misconception when ranks awarded. PP rankings are awarded at the end of each cycle for the next cycle. How high your ranking is depends on how your merit end balance before decay.

When the cycle ticks merits decay at a 50% rate and merits older than four cycles are completely discarded one month after you earned them (after decaying three times). Look at this FDev post to assure that's how it actually works.

I.e. in your screenshot you had at least 100 merits last week. So you are rank 2 now. To keep rank 2 you'll have to do at least 17 merits this week. 18 to be sure rounding doesn't play tricks on you, it's always dangerous to just go to the exact number.

So yes to be rank 5 in the following cycle you must have an end balance of at least 10k merits this cycle. The guides you read were probably min-maxing ones with minimal (constant) weekly merit counts required to keep a rank.

I.e. if you do 5334 merits your week that's the most efficient way to keep rank 5: 5334 +5334*0.5 + 5334*0.5² + 5334*0.5³ + 5334*0= 10001.25

You are correct in your thought that doing 5334 every week is not what you want to do if you have fluctuations in your merit earnings. If you do 9k one week your merit load will be a lot lighter in the following cycle if you just want to reach 10k again. However in the long run the 5334 every cycle is the most efficient way to stay rank 5.

 

[garlenife]

'Table for 5334 merits per week', include.

Your comment is ringing some-more idea. Now, I see that my screen-shot above didn't tell the whole things. I remembers FDev post well.
You are almost right about '5334 merits every week'. But 5334 isn't the most efficient way for ratings 5 anymore. It's the safely and efficient way, then it complicates thing.
We CMDR aware the risk of invest 100,000,000cr and start the ratings 5 at next cycle right-away. One mightn't make 10,000 merits in-time, I did. When it come to maintain the ratings. Do we just work up to exact-10,000-merits again before the cycle end? Or do we even need to exceed 10,000 merits, so at the first minute of next cycle our merit still higher than 10,000? How about testing things out, so we might go down to rating 4? No way! XD Then we play safe, exceed 10,000 merits. And it's work.
equation of safely maintain ratings 5 is below

Spoiler

Algorithm for safely maintain ratings 5

c(0) = 0 {You're starting with 0 merit.}

n	{Power Play Cycle}	1	2	3	4	5	6	7	8	9	10
e	{exceed & overflow merit}	0	0	668	2668	4001	4667	5000	5167	5250	5292
r	{merit Achieving before the cycle end}	5334	8001	10668	12668	14001	14667	15000	15167	15250	15292
c	{merit at first minute of current cycle}	0	2667	5334	7334	8667	9333	9666	9833	9916	9958
m	{merit Gaining at current cycle}	5334	5334	5334	5334	5334	5334	5334	5334	5334	5334
c(n-1)	{merit fall off from last cycle}	0	2667	2667	2667	2667	2667	2667	2667	2667	2667
c(n-2)		0	0	1333	1333	1333	1333	1333	1333	1333	1333
c(n-3)		0	0	0	666	666	666	666	666	666	666

r = c+m
"c = [c(n-1) + m(n-1) + c(n-2) + c(n-3) + c(n-4)] / 2" only true if "at n >= 3, r >= 10000"

Always earn 5333 Merit for each cycle, m.
RESULT: (starting from Cycle 1 to 10)

earn ratings 5 at	cycle 4 (21 days)
earn ratings 5 for	7 cycles (49 days)
total merit Gaining needed between cycle 4 to 10	37338
total overflow merit between cycle 4 to 10	32045

'5334 merits per week' is OK if you working for Li Yong-Rui, gain 200% exploration data payout. But newcomer who want to tryout ratings 5 (or try to earn income from FAST TRACK alone), 'more 1934 merits per week' can make the difference. (5334-3400 = 1934) And that's why the Power Play is dying out.
We can improve the efficiently. Simply by gaining 5334 per week, and after you reach 10,000, don't FAST TRACK to exceed 10,000 merit. It's a waste.
Equation of safe and efficiently maintain ratings 5 is below;

Spoiler

Algorithm for safe and efficiently maintain ratings 5

c(0) = 0 {You're starting with 0 merit.}

n	{Power Play Cycle}	1	2	3	4	5	6	7	8	9	10
e	{exceed & overflow merit}	0	0	0	0	0	0	0	0	0	0
r	{merit Achieving before the cycle end}	5334	8001	10000	10000	10000	10000	10000	10000	10000	10000
c	{merit at first minute of current cycle}	0	2667	5334	7000	7166	6666	6375	6375	6499	6567
m	{merit Gaining at current cycle}	5334	5334	4666	3000	2834	3334	3625	3625	3501	3433
c(n-1)	{merit fall off from last cycle}	0	2667	2667	2333	1500	1417	1667	1812	1812	1750
c(n-2)		0	0	1333	1333	1166	750	708	833	906	906
c(n-3)		0	0	0	666	666	583	375	354	416	453

Earn 5333 Merit for each cycle, but avoid an exceeded-10,000-merits.
RESULT: (starting from Cycle 1 to 10)

earn ratings 5 at	cycle 4 (21 days)
earn ratings 5 for	7 cycles (49 days)
total merit Gaining needed between cycle 4 to 10	23352
total overflow merit between cycle 4 to 10	0

Remember, the Thargoid and Pirate cannot steal your merit, the only way you could steal your own merit is to blow-up your own allies ship. So, let the Power on playing again.

 

[SHEPR0N]

Sorry didn't really notice your formula work in my first reply.

