Visual Price Curves
Bonding Curve Model
Mathematical Formula
Core FormulaWhere:
S
= Current token supplyS_final
= Final token supplyR
= Amount raised so farR_target
= Target amountexponent = 1 / (1 + aggressivenessFactor/100)
Understanding the Exponent
The aggressiveness factor controls how the exponent affects price progression:Aggressiveness | Exponent | Formula Becomes | Price Behavior |
---|---|---|---|
0 | 1.00 | S = S_final × (R/R_target) | Linear - constant tokens per ETH |
25 | 0.80 | S = S_final × (R/R_target)^0.80 | Slightly curved |
50 | 0.67 | S = S_final × (R/R_target)^0.67 | Moderate curve |
75 | 0.57 | S = S_final × (R/R_target)^0.57 | Steep curve |
100 | 0.50 | S = 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)Progress | Aggressiveness = 0 | 25 | 50 | 75 | 100 |
---|---|---|---|---|---|
10% | 100,000 | 158,489 | 215,443 | 268,270 | 316,228 |
20% | 200,000 | 275,946 | 341,995 | 398,647 | 447,214 |
30% | 300,000 | 381,678 | 448,140 | 502,588 | 547,723 |
40% | 400,000 | 480,450 | 542,884 | 592,387 | 632,456 |
50% | 500,000 | 574,349 | 629,961 | 672,950 | 707,107 |
60% | 600,000 | 664,540 | 711,379 | 746,843 | 774,597 |
70% | 700,000 | 751,759 | 788,374 | 815,614 | 836,660 |
80% | 800,000 | 836,512 | 861,774 | 880,284 | 894,427 |
90% | 900,000 | 919,166 | 932,170 | 941,571 | 948,683 |
100% | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 | 1,000,000 |
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!)
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 sends: 1M B3 tokens
- Trading fee (3%): 30K B3 goes to fee recipients
- Amount for curve: 970K B3 advances the project to ~9.7% progress
- Tokens received: ~306,000 tokens (calculated from bonding curve)
Project Progress | Alice’s 1M B3 Gets Her | Price 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 |
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
Choosing Your Aggressiveness Factor
Decision Framework
Low (0-30)
Best for:
- Fair launches
- Community tokens
- Stable pricing
- Equal opportunity
- Predictable costs
- Less FOMO
- No early incentive
- Slower momentum
Medium (30-70)
Best for:
- Most projects
- Balanced approach
- Moderate rewards
- Some early advantage
- Still accessible
- Good momentum
- Moderate complexity
- Some price variance
High (70-100)
Best for:
- Hype launches
- Reward early adopters
- Fast fundraising
- Strong early incentive
- Creates urgency
- Rewards believers
- Can seem unfair
- High price variance
- FOMO-driven
Selling Mechanics
When users sell tokens back to the curve:- Price Calculation: Uses inverse of buying formula
- Fee Deduction: 5% fee applied to proceeds
- Curve Update: Reduces total raised amount
- Price Impact: Large sells significantly impact price
Sell Price Formula
Edge Cases & Limits
Important Considerations:
- Refunds: If a buy would exceed target, excess ETH is refunded
- Minimum Amounts: Very small trades may revert due to rounding
- Maximum Supply: Cannot exceed
finalTokenSupply
- Price Limits: Extreme aggressiveness can cause price spikes
- 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