Boost Calcuration

Info

A range of 1x to 2.5x of the calculated APR is possible. A user may be interested in the minimum amount of sZ for max boost, how their boost is calculated, and the maximum boost they can receive in cases where 2.5x is not attainable.

For these calculations consider the following:

• l = the liquidity a user will provide and stake in a gauge

• L = the total liquidity which is staked in a pool before a user stakes their own

• L' = The total liquidity staked in the gauge after a user stakes

$$L'=L+l$$

• workingSupply = Working supply is related to the amount of sZ corresponding to the individual stakers and total pool liquidity staked. This will be denominated in terms of the user and the pool.

$$workingSupply = min(0.4*l+0.6*L'*\frac{ sZ\:Held}{ Total\:sZ }, l)$$

• min_sZ = Minimum sZ needed for maximum boost (2.5x)

Minimum sZ for Maximum Boost The minimum sZ a liquidity provider will require in order to receive maximum incentives boost on their staked amount is calculated as follows:

$$Min\:sZ_{max boost} = Total\:sZ*\frac{l }{ L' }$$

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Calculating Your Boost

For a user to calculate their incentives boost they must go through the following steps:

1. Calculate the users' working supply

$$workingSupply_{user} = min(0.4*l+0.6*L'*\frac{ sZ\:Held}{ Total\:sZ }, l)$$

1. Calculate the users' non-boosted, or minimum working supply

$$Non-boosted\:working\:supply_{user}=0.4*l$$

1. Calculate the user's boost multiplier using:

$$Boost=\frac{\frac{working\:supply_{user}}{working\:supply_{user}+total\:working\:supply_{pool}}}{\frac{Non-boosted\:working\:supply_{user}}{Non-boosted\:working\:supply_{user}+total\:working\:supply_{pool}-current\:working\:supply_{user}}}$$

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Calculating Maximum Boost

The maximum boost a user can receive in a pool will not always be 2.5x. Due to other holders in the pool, depending on their sZ holdings, there is a point where one cannot own enough sZ to dilute the rest of users to receive max boost.

$$maxBoost=2.5*\frac{Non-boosted\:working\:supply_{user}+total\:working\:supply_{pool}}{max\:working\:supply_{user}+total\:working\:supply_{pool}}$$

Similar to the user's boost above, if a user is adding more to their current position their current working supply must be subtracted to arrive at the correct result.

$$maxBoost=2.5*\frac{Non-boosted\:working\:supply_{user}+total\:working\:supply_{pool}-current\:working\:supply_{user}}{max\:working\:supply_{user}+total\:working\:supply_{pool}-current\:working\:supply_{user}}$$