Economic Theory & Rotations

Mathematical analysis and advanced economic patterns

⭐⭐⭐ Expert

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This section dives deep into the mathematical foundations of BAR economics and explores advanced rotation strategies used by the top 1% of players.

Advanced Economic Theory

Mathematical optimization and strategic rotations

📈 Economic Efficiency Mathematics

💰 Metal Efficiency Formula

The core metric for evaluating economic investments:

Metal Efficiency = Output per Second / Metal Cost

Example: T2 Mex upgrade costs 840M for +2.5 M/s improvement

Efficiency = 2.5 M/s ÷ 840M = 0.00298 income per metal

Payback time = 840M ÷ 2.5 M/s = 336 seconds (5.6 minutes)

💡 Application: Any investment that pays for itself in under 10 minutes is usually worthwhile. T2 mexes at 5.6 minutes are excellent investments.

⚡ Energy Cost-Benefit Analysis

Energy Source	Output (E/s)	Metal Cost	Energy Cost	M per E/s	Payback Time
T1 Solar	20	155M	0E	7.75	Immediate
T1 Wind @ 15	15	40M	0E	2.67	Immediate
T2 Advanced Solar	75	500M	6000E	6.67	Delayed
Fusion Reactor	1000	5000M	15000E	5.0	Delayed

🧮 Key Insight: Wind turbines at 15+ wind are the most metal-efficient energy source. Solar collectors provide guaranteed baseline power. Fusion reactors offer the best space efficiency for late-game scaling.

🔄 Advanced Economic Rotations

These are sophisticated economic strategies that adapt to changing game conditions:

🌪️ Wind-Adaptive Rotation

Dynamically adjust energy strategy based on changing wind conditions:

Phase 1: Wind Assessment

• Monitor wind for 2-3 minutes
• Build minimal energy (1-2 sources)
• Focus on mexes and storage
• Plan energy strategy based on average wind

Phase 2: Energy Commitment

• High wind (15+): Mass wind turbines
• Medium wind (8-14): Balanced wind/solar
• Low wind (<8): Solar collectors priority
• Build energy storage to buffer fluctuations

Phase 3: Stability Transition

• Transition to Fusion for stable power
• Keep best wind/solar as supplements
• Reclaim inefficient energy structures
• Focus on energy converters if surplus

⚖️ Resource Balance Rotation

Advanced players constantly adjust their resource focus:

Dynamic Priority System:

1. Metal Deficit: Build more mexes, upgrade existing mexes, consider energy converters
2. Energy Deficit: Build energy sources, add energy storage, reduce energy consumption
3. Build Power Deficit: More constructors, factory assists, nano towers
4. Resource Surplus: Scale build power, plan expansion, tech advancement

🎯 Situational Economic Adaptations

Advanced rotations based on game state:

🔥 Under Pressure Rotation

• Prioritize defensive mexes only
• Build minimal, safe energy infrastructure
• Focus on build power for rapid defense
• Delay T2 transition until secure
• Emphasize reclaim for emergency resources

🚀 Economic Dominance Rotation

• Aggressive expansion to all available mexes
• Rush T2 transition for maximum advantage
• Scale energy infrastructure rapidly
• Mass constructor production
• Deploy energy converters for metal surplus

🧠 Community-Developed Economic Theory

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Community Research Insights:

"The BAR community has conducted thousands of hours of economic analysis. These theories emerge from data-driven research and tournament-level testing, not just theoretical models."

📊 The "Golden Ratio" Theory

Community-discovered optimal resource ratios:

Optimal E:M Ratio = 2.8:1 ± 0.3

• Early Game: 3.2:1 (energy infrastructure costs)

• Mid Game: 2.6:1 (efficiency improvements)

• Late Game: 2.4:1 (T2 mex dominance)

• Deviation Tolerance: ±0.5 ratio without efficiency loss
• Critical Zone: Below 2.0:1 = severe stalls likely
• Waste Zone: Above 3.5:1 = energy overcapacity

⚡ Build Power Scaling Laws

Mathematical relationship between income and build power:

Optimal BP = √(Metal Income × 1000)

• 10 M/s → ~100 BP optimal

• 25 M/s → ~158 BP optimal

• 50 M/s → ~224 BP optimal

• Underpowered: BP < 0.8×optimal = wasted resources
• Overpowered: BP > 1.3×optimal = inefficient spending
• Sweet Spot: 0.9-1.1×optimal = maximum efficiency

🎯 T2 Transition Optimization

Community-tested transition mathematics:

T2 Readiness Score = (M/s × 4) + (E/s × 1.5) + (BP × 2)

• Score 200+: T2 transition ready

• Score 150-199: Borderline timing

• Score <150: Premature transition

• Minimum Thresholds: 18 M/s, 45 E/s, 80 BP
• Competitive Thresholds: 25 M/s, 60 E/s, 100 BP
• Aggressive Thresholds: 32 M/s, 80 E/s, 120 BP

🔄 Resource Velocity Theory

Speed of resource circulation through economy:

Velocity = Spending Rate / Storage Capacity

• High Velocity (2.0+): Aggressive expansion

• Medium Velocity (1.0-2.0): Balanced growth

• Low Velocity (<1.0): Conservative banking

• Optimal Range: 1.2-1.8 for sustained growth
• Risk Zone: >2.5 velocity = vulnerable to raids
• Stagnation Zone: <0.8 velocity = missed opportunities

🧮 Advanced Economic Models

📈 Exponential Growth Model

Mathematical representation of BAR economic growth:

Future Income = Initial × e^(growth_rate × time)

• Sustainable Growth Rate: 0.15-0.25 per minute

• Aggressive Growth Rate: 0.3-0.4 per minute

• Conservative Growth Rate: 0.1-0.15 per minute

Example: Aggressive Growth

• Start: 5 M/s at 2 minutes

• Growth: 0.35/minute

• 5 min: 5 × e^(0.35×3) = 14.3 M/s

• 8 min: 5 × e^(0.35×6) = 36.9 M/s

Example: Sustainable Growth

• Start: 5 M/s at 2 minutes

• Growth: 0.2/minute

• 5 min: 5 × e^(0.2×3) = 9.1 M/s

• 8 min: 5 × e^(0.2×6) = 16.6 M/s

⚡ Community Efficiency Discoveries

🎯 Investment Priority Matrix

T2 Mex Upgrade: Priority 1 ★★★

Geothermal/Tidal: Priority 1 ★★★

Fusion Reactors: Priority 2 ★★☆

T1 Mex Expansion: Priority 2 ★★☆

T2 Converters: Priority 3 ★☆☆

Rule: Always exhaust Priority 1 before Priority 2

⏰ Timing Optimization

First T2 Mex: 4:30-5:30

First Fusion: 7:00-9:00

Energy Converter: 8:00-12:00

T2 Constructor: 5:00-6:00

Mass Storage: 6:00-8:00

Note: Times vary ±30% based on map/conditions