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.

dLPp=dLPDeposits=$ZERO2×2DepositsdLP_p = \frac{dLP}{Deposits} = \frac{\$\textrm{ZERO}_2 \times 2}{Deposits}

Note: $ZERO2\$\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.

Zp=$ZERO1DepositsZ_p = \frac{\$\textrm{ZERO}_1}{Deposits}

Combining for Total Percentage (T_p)

Tp=4×dLPp+1×Zp=4×$ZERO2×2Deposits+1×$ZERO1Deposits 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(Tp)=f(4×$ZERO2×2Deposits+1×$ZERO1Deposits)={0if 0.00Tp<0.100.5if 0.10Tp<0.150.75if 0.15Tp<0.201.0if 0.20Tp<0.251.1if 0.25Tp<0.301.25if 0.30Tp<0.401.5if 0.40Tp<0.502.0if 0.50Tpf(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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