market-mechanics-betting
Market Mechanics & Betting
Table of Contents
What is Market Mechanics?
Market mechanics translates beliefs (probabilities) into actions (bets, decisions, resource allocation) using quantitative frameworks.
Core Principle: If you believe something with X% probability, you should be willing to bet at certain odds.
Why It Matters:
- Forces intellectual honesty (would you bet on this?)
- Optimizes resource allocation (how much to bet?)
- Improves calibration (betting reveals true beliefs)
- Provides scoring framework (Brier, log score)
- Enables aggregation (extremizing, market prices)
When to Use This Skill
Use when:
- Converting belief to action - Have probability, need decision
- Betting decisions - Should I bet? How much?
- Resource allocation - How to distribute finite resources?
- Scoring forecasts - Measuring accuracy (Brier score)
- Aggregating forecasts - Combining multiple predictions
- Finding edge - Is my probability better than market?
Do NOT use when:
- No market/betting context exists
- Non-quantifiable outcomes
- Pure strategic analysis (no probability needed)
Interactive Menu
What would you like to do?
Core Workflows
1. Calculate Edge - Determine if you have an advantage 2. Optimize Bet Size (Kelly Criterion) - How much to bet 3. Extremize Aggregated Forecasts - Adjust crowd wisdom 4. Optimize Brier Score - Improve forecast scoring 5. Hedge and Portfolio Betting - Manage multiple bets 6. Learn the Framework - Deep dive into methodology 7. Exit - Return to main forecasting workflow
1. Calculate Edge
Determine if you have a betting advantage.
Edge Calculation Progress:
- [ ] Step 1: Identify market probability
- [ ] Step 2: State your probability
- [ ] Step 3: Calculate edge
- [ ] Step 4: Apply minimum threshold
- [ ] Step 5: Make bet/pass decision
Step 1: Identify market probability
Sources: Prediction markets (Polymarket, Kalshi), betting odds, consensus forecasts, base rates
Converting betting odds to probability:
Decimal odds: Probability = 1 / Odds
American (+150): Probability = 100 / (150 + 100) = 40%
American (-150): Probability = 150 / (150 + 100) = 60%
Fractional (3/1): Probability = 1 / (3 + 1) = 25%
Step 2: State your probability
After running your forecasting process, state: Your probability: ___%
Step 3: Calculate edge
Edge = Your Probability - Market Probability
Interpretation:
- Positive edge: More bullish than market → Consider betting YES
- Negative edge: More bearish than market → Consider betting NO
- Zero edge: Agree with market → Pass
Step 4: Apply minimum threshold
Minimum Edge Thresholds:
| Context | Minimum Edge | Reasoning |
|---|---|---|
| Prediction markets | 5-10% | Fees ~2-5%, need buffer |
| Sports betting | 3-5% | Efficient markets |
| Private bets | 2-3% | Only model uncertainty |
| High conviction | 8-15% | Substantial edge needed |
Step 5: Make bet/pass decision
If Edge > Minimum Threshold → Calculate bet size (Kelly)
If 0 < Edge < Minimum → Pass (edge too small)
If Edge < 0 → Consider opposite bet or pass
Next: Return to menu or continue to Kelly sizing
2. Optimize Bet Size (Kelly Criterion)
Calculate optimal bet size to maximize long-term growth.
Kelly Criterion Progress:
- [ ] Step 1: Understand Kelly formula
- [ ] Step 2: Calculate full Kelly
- [ ] Step 3: Apply fractional Kelly
- [ ] Step 4: Consider bankroll constraints
- [ ] Step 5: Execute bet
Step 1: Understand Kelly formula
f* = (bp - q) / b
Where:
f* = Fraction of bankroll to bet
b = Net odds received (decimal odds - 1)
p = Your probability of winning
q = Your probability of losing (1 - p)
Maximizes expected logarithm of wealth (long-term growth rate).