So we agree that r (which defines rank for cycle = c + m

However your c formula is not correct. c is just the merits you earned in cycles c-1, c-2 and c-3. Of course properly discounted.

So using your notation: c = c(n-1) + c(n-2) + c(n-3)

All merits from cycle n-4 or older are completely discarded and have no influence on c.

There is some other error in your tables, probably a spreadsheet formula calculation mistake?

We know that the decay rate is 0.5 so c can be r(n-1)/2 at most ( =r(n-1)/2 if there are no old merits to completely discard). Unless there is a strange bug bitting the only inconsistency with that is on the +/-1 merit level from rounded numbers. If you look at your tables for all n > 2 cycles that's not true.


So your table should actually look like this (rounded numbers for c(n-2), c(n-3), c & r):

c(0) = 0 {You're starting with 0 merits.}

n	{Power Play Cycle}	1	2	3	4	5	6	7	8	9	10
e	{exceed & overflow merit}	0	0	0	1	1	1	1	1	1	1
r	{merit Achieving before the cycle end}	5334	8001	9335	10001	10001	10001	10001	10001	10001	10001
c	{merit at first minute of current cycle}	0	2667	4001	4667	4667	4667	4667	4667	4667	4667
m	{merit Gaining at current cycle}	5334	5334	5334	5334	5334	5334	5334	5334	5334	5334
c(n-1)	{merit fall off from last cycle}	0	2667	2667	2667	2667	2667	2667	2667	2667	2667
c(n-2)		0	0	1333	1333	1333	1333	1333	1333	1333	1333
c(n-3)		0	0	0	667	667	667	667	667	667	667
c(n-4)		0	0	0	0	0	0	0	0	0	0

The ever increasing c in your tables is actually not possible with a constant m over time because of the complete discarding of merits from cycles n-4 and older. What merit activity took place before that may as well have never happened, it's not an infinite series!

If your m is always constant, let's say m = 5334 it follows that c = c(n-1) + c(n-2) + c(n-3) = 2667 + 1333 + 667 = 4667 for all n (I know this is not the actual mathematical proof for that ).

If you look at your second table, with those m rates you'd actually never even reach rank 5 once!

 

[garlenife]

I'm happy my equation catch your attention. How accuracy the number on these table is not to be focus on, and I'll update my table soon enough. My emphasis for this Power play is "Do not FAST TRACK to exceed 10,000 of your total merit, at any cycle." Blowing enemy ships then exceed 10,000-merit is totally fine, you're going to gain Cr from voucher anyway.
My stand is;
"FAST TRACK for ratings 5 every cycle, do nothing else at all, and you still gain positive income from cycle 4 (28 days) and every next cycle."
And I take no offence from anyone who would disprove my stand. It's a good feedback.
You can have a life anytime you want to. Power Play is not hard to maintain. There are many others things you can do while letting your ratings 5 go on with 4-hours maintenance. (But not for Colonia, just no. You don't go 20,000 ly away, with ratings 5 dragging you back to home-system.)

 

[CMDR Endincite]

5333 merit per cycle to stay rating 5. Your merit that exceeded 10,000, are wasted.

Your misconception lies in the fact that no one is saying you need 5334 to maintain every cycle, we're saying 5334 is the minimum constant needed every cycle, if you choose to do exactly the same number of merits. Let's go through a few weeks (not recommended to actually do this from R1; it's a tremendous waste of time & cash).

Week 1: [5334]
Week 2: [5334] + [2667 carryover] = 8001
Week 3: [5334] + [2667 + 1333.5] = 9334.5
Week 4: [5334] + [2667 + 1333.5 + 666.75] = 10001.25 (R5)
Week 5: [5334] + [2667 + 1333.5 + 666.75] = 10001.25 (R5)
Week 6 (and so on): [5334] + [2667 + 1333.5 + 666.75] = 10001.25 (R5)

If you instead randomly do whatever is needed to make 10,000, you'll end up doing a cycle of more/less/more/less needed (because your carryover will change based on what you did last cycle). That's fine, but the end result in both cases is to reach near-exactly 10000 merits each cycle. No one is recommending waste. More a matter of people not wanting to do e.g. 1950 merits one cycle and then 5575 the next because you only did 1950 last cycle.

Let's say you have this carryover
[4600 + 2300 + 1150] = 8050 (1950 needed)
and only do the 1950 that cycle to reach 10000, you'll have to do a great deal more next cycle to maintain.
[975 + 2300 + 1150 carryover] = 4425 (5575 needed)
[2212.5 + 487.5 + 1150 carryover] = 3850 (6150 needed)
[3075 + 1106.25 + 243.75 carryover] = 4425 (5575 needed)
[2787.5 + 1537.5 + 553.125 carryover] = 4878.125 (5122 needed)
[2561 + 1393.75 + 768.75 carryover] = 4723.5 (5277 needed)
etc.

Rather a lot of people like having the same amount to do each cycle, e.g. so they can plan their other activities & time available.
Neither way is more efficient, the constant is just desirable to many.

 

[garlenife]

It's taking me so long.

Too bad I didn't discover something new for the community, it seem. I still believe, I found at least 1 discussion said "we need around 3,400 merit". That would made 100% FAST TRACK on Rating 5, profitable. Then, I lost that discussion's URL. It's gone. So I'd prove the myth or find someone to help me out. And after you guys help me out, look like my discussion are going to join their rank soon(the lost discussion).
But I glad, I didn't post it on Guide Page. Then here lies the remain of my misconception that I hope to be made as example to prevent anyone to do so.