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Swap Slippage

Platypus is known for its ability to provide one of the lowest slippages available in the market.
The swap slippage is calculated by:
Sij=Si+(Sj)=SiSjS_{i \rightarrow j} = S_i + (-S_j) = S_i - S_j
and
Si=g(ri)g(ri)ririS_i = \dfrac{g(r'_i) - g(r_i)}{r'_i - r_i}
where
rir_i
is the original coverage and
rir'_i
is the final coverage.
If the swap amount is small, the slippage can be give by
Sij=g(ri)g(ri)S_{i \rightarrow j} = g'(r_i) - g'(r'_i)
When performing a swap, the coverage ratio of the token you’re swapping increases while it decreases for the token you’re swapping to. The Platypus model is designed to penalize actions that enlarge the coverage ratio to maintain equilibrium.

Practical example of slippage calculation

We take the coverage ratio of USDT at 0.909 and ETH at 1.033. Working this out, we’d get:

USD

g(0.909)=0.0000270.9098=0.03%g'(0.909) = -\dfrac{0.00002*7}{0.909^8} = 0.03\%

ETH

g(1.033)=0.0000271.0338=0.01%g'(1.033) = -\dfrac{0.00002*7}{1.033^8} = 0.01\%
Hence we have
SUSDTETH=0.03%0.01%=0.02%S_{USDT \rightarrow ETH} = 0.03\% - 0.01\% = 0.02\%
This represents the marginal slippage when someone is performing a small amount of swap at this coverage ratio. And yes, the slippage is positive and user can benefit from the swap!