Kelly Criterion for Prediction Markets: How to Size Your Bets

The Kelly Criterion is a mathematical formula that tells you the optimal fraction of your bankroll to bet on a positive expected value opportunity. It was developed by John Kelly at Bell Labs in 1956 and has been used by professional gamblers, card counters, and hedge fund managers ever since.

The central insight of Kelly is this: betting too little leaves money on the table; betting too much risks ruin. Kelly finds the exact fraction that maximises the long-run growth rate of your bankroll. It's not about maximising expected value of any single bet — it's about maximising the geometric growth of your capital over many bets.

For prediction market traders with genuine edge, proper bet sizing via Kelly (or fractional Kelly) is often the difference between a profitable portfolio and a blown account, even when the underlying trade analysis is correct.

The Kelly formula for binary outcomes (YES/NO prediction markets) is:

f* = (p × b - q) / b

For prediction markets, b is easy to calculate. If you buy YES at 65¢ and it resolves YES, you receive $1 — a profit of 35¢ on a 65¢ stake. So b = 35/65 ≈ 0.538.

Example: You believe a candidate has a 72% chance of winning. Market prices YES at 60¢. So p = 0.72, q = 0.28, b = 40/60 = 0.667.

f* = (0.72 × 0.667 - 0.28) / 0.667 = (0.480 - 0.28) / 0.667 = 0.200 / 0.667 ≈ 30%

Full Kelly says bet 30% of your bankroll on this position. As we'll see, that's almost certainly too aggressive.

Full Kelly maximises long-run growth rate — in theory. In practice, three factors make it dangerous:

Estimation error — Your probability estimate is not perfectly accurate. If you think the true probability is 72% but it's actually 65%, your Kelly fraction is wildly overstated. Small estimation errors compound dramatically at full Kelly. A study of prediction market participants found that most are systematically overconfident by 5-10 percentage points. This alone would make full Kelly ruinous.

Correlated positions — Kelly assumes each bet is independent. But your prediction market positions are often correlated. Multiple political markets may all move together on election night. Kelly's math breaks down when correlations are high.

Drawdown pain — Even mathematically correct full Kelly creates terrifying drawdowns. A 30-bet losing streak (which is probabilistically expected periodically) can reduce your bankroll by 90%+ even if every single bet was positive EV. Most people cannot psychologically sustain this and make poor decisions.

Professional traders use fractional Kelly — typically between 1/4 and 1/2 of the Kelly-optimal fraction. This accepts a lower expected growth rate in exchange for dramatically reduced variance and drawdown risk.

For prediction markets, quarter-Kelly is a reasonable starting point for most traders. As you accumulate a track record and can verify that your probability estimates are well-calibrated, you might move toward half-Kelly on your highest-conviction positions.

A useful rule of thumb: never bet more than 10% of your bankroll on a single prediction market position, regardless of what Kelly says. Markets can move against you before resolution, and the psychological cost of large losses distorts future decision-making.

Kelly gets more complex when you're running multiple positions simultaneously — which is the normal state for an active prediction market trader.

The simple approximation: sum your individual Kelly fractions and check whether the total exceeds 100%. If it does, scale all positions proportionally until the total is 100%. This is suboptimal mathematically but practically sensible.

A better approach for correlated positions: group correlated bets (e.g., all election markets that are correlated to the same political environment) and treat them as a single Kelly bet. Apply Kelly to the combined position, then allocate within the group based on relative conviction.

The working rule: if your correlated positions could all resolve against you on the same night (election night, Fed meeting, etc.), their combined Kelly fraction should not exceed 20-25% of your bankroll.

One of Kelly's most useful applications is telling you not to bet at all. If your probability estimate is not significantly higher than the market's implied probability, the Kelly fraction is zero or negative — meaning no bet.

If you think an event has a 65% probability and the market prices it at 62%, the Kelly fraction is approximately: (0.65 × 38/62 - 0.35) / (38/62) ≈ 3.5%. After adjusting for your estimation error (say you're typically ±7% accurate), your real Kelly fraction is likely negative.

This is the discipline that separates profitable traders from recreational bettors. You don't need to have a position on every market. The best trade is often no trade — when your edge is too small to justify the risk after accounting for your own estimation uncertainty.