Proof That One Cannot Rank Up All Six Syndicates At The Same Time

[Renegade343]

So, the Wiki has listed the ways that a player can rank up Syndicates (as in: Gain points) at the same time (for the sake of this thread, when I mean "at the same time", I mean, "using the same method for ranking up Syndicates for some appreciable length of time, and working for at least two Syndicates".). Now, as some players are wondering if one could rank up all six Syndicates at the same time, the short answer is: No. 

 

The long answer is: 

 

Version 1: 

 

 

Yes, I know the proof has a bit of hand-waving, but for the most part, it looks solid. This only applies to Rank 0, as with higher ranks come higher Syndicate point capacity, meaning that this proof starts falling apart due to being able to store more points as a buffer. 

 

EDIT: Re-reading the proof again, I made a small mistake, and that is saying the proof does apply for Rank 0 only. It can be applied to all combinations of Syndicate ranks, as this proof calculates the change of Syndicate points with respect to percentage of time spent in a Syndicate in a particular method of gaining Syndicate points (e.g.: If I spend 100% of my time in RV, then I used 100% of my time to gain 100% of RV Syndicate points, converted from Affinity, and 100% of my time to gain -100% of AH Syndicate points, converted from Affinity). That means my conclusion is actually the implication from the result that one cannot gain positive Syndicate points for all Syndicates at the same time. 

 

But this assumes that the percentage of time spent in a Syndicate will produce a proportional amount of Affinity. 

 

2nd EDIT: SM, RV, NL, PS, CS, AH should be ≥ 0 rather than > 0.

 

Version 2 (the improved/more clearer version): 

 

Edited December 3, 2015 by Renegade343

[Eda.Mone]

stop pls

 

 

 

i have to code some stuff for class in a bit and this is killing me

[Auramaru]

Holy S#&$

 

Did you just use algebraic matrices manipulation to disprove reputation grind?

Edited November 28, 2015 by Aura

[Cyborg-Rox]

And... this needed proving?

[Thural]

once I've maxed 4, can I get the other two in the postive without losing ranks?

[Tesseract7777]

This is just beautiful. There is nothing like a well put together proof... it's like a work of art. 

 

 

<-- Gigantic math nerd here, raised by an actuary. ^_^ 

 

 

Edit: Do you think the formula could be tweaked slightly to use a general solution for all possible syndicate rank combinations/variations? For example, having several of the syndicates already at max rank/points as a buffer before you go for the last couple. 

Edited November 28, 2015 by Tesseract7777

[9tailboy]

Holy S#&$

 

Did you just use algebraic matrices manipulation to disprove reputation grind?

I thought the same

 

And... this needed proving?

Ikr

 

once I've maxed 4, can I get the other two in the postive without losing ranks?

THE MAN JUST SAID NO

[tinyranitar]

Renegade - Doing Maths and kicking &amp;#&#33;

[Renegade343]

And... this needed proving?

This is to show that it is impossible to rank up all six Syndicates at the same time, meaning that at least two methods are required to rank up all the Syndicates. 

 

I might make an improved proof once I get more knowledge, but off the top of my head, the best proof for higher ranks assumes all the Syndicates are of the same rank. 

[Renegade343]

Edit: Do you think the formula could be tweaked slightly to use a general solution for all possible syndicate rank combinations/variations? For example, having several of the syndicates already at max rank/points as a buffer before you go for the last couple. 

Not that I can think of yet, although now that I think of it, there might be a way. 

 

Or, re-reading my proof again, this proof does seem to already apply to all combinations of Syndicate ranks, as I am calculating the change of Syndicate points with respect to percentage of time spent. 

[bejuizb]

I wish I could understand math. Anything past algebra kicks my arse really hard.

[.Ivo]

My Algebra I at its finest D:

I saw someone with all the syndicates in blue. Ok, you cannot level up a syndicate without putting anoter one in the red fields, but you can be at good standing with all of them at some point and stop leveling them.

Edited November 28, 2015 by WingedMenace1

[Renegade343]

I saw someone with all the syndicates in blue. Ok, you cannot level up a syndicate without putting anoter one in the red fields, but you can be at good standing with all of them at some point and stop leveling them.

