Reward Pool Sustainability

3.1 Dynamic Reward Adjustments 📈

Ensure sustainability by adjusting rewards based on the current size of the reward pool.

$$\text{Reward} = \left( \frac{\text{Staked Tokens} \times \text{Duration Days} \times \text{Category Multiplier}}{100} \right) \times \left( 1 + \frac{\text{Pool Size Factor}}{100} \right)$$

Where:

$$\text{Pool Size Factor} = \min\left( 100, \frac{\text{Current Pool Size}}{\text{Initial Pool Size}} \times 100 \right)$$

Burn Formula

When users fail to meet their goals, a portion of their staked tokens is burned according to the following formula:

$$\text{Burn Amount} = \text{Staked Amount} \times \text{Burn Rate}$$

Burn Rates Based on Duration:

• 1 day: 90% burned

• 1-7 days: 70% burned

• 8-30 days: 50% burned

• 30+ days: 30% burned

Where burned tokens go:

• 80% → Reward Pool (for successful stakers)

• 20% → Protocol Treasury

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3.2 Example ⚠

Reward Calculation Example

Given Values:

• Staked Tokens: 100,000 GRIND

• Duration Days: 30 days

• Category Multiplier: 2.0 (e.g., Running activity)

• Initial Pool Size: 200,000,000 GRIND

• Current Pool Size: 250,000,000 GRIND

Step-by-Step Calculation:

1. Calculate the Basic Reward:

   $$\text{Basic Reward} = \frac{\text{Staked Tokens} \times \text{Duration Days} \times \text{Category Multiplier}}{100}$$

   Substituting the given values:

   $$\text{Basic Reward} = \frac{100,000 \times 30 \times 2.0}{100} = \frac{6,000,000}{100} = 60,000 \text{ GRIND}$$
2. Calculate the Pool Size Factor:

   $$\text{Pool Size Factor} = \min\left( 100, \frac{\text{Current Pool Size}}{\text{Initial Pool Size}} \times 100 \right)$$

   Substituting the given values:

   $$\text{Pool Size Factor} = \min\left( 100, \frac{250,000,000}{200,000,000} \times 100 \right) = \min\left( 100, 1.25 \times 100 \right) = \min\left( 100, 125 \right) = 100$$
3. Calculate the Final Reward:

   $$\text{Reward} = \left( \frac{\text{Staked Tokens} \times \text{Duration Days} \times \text{Category Multiplier}}{100} \right) \times \left( 1 + \frac{\text{Pool Size Factor}}{100} \right)$$

   Substituting the calculated values:

   $$\text{Reward} = 60,000 \times \left( 1 + \frac{100}{100} \right) = 60,000 \times 2 = 120,000 \text{ GRIND}$$

Result:

• User Stakes: 100,000 GRIND

• Earns: 120,000 GRIND as a reward

Burn Calculation Example

Given Values:

• Staked Tokens: 100,000 GRIND

• Duration Days: 7 days

• Burn Rate: 70% (for 1-7 days)

1. Calculate the Burn Amount:

   $$\text{Burn Amount} = \text{Staked Amount} \times \text{Burn Rate}$$

   Substituting the given values:

   $$\text{Burn Amount} = 100,000 \times 0.70 = 70,000 \text{ GRIND}$$
2. Distribution of Burned Tokens:

   • 80% to Reward Pool: ( 70,000 \times 0.80 = 56,000 GRIND)

   • 20% burned : ( 70,000 \times 0.20 = 14,000 GRIND )

3. Remaining Tokens Returned to User:

   $$\text{Remaining Tokens} = 100,000 - 70,000 = 30,000 \text{ GRIND}$$

Result:

• User Stakes: 100,000 GRIND

• Burns: 70,000 GRIND

• Remaining: 30,000 GRIND returned to user