Visual Price Curves

Bonding Curve Model

Mathematical Formula

Core Formula
S = S_final × (R / R_target)^exponent
Where:
  • S = Current token supply
  • S_final = Final token supply
  • R = Amount raised so far
  • R_target = Target amount
  • exponent = 1 / (1 + aggressivenessFactor/100)

Understanding the Exponent

The aggressiveness factor controls how the exponent affects price progression:
AggressivenessExponentFormula BecomesPrice Behavior
01.00S = S_final × (R/R_target)Linear - constant tokens per ETH
250.80S = S_final × (R/R_target)^0.80Slightly curved
500.67S = S_final × (R/R_target)^0.67Moderate curve
750.57S = S_final × (R/R_target)^0.57Steep curve
1000.50S = S_final × √(R/R_target)Very steep (square root)

Aggressiveness Factor Impact

Cumulative Token Distribution

See how tokens are distributed throughout the bonding process with different aggressiveness factors. Example: 10M B3 target, 1.25M total token supply (1M available for bonding, 250K reserved for LP)
ProgressAggressiveness = 0255075100
10%100,000158,489215,443268,270316,228
20%200,000275,946341,995398,647447,214
30%300,000381,678448,140502,588547,723
40%400,000480,450542,884592,387632,456
50%500,000574,349629,961672,950707,107
60%600,000664,540711,379746,843774,597
70%700,000751,759788,374815,614836,660
80%800,000836,512861,774880,284894,427
90%900,000919,166932,170941,571948,683
100%1,000,0001,000,0001,000,0001,000,0001,000,000
Key Insight: Higher aggressiveness front-loads token distribution to early buyers. At 10% progress:
  • Aggressiveness 0: 100,000 (linear)
  • Aggressiveness 100: 316,228 (3.16x advantage!)
Early buyers with aggressive curves get significantly more tokens for their B3, while late buyers face much higher prices.

Real-World Example: Alice’s Purchase

Let’s follow Alice, who wants to buy tokens from a new project at launch: Project Setup:
  • Total Supply: 1.25M tokens (1M for bonding + 250K for LP)
  • Target: 10M B3 to reach migration
  • Aggressiveness: 100 (maximum reward for early buyers)
  • Current Progress: 0% (project just launched)
Alice’s Purchase: Alice decides to buy 1M B3 worth of tokens right at launch (0% progress).
  1. Alice sends: 1M B3 tokens
  2. Trading fee (3%): 30K B3 goes to fee recipients
  3. Amount for curve: 970K B3 advances the project to ~9.7% progress
  4. Tokens received: ~306,000 tokens (calculated from bonding curve)
Comparing Different Entry Points: If Alice waited and bought the same 1M B3 worth at different project stages:
Project ProgressAlice’s 1M B3 Gets HerPrice per Token
0% (launch)~306,000 tokens~3.3 B3/token
50% progress~114,000 tokens~8.8 B3/token
90% progress~49,000 tokens~20.4 B3/token
Early Buyer Advantage: Alice gets 6.2x more tokens by buying at launch versus waiting until 90% progress!
Key Takeaway: With maximum aggressiveness (100), buying 1M B3 at launch gets Alice 6.2x more tokens than waiting until 90% progress. The bonding curve heavily rewards early participation!

Interactive Price Calculator

// Calculate tokens received for a given trading token amount
function calculateTokensReceived(
  tradingTokenAmount: number,
  currentRaised: number,
  targetAmount: number,
  totalSupply: number,
  aggressiveness: number
): number {
  const exponent = 1 / (1 + aggressiveness / 100);
  
  // Calculate supply at current raised
  const currentSupply = totalSupply * 
    Math.pow(currentRaised / targetAmount, exponent);
  
  // Calculate supply after purchase
  const newRaised = currentRaised + tradingTokenAmount;
  const newSupply = totalSupply * 
    Math.pow(newRaised / targetAmount, exponent);
  
  // Tokens received = difference in supply
  return newSupply - currentSupply;
}

// Example usage
const tokens = calculateTokensReceived(
  1,        // 1 ETH purchase
  5,        // 5 ETH already raised
  10,       // 10 ETH target
  1000000,  // 1M total supply
  50        // 50% aggressiveness
);
console.log(`You'll receive ${tokens.toFixed(0)} tokens`);

Choosing Your Aggressiveness Factor

Decision Framework

Low (0-30)

Best for:
  • Fair launches
  • Community tokens
  • Stable pricing
Pros:
  • Equal opportunity
  • Predictable costs
  • Less FOMO
Cons:
  • No early incentive
  • Slower momentum

Medium (30-70)

Best for:
  • Most projects
  • Balanced approach
  • Moderate rewards
Pros:
  • Some early advantage
  • Still accessible
  • Good momentum
Cons:
  • Moderate complexity
  • Some price variance

High (70-100)

Best for:
  • Hype launches
  • Reward early adopters
  • Fast fundraising
Pros:
  • Strong early incentive
  • Creates urgency
  • Rewards believers
Cons:
  • Can seem unfair
  • High price variance
  • FOMO-driven

Selling Mechanics

When users sell tokens back to the curve:
  1. Price Calculation: Uses inverse of buying formula
  2. Fee Deduction: 5% fee applied to proceeds
  3. Curve Update: Reduces total raised amount
  4. Price Impact: Large sells significantly impact price

Sell Price Formula

// Calculate trading token received for selling tokens
function calculateTradingTokenReceived(
  tokenAmount: number,
  currentSupply: number,
  currentRaised: number,
  targetAmount: number,
  totalSupply: number,
  aggressiveness: number
): number {
  const exponent = 1 / (1 + aggressiveness / 100);
  
  // Calculate new supply after sell
  const newSupply = currentSupply - tokenAmount;
  
  // Calculate corresponding raised amount
  const supplyRatio = newSupply / totalSupply;
  const newRaised = targetEth * 
    Math.pow(supplyRatio, 1 / exponent);
  
  // ETH received (before fees)
  const ethBeforeFees = currentRaised - newRaised;
  
  // Apply 5% fee
  return ethBeforeFees * 0.95;
}

Edge Cases & Limits

Important Considerations:
  1. Refunds: If a buy would exceed target, excess ETH is refunded
  2. Minimum Amounts: Very small trades may revert due to rounding
  3. Maximum Supply: Cannot exceed finalTokenSupply
  4. Price Limits: Extreme aggressiveness can cause price spikes
  5. Slippage: Always use minTokensOut for protection

Real-World Examples

Case Study: Fair Launch Token

  • Aggressiveness: 10
  • Target: 50 ETH
  • Result: Nearly linear pricing, community appreciated fairness

Case Study: Hype Token

  • Aggressiveness: 85
  • Target: 100 ETH
  • Result: Reached target in 2 hours, early buyers gained 8x

Case Study: Balanced Project

  • Aggressiveness: 45
  • Target: 25 ETH
  • Result: Steady growth over 3 days, 2.5x advantage for early buyers

Next Steps