What Is Kelly Criterion? The Math Behind Prediction Market Position Sizing
Kelly Criterion is the mathematical formula that tells you exactly how much of your bankroll to bet given your edge. Here is how it works, why full Kelly is dangerous, and how serious prediction market traders apply it.
1. Where Kelly Criterion Comes From
John L. Kelly Jr., a physicist at Bell Labs, published the formula in 1956 as a theory about information transmission over noisy communication channels. It was not written for gambling — but traders and professional bettors quickly recognized it solved their exact problem: how much of your bankroll should you risk when you have an edge?
The core insight is that maximizing expected log wealth, not expected wealth, produces the best long-run compounding. The distinction matters more than it first appears. Linear expectation can recommend bet sizes that produce the highest average outcome while simultaneously guaranteeing ruin with certainty. Kelly's formula avoids this by penalizing positions that risk too much of your bankroll regardless of the expected payout.
2. The Formula
Kelly percentage = (bp − q) / b, where b is the net odds received (profit per unit risked), p is your estimated probability of winning, and q is your probability of losing (1 − p).
On a prediction market where YES is trading at 40¢, you're getting net odds of 1.5:1 — you stake 40¢ to win 60¢. If your analysis puts the true probability at 62%, your Kelly percentage is (1.5 × 0.62 − 0.38) / 1.5 = 0.362, meaning 36.2% of your bankroll. That is full Kelly. In practice, nobody bets 36% of their bankroll on a single prediction market position.
3. Why Full Kelly Is Too Aggressive
Full Kelly maximizes long-run compounding but produces severe drawdowns along the way. A string of losing bets — which happens even with genuine edge — can reduce your bankroll to a fraction of its starting value. The mathematics are unforgiving: a 50% drawdown requires a 100% gain just to get back to even.
Quarter Kelly (25% of the full Kelly percentage) is the most common practical application among systematic bettors and quantitative traders. At the earlier example, that translates to 9% of bankroll — large enough to compound meaningful gains but small enough to survive an extended losing streak. Some traders use Half Kelly (12.5% in this example) as a middle ground between compounding speed and drawdown protection.
4. The Calibration Problem
Kelly assumes your probability estimate is accurate. In practice, most traders are overconfident — they assign 80% probability to events that are only 65% likely. An overconfident Kelly user is functionally over-betting, which increases drawdown risk without increasing expected edge.
Brier scores — a proper scoring rule that penalizes both overconfidence and underconfidence — are the standard measure of forecast calibration. If your historical predictions show a Brier score that indicates systematic overconfidence, you should scale your Kelly fraction down accordingly. AI agents can be recalibrated continuously as predictions are graded. Human traders, without structured feedback, rarely are.
5. Hard Caps and Liquidity Constraints
Most Kelly applications assume you can bet any fraction of your bankroll. Prediction markets have liquidity limits — large positions move the market price against you as you enter. A $2,000 position in a $5,000 liquidity market will shift the price by several percentage points, reducing the edge you entered for.
Hard caps of 10% of portfolio per single position and 80% total portfolio exposure prevent Kelly from recommending positions that would be self-defeating. These limits are not conservative adjustments to the math — they are recognitions that the math assumes you can execute at your target price, which liquidity constraints make impossible above certain sizes.