Expected Value (EV)
Definition
Expected Value (EV) = (payout × true probability) − price. Positive EV indicates a favorable trade in the long run.
The Formula
Basic EV
EV = (Payout × Probability) - Cost
For Prediction Markets
EV = (p × $1.00) - price
Where:
- p = your estimated probability (0-1)
- price = current market price
Example 1: Positive EV
Market: "Will it rain tomorrow?"
- Market price: $0.40
- Your estimate: 60% chance (p = 0.60)
- Payout if correct: $1.00
Calculation:
EV = (0.60 × $1.00) - $0.40
EV = $0.60 - $0.40
EV = $0.20
Result: +$0.20 EV per contract (good bet!)
Example 2: Negative EV
Market: "Will GDP exceed 3%?"
- Market price: $0.70
- Your estimate: 50% chance (p = 0.50)
- Payout if correct: $1.00
Calculation:
EV = (0.50 × $1.00) - $0.70
EV = $0.50 - $0.70
EV = -$0.20
Result: -$0.20 EV per contract (bad bet!)
Example 3: Zero EV (Fair Price)
Market: "Will the coin land heads?"
- Market price: $0.50
- True probability: 50% (fair coin)
- Payout if correct: $1.00
Calculation:
EV = (0.50 × $1.00) - $0.50
EV = $0.50 - $0.50
EV = $0.00
Result: $0 EV (break-even bet)
Interpreting EV
Positive EV (+)
- Expected to profit long-term
- Take the bet
- Larger is better
- Compound over time
Negative EV (-)
- Expected to lose long-term
- Avoid the bet
- Even small -EV adds up
- Grind down bankroll
Zero EV (0)
- Break-even long-term
- Neither good nor bad
- Liquidity provision
- Entertainment value
EV Over Multiple Bets
Law of Large Numbers
With many bets, results converge to EV:
Example: +$0.20 EV bet, repeated 100 times
- Expected profit: 100 × $0.20 = $20.00
- Actual results: Will vary around $20
- More bets: Closer to expectation
EV vs Probability
Common Confusion
- High probability ≠ Positive EV
- Low probability ≠ Negative EV
It's About Price
- 90% event at $0.85 = +EV
- 90% event at $0.95 = -EV
- 10% event at $0.05 = +EV
- 10% event at $0.15 = -EV
Calculating Your Edge
Edge Formula
Edge = True Probability - Market Price
Relationship to EV:
EV = Edge × Payout
For $1 payout markets:
EV = Edge
EV in Practice
Step-by-Step
- Research: Gather information
- Estimate: What's the true probability?
- Compare: To market price
- Calculate: EV = (p × $1) - price
- Decide: Take if positive
Example Workflow
Question: "Will CPI exceed 3%?"
-
Research:
- Historical data
- Economic trends
- Expert forecasts
-
Estimate: 65% probability
-
Market shows: $0.55
-
Calculate:
EV = (0.65 × $1) - $0.55 = +$0.10 -
Action: Buy Yes shares
Common Mistakes
Mistake 1: Ignoring Fees
Wrong:
EV = (0.60 × $1) - $0.40 = $0.20
Right (with 2% fee):
EV = (0.60 × $1) - $0.40 - $0.02 = $0.18
Mistake 2: Confusing Price and Probability
- Market price ≠ true probability
- That's why EV exists
- Find mispricings
Mistake 3: Short-Term Thinking
- One bet can lose even with +EV
- Need many bets to realize EV
- Variance matters
EV and Bankroll Management
Position Sizing
Higher EV justifies larger bets:
| EV | Kelly Fraction | Position Size (10k bankroll) | |----|----------------|------------------------------| | +$0.05 | ~8% | $800 | | +$0.10 | ~16% | $1,600 | | +$0.20 | ~33% | $3,300 |
Risk-Adjusted EV
Consider variance:
- High EV, high variance = reduce size
- Moderate EV, low variance = comfortable
- Use Kelly Criterion for optimization
EV for Different Outcomes
Binary Markets
Simple calculation per share
Categorical Markets
Calculate EV for each outcome:
Total EV = Σ (Probability_i × Payout_i) - Total Cost
Portfolio EV
Sum across all positions:
Portfolio EV = EV_1 + EV_2 + ... + EV_n
When EV Isn't Enough
Non-Financial Factors
- Liquidity: Can you exit?
- Timing: When does it resolve?
- Correlation: Related to other bets?
- Opportunity cost: Better uses of capital?
Utility Theory
- EV assumes linear utility
- Real preferences may curve
- Risk aversion matters
- Diminishing returns to wealth
Maximizing EV
The Goal
Consistent +EV decisions = long-term profit
How to Find +EV
- Better information: Research others miss
- Better models: Statistical analysis
- Faster reaction: Trade news quickly
- Market inefficiencies: Exploit biases
Compound Growth
- Reinvest profits
- Grow bankroll
- Take larger +EV bets
- Exponential returns