The gravity coefficient

A coefficient used in the calculations of the earning model is tied to each Creator's account : the Creator Badge. The evolution of the Content Badge depends on the gravity coefficient $\gamma_k$​.

The gravity coefficient of a given content $k$ is a function with two variables : $\Delta_k$​and $\Omega_k$​.

	Symbol
Percentage of minted Fraktions out of the the total number of the supply	$\Delta_k$​
Relative Growth of the consumption of the content $k$​	$\Omega_k$​

$$\gamma_k=\Delta_k \times \Omega_k$$

For a given week $w$, the gravity coefficient is calculated as below:

$$\gamma_k(w)=\Delta_k(w) \times \Omega_k(w)$$

Percentage of minted Fraktions $\Delta_k$

​$\Delta_k(w)$ is calculated like below:

$$\Delta_j(w) =\cfrac{\sum_{k=1}^{w-1}\rho_{j}(k)}{\sum_{k=1}^{w-1}\sigma_{j}(k)}$$

​with:

• $\sigma(k)$​: number of Fraktions of content $j$ supplied during week $k$
• $\rho_j(k)$: the number of Fraktions of content $j$already minted at week ​$k$

If $\sum_{k=1}^{w-1}\rho_{j}(k)=0$ or $\sum_{k=1}^{w-1}\sigma_{j}(k)$=0 then $\Delta_j(w)=1$.

$\Delta_j(1) =1$

Growth of the consumption $\Omega_k$

$\Omega_k$ is the relative growth of the number of $CCU$, ie the ratio between the growth (positive or negative) of units of content consumed last week divided by the total number of units of content consumed from the beginning:

$$\Omega_j(w)=1+\cfrac{\Delta CCU_{j}}{\sum_{k=1}^{w-1} CCU_{j}(k)}=1+\cfrac{CCU_{j}(w-1)-CCU_{j}(w-2)}{\sum_{k=1}^{w-1} CCU_{j}(k)}$$

with $CCU_j(w)$, number of Consumed Content Units (Number of minutes played for video and audio, Number of minutes read for text) of content $j$ during the week $w$.

If $CCU_j(w-2)=0$ or $CCU_j(w-1)=0$ then $\Omega_j=1$