Performance improvement

The increase in performance due to compounding fees will be widely different across positions, and in some cases, the gas costs of compounding the fees may not be offset by the increased fees collected due to the compounding effect for more than a year.
Costs of Compounding
We can estimate the costs of compounding fees without using the auto-compounder on Mainnet (25 Gwei), Polygon (50 Gwei), Optimism (0.25 Gwei), and Arbitrum (0.2 Gwei) as per the following table[^2]. Assuming separate transactions and ETH price of $1000 and MATIC price of $0.5. For Optimism and Arbitrum estimated Gwei amounts were used to avoid doing L2 gas price calculation.
Gas cost
Add liquidity
Likewise we can estimate the gas costs for compounding a position using the Compoundor contract on the same chains as shown below.
Gas cost
Estimating Benefits of Auto-compounding
We define the relevant parameters for our estimations as follows:
P = Principal amount (current value of LP position) APR = annual percentage rate from fees only (fee APR) GASCOST = current gas costs of compounding fees PREWARD = fraction of compounded fees paid to the protocol CREWARD = fraction of the compounded fees paid to the account that calls the contract function and pays for the gas. This value is always equal or less than PREWARD, as it defines the fraction of the protocol rewards assigned to the caller.
Number of Yearly Compoundings
To estimate the number of compoundings the protocol would execute for a given position we assume that auto-compounding happens when the compounder reward, which is a fraction of the uncollected fees, reaches the gas cost for executing the operation. In practice, the number of compoundings will be slightly lower because compoundors will execute the function when it is profitable.
The number of compoundings that will be executed is a function of the estimated APY, this makes calculating these values self-referential. One way to approximate the number of compoundings is to compute the APY assuming continuous compounding which gives us an upper bound, to get a lower bound we can calculate the number of compoundings possible given the non-compounded APR. In reality the real value will fall between these bounds, for the purposes of our calculations we use $n_{min}$ which is precise enough for realistic P and APR values.
Estimated APY
To calculate the projected APY for an auto-compounded position we use the formula for compound interest with the estimated number of compoundings per year, and we subtract the protocol reward from the APR.
Compounding Improvement
The expected improvement in performance for a position during a 1 year period is the difference between the APY and the APR.
The below chart uses the estimated gas cost values from the table above and values of PREWARD=0.02, CREWARD=0.01 to estimate APY improvements, over a 1 year period, from compounding for positions of sizes 1k USD, 10k USD, 100k USD, and 1m USD.