deconstructing-the-weighted-percentage-t_p-calculation.md

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Deconstructing the Weighted Percentage (T_p) Calculation

In ZeroLend's model, T_p represents the Total or Weighted Percentage, crucial for determining rewards. This metric combines the proportions of dynamic Liquidity Provision (dLP_p) and single-staked $ZERO (Z_p) relative to the total USD value of a user's lending deposits. Here's a clearer breakdown:

Calculating dLP_p and Z_p

dLP_p Calculation: Measures the USD value of dLP locked, factoring in the double valuation of $ZERO within LP tokens.

$$ dLP_p = \frac{dLP}{Deposits} = \frac{$\textrm{ZERO}_2 \times 2}{Deposits} $$

Note: $$$\textrm{ZERO}_2$$ adjusts with LP token ratios, while $veZERO earnings depend solely on the $ZERO quantity at deposit time.

Z_p Calculation: Relates to the USD value of $ZERO locked in single asset staking.

$$ Z_p = \frac{$\textrm{ZERO}_1}{Deposits} $$

Combining for Total Percentage (T_p)

$$ T_p = 4 \times dLP_p+1\times Z_p = 4 \times \frac{$\textrm{ZERO}_2 \times 2}{Deposits} + 1 \times \frac{$\textrm{ZERO}_1}{Deposits} $$

and,

$$ f(T_p) = f(4 \times \frac{$\textrm{ZERO}_2 \times 2}{Deposits} + 1 \times \frac{$\textrm{ZERO}_1}{Deposits}) = \begin{cases} 0 & \text{if } 0.00 \leq T_p< 0.10 \ 0.5 & \text{if } 0.10 \leq T_p <0.15\ 0.75 & \text{if } 0.15 \leq T_p < 0.20 \ 1.0 & \text{if } 0.20 \leq T_p <0.25\ 1.1 & \text{if } 0.25 \leq T_p < 0.30 \ 1.25 & \text{if } 0.30 \leq T_p <0.40\ 1.5 & \text{if } 0.40 \leq T_p < 0.50 \ 2.0 & \text{if } 0.50 \leq T_p \

\end{cases} $$

This function assigns reward levels based on the calculated T_p value, with different tiers from 0 to 2.0, enhancing rewards progressively as T_p increases.

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