Case Study 1: From Gut Feeling to Quantified Edge: A Trader's Journey

Overview

This case study follows Maria, an experienced political analyst who transitions from casual prediction market participation to a disciplined, quantified trading approach. We trace her journey through analyzing a political market, estimating probabilities using multiple methods, calculating edge, sizing positions with the Kelly criterion, and tracking her results over 50 trades. The data and analysis illustrate the concepts from Chapter 13 in a realistic, end-to-end scenario.

Part 1: The Starting Point -- Gut-Feel Trading

Maria has followed politics professionally for 12 years. She reads extensively, has contacts in political circles, and considers herself well-informed. Six months ago, she opened a prediction market account with $5,000 and began trading political markets based on her instincts.

After 30 trades over three months, Maria reviews her results:

Maria is pleased that she is profitable, but $150 over three months on a $5,000 bankroll is disappointing. She also notices something troubling: she cannot determine whether her profits are due to skill or luck. With a 56.7% win rate and average bet sizes, random chance could easily explain her results.

Key problem: Maria has no systematic way to measure her edge, and her position sizing is ad hoc (she bets "whatever feels right," usually $100-$200 per trade).

Part 2: Adopting a Framework

Maria reads Chapter 13 and decides to implement a disciplined approach. She commits to:

1. Recording a specific probability estimate for every trade before looking at the market price
2. Computing her edge and EV for every trade
3. Using fractional Kelly for position sizing
4. Tracking her results systematically

Setting Up the System

Maria creates a simple tracking spreadsheet (she later upgrades to the Python system in code/example-03-edge-tracker.py). For each trade, she records:

• Market question
• Her probability estimate (with rationale and confidence interval)
• Market price
• Computed edge, EV, and Kelly fraction
• Actual position size and reasoning for any deviation from Kelly
• Edge source classification
• Outcome and P&L

Part 3: The First Disciplined Trade

The Market

Question: "Will Governor Smith win the gubernatorial primary in State X?" Market price: YES at $0.45

Maria's Analysis

Step 1: Base rate. Incumbent governors seeking re-election in primaries have historically won about 85% of the time over the last 40 years in the US. However, Governor Smith is not an incumbent in this race -- she is a sitting governor running for a different office. The base rate for sitting governors winning primaries for other offices is harder to pin down. Maria estimates approximately 65% based on a smaller sample of comparable cases.

Step 2: Specific factors. - Governor Smith has a 52% approval rating (moderate, not strong) - Her primary opponent is a well-funded challenger with 35% name recognition - Recent polling shows Smith leading 48-38 with 14% undecided - Historical pattern: candidates leading by 10+ points in primaries at this stage win about 75% of the time

Step 3: Combining estimates. - Base rate estimate: 65% - Polling-based estimate: 75% - Qualitative assessment (strong campaign infrastructure, endorsements): 70%

Simple average: $(65 + 75 + 70) / 3 = 70\%$

Weighted average (40% polling, 30% base rate, 30% qualitative): $0.40 \times 75 + 0.30 \times 65 + 0.30 \times 70 = 30 + 19.5 + 21 = 70.5\%$

Step 4: Confidence interval. Maria estimates her 80% confidence interval as [60%, 80%]. She is fairly confident in her estimate but acknowledges significant uncertainty -- the primary is still two months away and surprises can happen.

Step 5: Final estimate: $q = 0.70$, CI = [0.60, 0.80]

Edge and EV Calculation

$$ \text{Edge} = q - p = 0.70 - 0.45 = 0.25 $$

$$ \text{EV per contract} = 0.70 - 0.45 = \$0.25 $$

$$ \text{EV\%} = \frac{0.25}{0.45} = 55.6\% $$

This is a very large edge. Maria is suspicious -- why is the market so low? She investigates and finds that the market is on a smaller platform with limited liquidity. The last trade was two days ago, and recent polling had not been incorporated. She also notes that the market has only 12 active traders.

This partially explains the large edge: it is a combination of information edge (she has seen the latest polling) and a liquidity/platform inefficiency.

Position Sizing

Full Kelly fraction:

$$ f^* = \frac{0.70 - 0.45}{1 - 0.45} = \frac{0.25}{0.55} = 0.4545 $$

This would mean betting 45.45% of her $5,000 bankroll = $2,273.

Maria uses several adjustments: 1. Conservative probability: Using the lower bound of her CI (60%): $f^* = (0.60 - 0.45)/(1 - 0.45) = 0.2727$ 2. Half Kelly on conservative estimate: $f = 0.50 \times 0.2727 = 0.1364$ 3. Maximum position size rule: Maria limits any single trade to 10% of bankroll = $500.

Final position: $500 (10% of bankroll), constrained by her maximum position rule.

At $0.45 per contract, she buys 1,111 YES contracts (rounding down).

Outcome

Governor Smith wins the primary. Maria's contracts pay out $1 each.

• Revenue: 1,111 x $1.00 = $1,111
• Cost: 1,111 x $0.45 = $500
• Profit: $611
• Return on investment: 122.2%

Maria's bankroll grows from $5,000 to $5,611.

Part 4: Trading 50 Markets

Over the next four months, Maria trades 50 markets using her disciplined framework. Here is a summary of her complete trading record.

Aggregate Statistics

Performance by Edge Source

Key Observations

Information edge is the strongest contributor. Maria's 12 trades with an information edge (political contacts, early access to data) had a 75% win rate and contributed nearly half her total profits. This makes sense: she has genuine domain expertise.

