Kelly Criterion Position Sizing for Prediction Markets

The Kelly Criterion is the mathematically optimal formula for sizing bets when you have a genuine edge. Most prediction market traders either ignore it entirely (and over-bet into ruin) or misapply it (and leave money on the table).

This guide covers exactly how to apply Kelly to Polymarket and Kalshi positions, including worked examples, the case for fractional Kelly, and the mistakes that trip up even experienced traders.

Why Position Sizing Matters as Much as Finding Edge

Most traders spend 90% of their time finding edges and 10% thinking about position sizing. That ratio is backwards.

Consider two traders with identical probability estimates and identical accuracy. Trader A bets 2% of bankroll on every position. Trader B uses Kelly sizing. Over 100 trades, Trader B compounds wealth at the maximum rate possible given their edge — the Kelly Criterion solves for the bet size that maximizes expected growth rate, not just expected value on any single bet. That distinction is everything.

The Kelly Formula

For a binary prediction market bet:

• f* = fraction of bankroll to bet
• b = net odds (payout per unit risked if you win)
• p = your probability of winning
• q = probability of losing (1 − p)

Prediction Market Version

On Polymarket and Kalshi, prices are expressed as probabilities. If you're buying YES at 40 cents (40%), the implied odds are: you risk 40 cents to win 60 cents (b = 0.6 / 0.4 = 1.5).

If you think the true probability is 55%:

That's a large position — because a 15-point edge at 40 cents represents enormous value. Use the PolyMath Kelly Calculator to run these numbers instantly for any market.

Worked Example: Fed Rate Decision

Suppose the Fed rate decision market on Kalshi shows 30% chance of a 25bps cut, but your analysis of recent economic data puts it at 45%.

Kelly says bet 21.5% of your bankroll. That's a meaningful position, reflecting a genuine 15-point edge on a 30-cent market.

Fractional Kelly: The Practical Choice

Full Kelly sizing is theoretically optimal but practically challenging for three reasons:

1. Edge estimation error: Your probability estimates aren't perfect. If you're wrong about your edge, full Kelly oversizes.
2. Correlation risk: Multiple positions sized at full Kelly create compounded drawdown risk.
3. Liquidity constraints: Large positions on illiquid markets move the price against you.

Half-Kelly is the standard solution: divide f* by 2. Half-Kelly gives you ~75% of the long-run expected return of full Kelly with much lower variance. Most professional prediction market traders use half-Kelly or quarter-Kelly.

Kelly With Multiple Simultaneous Positions

This is where most traders go wrong. If you hold 5 positions each sized at full Kelly, your combined exposure may exceed 100% of bankroll — guaranteed ruin.

The correct approach:

1. Calculate Kelly fraction for each position independently
2. Sum all Kelly fractions
3. If the sum exceeds target portfolio exposure (e.g., 50%), scale each position proportionally

Use the PolyMath Portfolio Tool to manage position sizing across multiple open trades.

Common Kelly Mistakes on Prediction Markets

The Full Workflow

1. Find a market where your probability estimate differs from market price by ≥5 points
2. Confirm positive EV with the EV Calculator
3. Calculate your Kelly fraction with the Kelly Calculator
4. Apply half-Kelly unless you have very high confidence in your edge estimate
5. Check portfolio-level exposure with the Portfolio Tool
6. After resolution, log your estimate vs. outcome in the Calibration Tool