market-mechanics-betting

What this skill does

# Market Mechanics & Betting

## Table of Contents
- [Interactive Menu](#interactive-menu)
- [Quick Reference](#quick-reference)
- [Resource Files](#resource-files)

---

## Interactive Menu

**What would you like to do?**

### Core Workflows

**1. [Calculate Edge](#1-calculate-edge)** - Determine if you have an advantage
**2. [Optimize Bet Size (Kelly Criterion)](#2-optimize-bet-size-kelly-criterion)** - How much to bet
**3. [Extremize Aggregated Forecasts](#3-extremize-aggregated-forecasts)** - Adjust crowd wisdom
**4. [Optimize Brier Score](#4-optimize-brier-score)** - Improve forecast scoring
**5. [Hedge and Portfolio Betting](#5-hedge-and-portfolio-betting)** - Manage multiple bets
**6. [Learn the Framework](#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](#interactive-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:**
1. Define dedicated betting bankroll (money you can afford to lose)
2. Minimum bet size (market minimums)
3. Maximum bet size (market/liquidity limits)
4. 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](#interactive-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:**
1. **Bounded [0%, 100%]:** Cap at 99%/1% if needed
2. **Reasonableness:** Does result "feel" right?
3. **Compare to best individual:** Extremized should be close to best forecaster

**Next:** Return to [menu](#interactive-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