Analytical edge is consistent but smaller. Her 20 model-based trades had a 60% win rate with a smaller average edge. Her quantitative model adds value but is not dramatically better than the market.

Behavioral edge shows promise. Trading against apparent market overreactions (buying after panic dips, selling into hype) was profitable but with a small sample.

Timing edge is weak. Maria's attempts to time entries (buying dips, waiting for better prices) actually hurt her performance. Her 40% win rate on timing-motivated trades suggests she should enter immediately when she identifies edge rather than trying to time the market.

"Unknown" edge trades performed worst. The three trades where Maria could not clearly identify her edge source had the lowest win rate and smallest edge. This validates the principle that if you cannot articulate your edge, you probably do not have one.

Calibration Analysis

Maria bins her probability estimates and compares them to actual outcomes:

Maria notices she is slightly overconfident in the high-probability range: her 70-80% estimates only come true 62.5% of the time, and her 80-90% estimates come true only 66.7% of the time (though the sample is small). She is well-calibrated in the 50-70% range.

Brier score comparison: - Maria's Brier score: 0.198 - Market prices' Brier score (for the same events): 0.217

Maria's forecasts are meaningfully better than the market prices, confirming that she has genuine forecasting skill.

Part 5: Position Sizing Analysis

Maria compares her actual position sizing to what full Kelly and half Kelly would have recommended:

Maria's actual performance is close to quarter Kelly, which makes sense since her 10% position cap constrained most of her trades below the Kelly-recommended size. The simulation shows that half Kelly would have been more profitable with manageable drawdowns, but full Kelly would have produced a terrifying 38.7% drawdown at one point.

Going forward, Maria decides to: - Increase her maximum position size from 10% to 15% of bankroll - Use half Kelly on the conservative (lower CI bound) probability - Only deviate from this when she has strong conviction (and document why)

Part 6: Edge Decomposition Deep Dive

Maria decomposes her total average edge of 8.3 percentage points:

Calibration edge: +1.9 pp. The markets she traded were systematically miscalibrated (events priced at 50% occurred 52% of the time on average; events priced at 30% occurred 28% of the time, etc.). This small calibration edge comes "for free" and does not require Maria's expertise.

Information edge: +3.2 pp. After removing her private information sources, Maria's average probability estimate is 3.2 percentage points closer to the market price. Her political contacts and early data access contribute significantly to her edge.

Model edge: +1.8 pp. Her quantitative analysis (base rate adjustments, polling model) adds 1.8 percentage points beyond what a naive trader using public information would achieve.

Timing edge: -0.3 pp. Maria's market timing actually hurts her slightly. She sometimes waits for better prices and misses favorable moves.

Residual: +1.7 pp. The remaining edge comes from interactions between components and factors not easily categorized.

Implications

Maria concludes that she should: 1. Protect her information edge by maintaining her political contacts and data sources 2. Invest in her model edge by improving her quantitative framework 3. Stop trying to time entries and instead trade immediately when she identifies edge 4. Acknowledge the calibration edge is a market-wide phenomenon that may shrink as markets mature

Part 7: Lessons Learned

After 50 trades with a disciplined framework, Maria reflects on her key lessons:

Lesson 1: Quantification Transforms Trading

Before adopting the framework, Maria was making money but had no idea why or whether it was sustainable. After quantifying her edge, she knows exactly where her profits come from and can make informed decisions about resource allocation.

Lesson 2: Position Sizing Matters as Much as Prediction

Several of Maria's best predictions resulted in modest profits because she bet too little. Several mediocre predictions resulted in outsized losses because she bet too much. Consistent Kelly-based sizing would have significantly improved her risk-adjusted returns.

Lesson 3: Not Every Trade Needs an Edge

Maria traded three markets where she could not identify her edge. All three were marginally profitable, but her win rate and edge were the lowest in this category. She resolves to skip trades where she cannot clearly articulate her advantage.

Lesson 4: Overconfidence Is Real

Maria's calibration analysis revealed she was overconfident in the 70-90% range. Her "I'm 80% sure" was really more like 67%. She adjusts her future estimates downward in this range.

Lesson 5: Edge Tracking Is Essential

Without her tracking system, Maria would have attributed her profits entirely to her analytical skill. In reality, her information edge is her biggest advantage, and her timing attempts are counterproductive. This knowledge is invaluable for improving her strategy.

Lesson 6: Starting Conservative Was the Right Choice

Maria's conservative position sizing (capped at 10%) meant she left money on the table compared to full Kelly, but it also limited her drawdowns to a psychologically manageable level. As she gains more data on her edge, she can gradually increase position sizes.

Part 8: Going Forward

Maria creates a plan for the next 50 trades:

1. Increase to half Kelly on conservative estimates, with a 15% position cap
2. Focus on information-edge and analytical-edge trades, avoiding pure timing plays
3. Improve her polling model by incorporating additional data sources
4. Monitor edge decay by plotting her rolling average edge monthly
5. Target Brier score below 0.18 (improvement from current 0.198)
6. Maintain a minimum edge threshold of 5 percentage points -- no trades below this unless the market resolves within 1 week (where smaller edges can be annualized to attractive returns)

Maria's journey illustrates the core message of Chapter 13: edge is not something you feel -- it is something you measure, track, and optimize. The transition from gut-feel trading to quantified edge is the single most important step a prediction market trader can take.

Code

The complete simulation code for this case study, including data generation, analysis, and visualization, is available in code/case-study-code.py.