Yes, but that means you are swapping to a different system, meaning you are using two systems, not one single system to rank up your Syndicates. 

[ThePredicament]

It's possible to get four, possible 5, rank 5 syndicates with the rest at level 0 and 1 with a MR20-21 account. At R5 there's a 132k standing limit and  it takes 71k to go from the very bottom back to rank 0, leaving about 61k space to get to R1 for the main opposing. The possible 5 syndicate at rank 5 is using counterbalancing sigils with alerts that would result in just opposing syndicate gains with little to no loss.

 

For example.

Max Meridian (132k) and Veil (132k)

Max Suda (132k), Hexis (132k). Hurting Veil (66k)

Offload Meridian points (7k-32k), max again to max out Veil (132k, 132k)

Now, counterbalance alert to max out Perrin (ridiculous amount of time).

Now with 5 maxed syndicates.

Level Loka until R1 (44+22+5+22=93k) leaving Suda with 39k R5.

[Magnulast]

Matrices.-A use for them....in real life...Amazing.....

 

Technically, you could just show them the counter action effect in a smart art chart...

But this, it's amazing.

 

 

stop pls

 

 

 

i have to code some stuff for class in a bit and this is killing me

 

Hexadecimal or binary?

....nvm

Edited November 28, 2015 by Magnulast

[Renegade343]

Matrices.-A use for them....in real life...Amazing.....

 

Technically, you could just show them the counter action effect in a smart art chart...

But this, it's amazing.

The art chart would not show how ranking up all six Syndicates at the same time is impossible. If anything, things would get more confusing. 

 

And matrices are a powerful tool, even if they are just for storing the coefficients of the variables. 

[TARINunit9]

once I've maxed 4, can I get the other two in the postive without losing ranks?

Just barely, but yes

[ThunderZsolt]

man, i haven't seen a matrix since i've finished my studies @ the university...

 

some people come up with serious maths on this forums, but you clearly won the internet

at least for today

 

but seriously, nice work!

i had a feeling that you can't level ALL of them to the max, but i don't care much about it, because more than 3 has very low efficiency at leveling

[.--Seiryu--.]

XD

 

I Love math :)) 

Edited November 28, 2015 by ---Divinity---

[Cyborg-Rox]

This is to show that it is impossible to rank up all six Syndicates at the same time, meaning that at least two methods are required to rank up all the Syndicates. 

 

I might make an improved proof once I get more knowledge, but off the top of my head, the best proof for higher ranks assumes all the Syndicates are of the same rank. 

 

Well it's already common knowledge that you can only reach max rank in 4 syndicates, while having 2 at the 4th rank.

It's like, you write an entire page of equations to prove that a ball is, in fact, round.

[ThorienKELL]

"Just because you can doesn't mean you should"

 

3 is OK

4 is bit cumbersome but entirely possible

5 is pushing it, no need to do this really unless you're and OCD completitionist

6 plse stahp, what are you doing?

[Thural]

Just barely, but yes

oh goody, I just hate those roller attacks, they're so dangerous you know

[Renegade343]

Well it's already common knowledge that you can only reach max rank in 4 syndicates, while having 2 at the 4th rank.

It's like, you write an entire page of equations to prove that a ball is, in fact, round.

But it is not common knowledge that it is impossible to rank up all Syndicates at the same time. Or, at the very least, no one has shown it to be true beyond gut feeling. 

 

Also, we can write an entire page of equations to prove whether a ball is round or not. What we need is: 

 

- Eccentricity and loci (find the formula for the ellipse, then set eccentricity = 0 to reduce the formula to a circle).

- Volume of revolution (i.e.: Integration). 

- Surface area for sanity checks (i.e.: More integration).

- Length of cross section for even more sanity checks (i.e.: Even more integration).

Edited November 28, 2015 by Renegade343

[Grulos]

once I've maxed 4, can I get the other two in the postive without losing ranks?

 I also want to know that.

[ThorienKELL]

Of course you cannot. 

[Grulos]

Of course you cannot. 

So when I lose a rank, I have to pay the sacrifice again?