# Calculating EC and other dependent & independent params

Last updated

Last updated

EC is the most important parameter in the Āut's Participation framework.

It determines the *expected contributions* of a contributor of a Hub during a specific period.

It’s based on the Commitment Level chosen by the Individual Member, and it’s necessary to determine the ratio between the promise / commitment of a contributor, and their actual participation.

It’s calculated as:

$EC = fiCL \times TCP$

where:

TCP: Total Contributions Points in a Community. Sum of all contributions points available in a community in a given period. They can be acquired by members by completing tasks and interactions. Each Task and Interaction has a custom weight (spacing between 1 and 10).

fiCL: Fractional Commitment Level per Individual

**Deep-dive:** *Fractional Commitment Level*

The Fractional Commitment Level is the iCL of a Hub’s participant (*j*) in relation to the total.

It is calculated as $fiCL_{j} = \frac{iCL_{j}}{iCL_{tot}}$ where $iCL_{ tot}$ is the sum of all Participants’ iCL, calculated as the ratio between and individual’s commitment level, and the sum of all the commitment levels of all Participants to a Hub in a given period:

$fiCL = \frac{iCL}{iCL_{tot}}$

with:

$iCL_{j}$: individual Commitment Level of

*j*$tiCL$: sum of all iCLs of participants in the Hub $[\tt h \cdot]$: $tiCL = \sum iCL_{[\tt h \cdot]}$

EC’ **= normalized EC accounting the time factor ΔT**

where:

This way it's possible to create a generalized abstraction to factor in participants who join a community after the start of the period *T*.

This works simply by accounting all absolute time available in a community in relation to each individual member:

This allows for a continuous calculation of *EC* for all members in different, arbitrarily small intervals within the same period T.

We may consider a time factor ($tf$ or $\Delta{T}$) to determine *EC* based on the time left in a period:

$EC' = EC \times \Delta(T)$

$\Delta{T} \text{ is calculated as }= \frac {T_{l}} {T_{i}}$

$T_{l} \text { is the time left in a period } T$;

$T_{i} \text{ is the total time at the start of the period }T$;

$\sum (\Delta_{T}) = \frac {\sum (T_{l})} {\sum (T_{i})}$, from which we extrapolate a fractional $\Delta{T} \text{ as }\rightarrow(\frac {fT_{l}} {fT_{i}}) \times T$