Kelly position sizing answers a question expected value alone cannot: how much of your bankroll should you risk on one trade? Getting this wrong can hurt even a good edge.
The Kelly criterion is a formula from probability theory, adapted here for binary shares like YES/NO contracts on Polymarket. This guide covers the formula, fractional Kelly, and worked examples.
What Kelly Position Sizing Solves
Expected value tells you whether a trade is favorable. It does not tell you how large a position to take. Bet too big, even with a real edge, and normal losing streaks can wipe out your bankroll.
Kelly position sizing calculates the fraction of your bankroll to risk that maximizes long-run growth, given your edge and the odds offered. It assumes you can estimate probability reasonably well.
The Kelly Formula for Binary Shares
For a YES share priced at c (between 0 and 1) with your believed probability p that YES happens, the Kelly fraction is:
f* = (p − c) / (1 − c)
Here, f* is the fraction of your bankroll to allocate. If f* is zero or negative, the Kelly criterion says don't bet: your edge doesn't justify a position.
Worked Example 1
A share is priced at c = 0.40, and you estimate p = 0.55.
f* = (0.55 − 0.40) / (1 − 0.40)
f* = 0.15 / 0.60 = 0.25
Full Kelly suggests risking 25% of your bankroll. That is aggressive for most traders, which is why fractional Kelly exists.
Worked Example 2
A share is priced at c = 0.70, and you estimate p = 0.55.
f* = (0.55 − 0.70) / (1 − 0.70)
f* = −0.15 / 0.30 = −0.50
A negative result means no bet: the price already exceeds your estimated probability.
Why Fractional Kelly Is Recommended
Full Kelly assumes your probability estimate is exact. In practice, estimates carry error, and full Kelly can produce large swings in your bankroll even when the underlying edge is real.
Most practitioners use fractional Kelly, betting a fraction such as one-quarter or one-half of the full Kelly amount:
| Kelly fraction used | Example 1 stake (25% full Kelly) |
|---|---|
| Full Kelly (100%) | 25% of bankroll |
| Half Kelly (50%) | 12.5% of bankroll |
| Quarter Kelly (25%) | 6.25% of bankroll |
Reducing the fraction lowers volatility and softens the impact of estimation error, at the cost of slower theoretical growth.
A Practical Approach
- Estimate p carefully, using evidence rather than preference.
- Calculate full Kelly with the formula above.
- Apply a fraction (often 25%–50%) to account for uncertainty.
- Never risk more than you can afford to lose on any single market.
Common Situations Where Kelly Sizing Helps
Kelly sizing is most useful when you trade several markets over time, not just a single bet. It helps you avoid concentrating too much capital in one uncertain outcome.
Consider a trader who repeatedly sizes positions using quarter Kelly. Even with some wrong estimates along the way, this discipline limits the damage from any single mistake.
Kelly sizing also interacts with correlated markets. If two markets depend on the same underlying event, treating them as independent bets can lead to unintentionally oversized total exposure.
Bet Sizing Discipline Over Time
Consistent bet sizing matters more than any single clever calculation. Traders who apply the same disciplined process across dozens of markets tend to see steadier results than those who size trades emotionally.
Write your target Kelly fraction down before you start trading a market. Keep a simple log of price, your estimate of p, calculated f*, and the fraction you actually used. Reviewing this log periodically reveals whether your bet sizing habits match your stated plan, and whether your probability estimates tend to run too high or too low.
Kelly Sizing Has Limits
Kelly position sizing assumes accurate probability estimates and independent bets, which is rarely fully true in real markets. It is a framework for thinking about size, not a precise guarantee of outcomes.
Reviewing expected value first helps you form the p used in this formula. Also check common mistakes traders make with position sizing, and read how prediction markets work for background on pricing.
Use the Kelly calculator to compute f* automatically, and the profit calculator to see potential payouts for a given stake.