# Alternative multiplier designs

In this note we elaborate on possible design alternatives to the current FIL+ program.

This note draws parallels to the derivation of possible duration quality multipliers [here](https://hackmd.io/@R02mDHrYQ3C4PFmNaxF5bw/BybIrWAuq), where the basis of that analysis was that from the perspective of the network, the value of a new sectors comes from two sources: the amount of pledged collateral, and the value of the storage power itself.

Lets define:
$a$= the amount of value that the raw-byte power of the sector represents to the network.
$b=$ the amount of value that the initial pledge from a sector represents to the network.

We now add a separate source of value,
$c=$ the amount of value that the **real data** contained in a sector represents to the network.

## Current FIL+

The current FIL+ mechanism assigns a multiplier of $m=10$ to sectors filled with verified data. *From this information we can derive what is the current value we assign to real data, or $c$*.

We define the value multiplier for a sector with a certain valuable feature as
$$m=\frac{\rm Value\,to\,the\,network\,of\,sector\,with\,feature}{\rm value\,to\,the\,network\,of\,sector\,without\,feature}$$

In this case, we are comparing a sector with verified data, to one without any data (a CC sector). We then have
$$m=\frac{a+mb+c}{a+b}$$
We can solve this for $c$ as
$$ c=a(m-1),$$
and given that $m=10$, this means, $c=9a$, that is, **we currently assign the verified data in a sector, 9 times the value we assign to the capacity of the sector by itself**

## Free multipliers

In the free multiplier version, we **decide that having real data is not important, and the value added to the sector comes only from the additional pledged collateral.** The multiplier then satisfies,
$$ m=\frac{a+mb}{a+b}$$
or,
$$ ma=a$$
This implies that either
1) $m=1$, or
2) $a=0$.

That means, if we want to have a free multiplier higher than 1, **that is equivalent to the statement that we place o value on a sector is comes purely from the locked collateral** That is, this statement is equivalent to transitioning to PoS, in terms of what the network gives value to.

## Alternate free multipliers,

The idea in this proposal we give a multiplier based on the deal revenue.

Let's assume for now that the value $c$, we assign to the real data in a sector **is equivalent to the amount of client deal payment, $d$**. We then have
$$m=\frac{a+mb+d}{a+b},$$
or
$$m=1+\frac{d}{a}$$

We can further refine this, Suppose the value the network assigns to the capacity of a sector, $a$, is given by the amount of block reward the network will give to that sector through its lifetime. For this we can define the network total QAP $P$, and the total amount of new block rewards that will be given throughout a sector's li$fetime, $N$. Such that
$$m=1+\frac{P}{N}d$$

This gives us a possible alternative of how we would assign a multiplier given a client deal. This version of the multiplier is **unbounded**, it could be in principle capped at 10

Note this arrives at a different proposal than our initial brainstorm [here](https://docs.google.com/document/d/1xiJ9xXf5eseKQhLRYe0Do2g0iVvb7DC-YrJ7qvhagmE/edit?usp=sharing)