Boost

Governance > $IDLE staking > LPs rewards boost

Liquidity providers for PYTs (or whitelisted pools for Gauges) can boost their $IDLE rewards by holding stkIDLE. The boost can be up to 2.5x the base rewards, based on the amount of stkIDLE holding.
The liquidity providers balance counted in the liquidity gauge is eligible to get boosted (depending on LPs vote weight) if LPs lock/stake their $IDLE (then as a result of this, holding stkIDLE).
Holding stkIDLE gives users more weight when collecting certain farming rewards. Part of the farming rewards that are distributed directly through the protocol is eligible for stkIDLE boosts.
External farming promoted by other external protocols (such as Sushi, Onsen) is typically not available for stkIDLE boosts since it is independent of the Idle protocol itself.
In a given gauge, owning stkIDLE increases a user share of the pool thus increasing the rewards received. Users holding no stkIDLE are anyway considered as providing 100% of their liquidity. If a user owns enough stkIDLE, the user can be considered as bringing up to 250% of its original liquidity (or a 2.5x boost compared to the original 100%).
The 2.5x multiplier in liquidity provided translates into a boost on rewards depending on the total liquidity provided in the pool and how it is considered by the gauge boost calculator.
Boosting formulae
Following the approach of the Angle protocol, we set 
liquidityuser=user liquidity in the poolliquiditypool=total liquidity in the poolstkIDLEuser=user stkIDLE balancestkIDLEtot supply=total stkIDLE supplyliquidity_{user} = \text{user liquidity in the pool} \qquad 
    liquidity_{pool} = \text{total liquidity in the pool} \\
    stkIDLE_{user} = \text{user stkIDLE balance} \qquad
    stkIDLE_{tot\,supply} = \text{total stkIDLE supply}liquidityuser​=user liquidity in the poolliquiditypool​=total liquidity in the poolstkIDLEuser​=user stkIDLE balancestkIDLEtotsupply​=total stkIDLE supply
The boost mechanism calculates user earning weight by taking the smaller amount of two values: the first value is the amount of liquidity the user is providing, while the second one is the amount of his maximum earning weight
min⁡(liquidityuser+1.5×liquiditypool×stkIDLEuserstkIDLEtot supply;2.5×liquidityuser)(1)\min\left(liquidity_{user} + 1.5 \times liquidity_{pool} \times \frac{stkIDLE_{user}}{stkIDLE_{tot\,supply}} ; 2.5 \times liquidity_{user}\right) \tag{1}min(liquidityuser​+1.5×liquiditypool​×stkIDLEtotsupply​stkIDLEuser​​;2.5×liquidityuser​)(1)
To achieve the maximum boost on rewards, the user needs to get 100% of the provided liquidity taken into account by the protocol. That is an equivalent share of stkIDLE supply bigger or equal to the share of liquidity in the pool
stkIDLEuserstkIDLEtot supply≥liquidityuserliquiditypool\frac{stkIDLE_{user}}{stkIDLE_{tot\,supply}} \ge \frac{liquidity_{user}}{liquidity_{pool}}stkIDLEtotsupply​stkIDLEuser​​≥liquiditypool​liquidityuser​​
The gauge model considers a user with a share of stkIDLE higher than his share of liquidity provision in the pool as having 2.5x more liquidity than another user with no stkIDLE holding (in the same pool).
Boosting examples
Example 1: One user with the complete majority of stkIDLE share in the pool
Users xxx
 and yyy
 provide the same liquidity (100 stETH) in the senior tranche of the Lido pool and stake their senior tranche tokens (i.e. AA_wstETH) receiving an equal amount of rewards each (50% of $IDLE daily emission).
User
LP
% rewards
​xxx
​
100 stETH (AA_wstETH)
​100200=0.5→50%\frac{100}{200} = 0.5 \to 50\%200100​=0.5→50%
 
​yyy
​
100 stETH (AA_wstETH)
​100200=0.5→50%\frac{100}{200} = 0.5 \to 50\%200100​=0.5→50%
 
