Option 1: Exponential Decay
weight = e^(-λ × position), where λ = 0.02
Characteristics:
• Very rapid decay at the beginning
• Smooth continuous curve
• Position 1: ~100 copies, Position 10: ~82 copies, Position 50: ~37 copies
• Good for heavily favoring recent videos
Option 2: Power Law Distribution
weight = position^(-α), where α = 0.7
Characteristics:
• Moderate decay rate
• More balanced than exponential
• Position 1: ~100 copies, Position 10: ~19 copies, Position 50: ~8 copies
• Good middle ground between recent and older videos
Option 3: Simple Inverse Relationship
weight = max(1, 100/position)
Characteristics:
• Hyperbolic decay
• Simple to calculate and understand
• Position 1: 100 copies, Position 10: 10 copies, Position 50: 2 copies
• Most practical and intuitive approach
All Three Methods Compared
Exponential (Blue):
Best for: Maximum recent bias
Use when: You want 90%+ plays from last 20 days
Power Law (Red):
Best for: Balanced distribution
Use when: You want good mix of recent and older content
Inverse (Green):
Best for: Simple and predictable
Use when: You want easy-to-understand probabilities
Recommendation:
Start with Inverse for simplicity, then try Power Law if you want more older content to play.