Step 2: Calculate full Kelly
Example:
- Your probability: 70% win
- Market odds: 1.67 (decimal) → Net odds (b): 0.67
- p = 0.70, q = 0.30
f* = (0.67 × 0.70 - 0.30) / 0.67 = 0.252 = 25.2%
Full Kelly says: Bet 25.2% of bankroll
Step 3: Apply fractional Kelly
Problem with full Kelly: High variance, model error sensitivity, psychological difficulty
Solution: Fractional Kelly
Actual bet = f* × Fraction
Common fractions:
- 1/2 Kelly: f* / 2
- 1/3 Kelly: f* / 3
- 1/4 Kelly: f* / 4
Recommendation: Use 1/4 to 1/2 Kelly for most bets.
Why: Reduces variance by 50-75%, still captures most growth, more robust to model error.
Step 4: Consider bankroll constraints
Practical considerations:
- Define dedicated betting bankroll (money you can afford to lose)
- Minimum bet size (market minimums)
- Maximum bet size (market/liquidity limits)
- Round to practical amounts
Step 5: Execute bet
Final check:
- Confirmed edge > minimum threshold
- Calculated Kelly size
- Applied fractional Kelly (1/4 to 1/2)
- Checked bankroll constraints
- Verified odds haven't changed
Place bet.
Next: Return to menu
3. Extremize Aggregated Forecasts
Adjust crowd wisdom when aggregating multiple predictions.
Extremizing Progress:
- [ ] Step 1: Understand why extremizing works
- [ ] Step 2: Collect individual forecasts
- [ ] Step 3: Calculate simple average
- [ ] Step 4: Apply extremizing formula
- [ ] Step 5: Validate and finalize
Step 1: Understand why extremizing works
The Problem: When you average forecasts, you get regression to 50%.
The Research: Good Judgment Project found aggregated forecasts are more accurate than individuals BUT systematically too moderate. Extremizing (pushing away from 50%) improves accuracy because multiple forecasters share common information, and simple averaging "overcounts" shared information.
Step 2: Collect individual forecasts
Gather predictions from multiple sources. Ensure forecasts are independent, forecasters used good process, and have similar information available.
Step 3: Calculate simple average
Average = Sum of forecasts / Number of forecasts
Step 4: Apply extremizing formula
Extremized = 50% + (Average - 50%) × Factor
Where Factor typically ranges from 1.2 to 1.5
Example:
- Average: 77.6%
- Factor: 1.3
Extremized = 50% + (77.6% - 50%) × 1.3 = 85.88% ≈ 86%
Choosing the Factor:
| Situation | Factor | Reasoning |
|---|---|---|
| Forecasters highly correlated | 1.1-1.2 | Weak extremizing |
| Moderately independent | 1.3-1.4 | Moderate extremizing |
| Very independent | 1.5+ | Strong extremizing |
| High expertise | 1.4-1.6 | Trust the signal |
Default: Use 1.3 if unsure.
Step 5: Validate and finalize
Sanity checks:
- Bounded [0%, 100%]: Cap at 99%/1% if needed
- Reasonableness: Does result "feel" right?
- Compare to best individual: Extremized should be close to best forecaster
Next: Return to menu
4. Optimize Brier Score
Improve forecast accuracy scoring.
Brier Score Optimization Progress:
- [ ] Step 1: Understand Brier score formula
- [ ] Step 2: Calculate your Brier score
- [ ] Step 3: Decompose into calibration and resolution
- [ ] Step 4: Identify improvement strategies
- [ ] Step 5: Avoid gaming the metric
Step 1: Understand Brier score formula
Brier Score = (1/N) × Σ(Probability - Outcome)²
Where:
- Probability = Your forecast (0 to 1)
- Outcome = Actual result (0 or 1)
- N = Number of forecasts
Range: 0 (perfect) to 1 (worst). Lower is better.