LIDO pool
200 stETH
​100%100\%100%
​
Now, let’s suppose that user xxx
 owns the total supply of stkIDLE in the pool (100%). The gauges boost calculator, using Equation (1), will consider user xxx
 as bringing 250 stETH of liquidity in the pool, consequently boosting x′sx'sx′s
 rewards by a multiplier of 1.42
User (stkIDLE)
Boosted liquidity
% pool holding
​xxx
 with 100% of stkIDLE
​100×2.5=250100 \times 2.5 = 250100×2.5=250
​
​250250+100×100=71%\frac{250}{250 + 100} \times 100 = 71\%250+100250​×100=71%
​
​yyy
 with 0% of stkIDLE
​100×1=100100 \times 1 = 100100×1=100
​
​100250+100×100=29%\frac{100}{250 + 100} \times 100 = 29\%250+100100​×100=29%
​
multiplier(x)=1+(71%−50%50%)=1.42multiplier(x) = 1 + \left(\frac{71\% - 50\%}{50\%}\right) = 1.42multiplier(x)=1+(50%71%−50%​)=1.42
Example 2: Two users with a significant difference in stkIDLE holding
User xxx
 provides 100 stETH and user yyy
 provides 9900 stETH in the senior tranche of the Lido pool. Assuming no stkIDLE holdings, user xxx
 will earn 1% of the total pool rewards (AA_wstETH) and user yyy
 99%.
User
LP
% rewards
​xxx
​
100 stETH
​10010000=0.01→1%\frac{100}{10000} = 0.01 \to 1\%10000100​=0.01→1%
 
​yyy
​
9900 stETH
​990010000=0.99→99%\frac{9900}{10000} = 0.99 \to 99\%100009900​=0.99→99%
 
LIDO pool
10000 stETH
​100%100\%100%
​
User xxx
 decides to stake his $IDLE and now owns 1% of the stkIDLE supply in the pool, assumingstkIDLEuser≥liquidityuserstkIDLE_{user} \ge liquidity_{user}stkIDLEuser​≥liquidityuser​
. The gauges boost calculator, using Equation (1) will consider user xxx
 as bringing 250 stETH of the liquidity in the pool, consequently boosting x′sx'sx′s
 rewards by a multiplier of 2.5.
User (stkIDLE)
Boosted liquidity
% pool holding
​xxx
 with 1% of stkIDLE
​100×2.5=250100 \times 2.5 = 250100×2.5=250
​
​250250+9900×100=2.5%\frac{250}{250 + 9900} \times 100 = 2.5\%250+9900250​×100=2.5%
​
multiplier(x)=1+(2.5%−1%1%)=2.5multiplier(x) = 1 + \left(\frac{2.5\% - 1\%}{1\%}\right) = 2.5multiplier(x)=1+(1%2.5%−1%​)=2.5
Similarly, if user yyy
 stakes her $IDLE, she would own 1% of the stkIDLE supply of the pool, as well. The gauges boost calculator, using Equation (1) will consider user yyy
 as bringing 1005 stETH of the liquidity in the pool, consequently boosting y′sy'sy′s
 rewards by a multiplier of 2.5.
User (stkIDLE)
Boosted liquidity
% pool holding
​yyy
 with 1% of stkIDLE
​9900+1.5×10000×1%=100509900 + 1.5 \times 10000 \times 1\% = 100509900+1.5×10000×1%=10050
​
​10050250+10050×100≈98%\frac{10050}{250+ 10050} \times 100 \approx 98\%250+1005010050​×100≈98%
​
Share of earnings for user yyy
 would go from 97.54% to: 10050250+10050=97.57%\frac{10050}{250+ 10050} = 97.57\%250+1005010050​=97.57%
 
Users who own bigger shares of the pool need to hold bigger shares of the stkIDLE to boost significantly their rewards. 

User	LP	% rewards
$x$	100 stETH (AA_wstETH)	$\frac{100}{200} = 0.5 \to 50\%$
$y$	100 stETH (AA_wstETH)	$\frac{100}{200} = 0.5 \to 50\%$
LIDO pool	200 stETH	$100\%$

User (stkIDLE)	Boosted liquidity	% pool holding
$x$ with 100% of stkIDLE	$100 \times 2.5 = 250$	$\frac{250}{250 + 100} \times 100 = 71\%$
$y$ with 0% of stkIDLE	$100 \times 1 = 100$	$\frac{100}{250 + 100} \times 100 = 29\%$

User	LP	% rewards
$x$	100 stETH	$\frac{100}{10000} = 0.01 \to 1\%$
$y$	9900 stETH	$\frac{9900}{10000} = 0.99 \to 99\%$
LIDO pool	10000 stETH	$100\%$

User (stkIDLE)	Boosted liquidity	% pool holding
$x$ with 1% of stkIDLE	$100 \times 2.5 = 250$	$\frac{250}{250 + 9900} \times 100 = 2.5\%$

User (stkIDLE)	Boosted liquidity	% pool holding
$y$ with 1% of stkIDLE	$9900 + 1.5 \times 10000 \times 1\% = 10050$	$\frac{10050}{250+ 10050} \times 100 \approx 98\%$

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