The kelly criterion, developed by John L. Kelly Jr. in 1956, provides a mathematical framework for optimal bet sizing. While originally designed for information theory and gambling, it has profound applications in prediction markets like Polymarket and Kalshi. However, prediction markets introduce unique considerations that traditional kelly analysis doesn't fully address.
Understanding the kelly formula
The kelly criterion calculates the optimal fraction of capital to bet:
Where:
- f*=fraction of capital to bet
- b=odds received (decimal odds - 1)
- p=probability of winning
- q=probability of losing (1 - p)
In prediction markets, this translates directly. If you believe a contract trading at $0.60 has a 70% chance of resolving to YES, you're getting net odds of 0.667 (you pay $0.60, receive $1.00 if YES, so profit is $0.40, and b = $0.40/$0.60 = 0.667). Kelly suggests betting approximately 25% of your capital: f* = (0.667 × 0.70 - 0.30) / 0.667 = 0.25.
Core principles that apply
Fractional kelly is safer
Full kelly maximizes long-term growth but comes with high volatility. Most practitioners use 25-50% of kelly (quarter-kelly or half-kelly) to reduce drawdowns while maintaining most of the growth benefit.
Edge estimation is everything
Kelly's output is only as good as your probability estimate. In prediction markets, this means having a systematic approach to assessing true probabilities, not just following market prices.
Logarithmic utility assumption
Kelly assumes logarithmic utility, you care about percentage returns, not absolute dollars. This aligns well with prediction market trading where you're building capital over time.
What's different in prediction markets
Binary outcomes with continuous pricing
Unlike traditional betting, prediction markets allow you to enter and exit positions at any time before resolution. This creates opportunities for dynamic position management that pure kelly doesn't account for.
Information asymmetry is the edge
Your edge in prediction markets comes from superior information or analysis, not from finding mispriced odds in a static market. Kelly assumes you know your true probability, but in prediction markets, this probability is constantly updating.
Liquidity constraints
Kelly suggests betting a fixed fraction, but prediction markets often have limited liquidity. You may need to scale positions based on available volume, not just kelly-optimal sizing. Additionally, minimum position sizes and discrete contract units can prevent exact kelly sizing, requiring rounding that introduces small deviations from optimal.
Multiple correlated positions
Prediction markets often have related contracts (e.g., "Biden wins" and "Democrats win Senate"). Kelly doesn't account for portfolio correlation, which is critical in prediction markets.
Practical application: a prediction market example
Scenario: A contract on Polymarket is trading at $0.45 (implied 45% probability). Your analysis suggests the true probability is 60%.
Market price: $0.45 (you pay $0.45, receive $1.00 if YES wins)
Net odds (b): Profit if YES wins = $1.00 - $0.45 = $0.55, so b = $0.55/$0.45 = 1.222
Your estimate: p = 0.60, q = 0.40
Kelly calculation: f* = (1.222 × 0.60 - 0.40) / 1.222 = 0.273
Full kelly: 27.3% of capital
Half-kelly (recommended): 13.7% of capital
Quarter-kelly (conservative): 6.8% of capital
However, consider, what's the liquidity? Are there correlated positions? How confident are you in that 60% estimate? These factors should adjust your sizing downward from pure kelly.
What to ignore: common misapplications
Ignore kelly for single trades
Kelly is designed for repeated betting over many opportunities. Using it for a single high-conviction trade misses the point. For one-off positions, use risk-based sizing (e.g., risk 1-2% of capital).
Ignore kelly when you don't have edge
If you're trading at market prices without an informational edge, kelly suggests betting zero. Don't force positions just because kelly says you can, first establish why you have an edge.
Ignore kelly's assumption of known probabilities
Kelly assumes you know the true probability. In prediction markets, you're estimating it. Account for estimation error by using conservative probability estimates or reducing kelly fractions further.
Key considerations for prediction markets
Prediction Market Principles
Risk vs. Uncertainty
"Kelly criterion assumes you know the probabilities. In prediction markets, you don't, you're estimating them. This is the difference between risk and uncertainty."
Key points:
- Kelly works in a world of known probabilities (risk), but prediction markets operate in uncertainty
- Your probability estimates have error bars, kelly doesn't account for this
- Use kelly only when you have a clear informational edge, not when following the crowd
- Consider tail risks, prediction markets can have binary outcomes that wipe out positions
- Fractional kelly (25-33%) is more robust to estimation errors
"The kelly criterion is elegant mathematics applied to the wrong problem. Prediction markets are about asymmetric information and tail events, not repeated independent trials."
Portfolio Sizing
Practical Framework
"Kelly criterion is about geometric growth, but prediction markets require convexity. You need positions that benefit from volatility and tail events."
Key points:
- Kelly optimizes for long-term geometric returns, which is appropriate for prediction markets
- However, prediction markets have path dependency, early losses reduce your ability to capitalize on later edges
- Consider portfolio-level kelly, how do correlated positions affect optimal sizing?
- Use kelly as a starting point, then adjust for liquidity, correlation, and tail risk
- In practice, most successful prediction market traders use 20-40% of full kelly
"The kelly criterion gives you the mathematical answer, but prediction markets require you to also answer: What's your edge? How liquid is it? What's the correlation? Kelly is one input, not the output."
Practical framework:
- Calculate full kelly based on your edge estimate
- Reduce by 50-75% for estimation uncertainty
- Further reduce for liquidity constraints
- Adjust for portfolio correlation
- Never exceed 10-15% of capital on a single position
Master position sizing with the right tools
Applying the Kelly Criterion correctly requires understanding your edge, managing correlation, and accounting for liquidity. Get early access to tools that help you calculate optimal position sizes and manage risk across your prediction market portfolio.
Synthesis: a practical framework
Combining kelly criterion with prediction market realities:
- Estimate your edge, what's your true probability vs. market price? Be conservative, overconfidence kills.
- Calculate full kelly, use the formula to get the theoretical optimal size.
- Apply fractional kelly, use 25-50% of full kelly to account for estimation error.
- Check liquidity, can you actually size to kelly? If not, size to available liquidity.
- Consider correlation, how does this position relate to your portfolio? Adjust for correlation.
- Set hard limits, never exceed 10-15% of capital on a single position, regardless of kelly.
- Monitor and adjust, as probabilities update, recalculate kelly and adjust positions.
Common mistakes to avoid
- Using full kelly without accounting for estimation uncertainty
- Applying kelly to single trades instead of repeated opportunities
- Ignoring liquidity constraints and forcing kelly-sized positions
- Not considering portfolio-level correlation between positions
- Using market prices as your probability estimate (this gives you zero edge)
Conclusion
The kelly criterion provides a rigorous mathematical foundation for position sizing in prediction markets. However, it's a starting point, not a destination. Prediction markets introduce complexity, liquidity constraints, correlation, estimation uncertainty, and tail risks, that require adjustments to pure kelly.
Use kelly as a framework for thinking about optimal sizing, but always combine it with practical considerations. Fractional kelly (25-50%), liquidity awareness, correlation management, and hard position limits create a robust approach to prediction market trading.
Remember, kelly maximizes long-term geometric growth, but only if you have a genuine edge and can survive the volatility. In prediction markets, survival comes first, use kelly to guide your sizing, but let prudence set your limits.
Optimize your position sizing strategy
The Kelly Criterion is powerful, but applying it to prediction markets requires careful consideration. Join prediction market traders who are using sophisticated position sizing tools to maximize long-term growth while managing risk effectively.