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 zLP_p and Z_p

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

$$zLP_p = \frac{zLP}{Deposits} = \frac{\$\textrm{ZERO}_2 \times 2}{Deposits}$$

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)

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

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.

This functionality is scheduled to go live shortly.