Step 2: Calculate your Brier score
Interpretation:
| Brier Score | Quality |
|---|---|
| < 0.10 | Excellent |
| 0.10 - 0.15 | Good |
| 0.15 - 0.20 | Average |
| 0.20 - 0.25 | Below average |
| > 0.25 | Poor |
Baseline: Random guessing (always 50%) gives Brier = 0.25
Step 3: Decompose into calibration and resolution
Brier Score = Calibration Error + Resolution + Uncertainty
Calibration Error: Do your 70% predictions happen 70% of the time? (measures bias) Resolution: How often do you assign different probabilities to different outcomes? (measures discrimination)
Step 4: Identify improvement strategies
Strategy 1: Fix Calibration
- If overconfident: Widen confidence intervals, be less extreme
- If underconfident: Be more extreme when you have strong evidence
- Tool: Calibration plot (X: predicted probability, Y: actual frequency)
Strategy 2: Improve Resolution
- Avoid being stuck at 50%
- Differentiate between easy and hard forecasts
- Be bold when evidence is strong
Strategy 3: Gather Better Information
- Do more research, use reference classes, decompose with Fermi, update with Bayes
Step 5: Avoid gaming the metric
Wrong approach: "Never predict below 10% or above 90%" (gaming)
Right approach: Predict your TRUE belief. If that's 5%, say 5%. Accept that you'll occasionally get large Brier penalties. Over many forecasts, honesty wins.
The rule: Minimize Brier score by being accurate, not by being safe.
Next: Return to menu
5. Hedge and Portfolio Betting
Manage multiple bets and correlations.
Portfolio Betting Progress:
- [ ] Step 1: Identify correlations between bets
- [ ] Step 2: Calculate portfolio Kelly
- [ ] Step 3: Assess hedging opportunities
- [ ] Step 4: Optimize across all positions
- [ ] Step 5: Monitor and rebalance
Step 1: Identify correlations between bets
The problem: If bets are correlated, true exposure is higher than sum of individual bets.
Correlation examples:
- Positive: "Democrats win House" + "Democrats win Senate"
- Negative: "Team A wins" + "Team B wins" (playing each other)
- Uncorrelated: "Rain tomorrow" + "Bitcoin price doubles"
Step 2: Calculate portfolio Kelly
Simplified heuristic:
- If correlation > 0.5: Reduce each bet size by 30-50%
- If correlation < -0.5: Can increase total exposure slightly (partial hedge)
Step 3: Assess hedging opportunities
When to hedge:
- Probability changed: Lock in profit when beliefs shift
- Lock in profit: Event moved in your favor, odds improved
- Reduce exposure: Too much capital on one outcome
Hedging example:
- Bet $100 on A at 60% (1.67 odds) → Payout: $167
- Odds change: A now 70%, B now 30% (3.33 odds)
- Hedge: Bet $50 on B at 3.33 → Payout if B wins: $167
- Result: Guaranteed $17 profit regardless of outcome
Step 4: Optimize across all positions
View portfolio holistically. Reduce correlated bets, maintain independence where possible.
Step 5: Monitor and rebalance
Weekly review: Check if probabilities changed, assess hedging opportunities, rebalance if needed After major news: Update probabilities, consider hedging, recalculate Kelly sizes Monthly audit: Portfolio correlation check, bankroll adjustment, performance review
Next: Return to menu
6. Learn the Framework
Deep dive into the methodology.
Resource Files
- Expected value framework, variance and risk, bankroll management, market efficiency
- Mathematical derivation, proof of optimality, extensions and variations, common mistakes
📄 Scoring Rules and Calibration
- Brier score deep dive, log score, calibration curves, resolution analysis, proper scoring rules
Next: Return to menu
Quick Reference
The Market Mechanics Commandments
- Edge > Threshold - Don't bet small edges (5%+ minimum)
- Use Fractional Kelly - Never full Kelly (use 1/4 to 1/2)
- Extremize aggregates - Push away from 50% when combining forecasts
- Minimize Brier honestly - Be accurate, not safe
- Watch correlations - Portfolio risk > sum of individual risks
- Hedge strategically - When probabilities change or lock profit
- Track calibration - Your 70% should happen 70% of the time
One-Sentence Summary
Convert beliefs into optimal decisions using edge calculation, Kelly sizing, extremizing, and proper scoring.
Integration with Other Skills
- Before: Use after completing forecast (have probability, need action)
- Companion: Works with
bayesian-reasoning-calibrationfor probability updates - Feeds into: Portfolio management and adaptive betting strategies
Resource Files
📁 resources/
- betting-theory.md - Fundamentals and framework
- kelly-criterion.md - Optimal bet sizing
- scoring-rules.md - Calibration and accuracy measurement
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