# Construction of zLP & $ZERO Power

ZeroLend's zLP power, closely mirroring Radiant Capital's model, is a pivotal metric in determining a user's influence within the protocol and their corresponding emissions rewards. Here's a streamlined explanation of how it works:

**zLP Power Calculation (P\_zLP)**

* **zLP Power (P\_zLP)**: This metric reflects a user's share of the total zLP pool, adjusted by a locking multiplier to reward longer commitments.

 $$P\_{zLP} = zLP\_{tp} \times L\_{zLP} = \frac{zLP}{\textrm{Total zLP}} \times L\_{zLP}$$

* $$P\_{zLP}$$ is the user's total percentage of zLP relative to the entire pool.
* $$L\_{zLP}$$ is the locking multiplier, enhancing power with longer lock periods.

{% hint style="info" %}
The longer the user locks zLP, the greater the power they have and, ultimately, the greater the emissions the user receives.
{% endhint %}

**Single-Staked $ZERO Power (P\_Z)**

* **$ZERO Power (P\_Z)**: Similar to zLP power, this calculates a user's stake in the total $ZERO pool, also influenced by the duration of the stake. 

$$
P\_{Z} = $\textrm{ZERO}*{tp} \times L*{Z} = \frac{$\textrm{ZERO}}{\textrm{Total ZERO}} \times L\_{Z}
$$

The following are the weighting coefficients:

| Time Lock | L\_d-Value | L\_z - Value |
| --------- | ---------- | ------------ |
| 1-Months  | 2          | 0.5          |
| 3-Months  | 6          | 1.5          |
| 6-Months  | 12         | 3            |
| 12-Months | 24         | 6            |
| 24-months | n/a        | 12           |
| 48-months | n/a        | 24           |

### **Combining Powers for Total Protocol Power**

By integrating both zLP and $ZERO powers, the total Protocol Power is derived, factoring in both contributions and their respective locking multipliers.

$$
P = P\_{zLP} + P\_{Z} = zLP\_{tp} \times L\_{zLP} + $\textrm{ZERO}*{tp} \times L*{Z} \  \hspace{2em}\\= \frac{zLP}{\textrm{Total zLP}} \times L\_{zLP} + \frac{$\textrm{ZERO}}{\textrm{Total ZERO}} \times L\_{Z}\hspace{0.8em}
$$

### Final Equation for Protocol Power

$$
\textrm{Protocol Power} = (P)  \times f(T\_p) \ = (\frac{zLP}{\textrm{Total zLP}} \times L\_{zLP} + \frac{$\textrm{ZERO}}{\textrm{Total ZERO}} \times L\_{Z}) \times f(4 \times \frac{$\textrm{ZERO}\_2 \times 2}{Deposits} + 1 \times \frac{$\textrm{ZERO}\_1}{Deposits})
$$

This formula underscores the significance of both liquidity provision and single asset staking in enhancing a user's impact on the protocol's governance and reward distribution, thereby incentivizing long-term participation and investment.

{% hint style="warning" %}
This functionality is scheduled to go live shortly. 
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