Kelly Criterion for Prediction Market Position Sizing

Kelly Criterion is the mathematical formula that tells you how much of your bankroll to risk on each trade. Applied correctly, it maximizes long-term wealth growth. Applied incorrectly, it goes broke faster than betting your gut. This guide covers the practical application for prediction markets.

## The Formula

For a binary outcome (YES/NO market), Kelly says:

f* = (p × b - q) / b

Where: - f* = fraction of bankroll to bet - p = your estimated probability of winning - q = 1 - p (probability of losing) - b = net odds received on the win (payoff per $1 wagered)

For Polymarket, if YES is trading at $0.40 and you think true probability is 55%: - p = 0.55 - q = 0.45 - b = (1 - 0.40) / 0.40 = 1.50 (60-cent payout on 40-cent risk)

Plug in: f* = (0.55 × 1.50 - 0.45) / 1.50 = (0.825 - 0.45) / 1.50 = 0.25

Kelly says bet 25% of your bankroll on this trade. That's enormous — and exactly why no professional bettor uses full Kelly.

## Why Full Kelly Is Dangerous

Full Kelly maximizes expected long-term growth IF your probability estimate is exactly right. The catch: your estimate is never exactly right. It has uncertainty around it.

If you bet 25% of bankroll on a position you think has +15pp edge, and your estimate is actually off by 5pp (you think 55%, true is 50%), you've dramatically over-bet. A losing streak that should have been recoverable becomes catastrophic.

Mathematical detail: the "growth" curve from Kelly betting is highly asymmetric. Betting at 0.5× Kelly captures 75% of full-Kelly growth with 25% of the variance. Betting at 0.25× Kelly captures 44% of growth with 6% of the variance. The trade-off is enormous in your favor for going smaller.

## Half-Kelly: The Practical Default

Half-Kelly is what most quant traders actually use. From the example above:

- Full Kelly: 25% of bankroll - Half Kelly: 12.5% - Quarter Kelly: 6.25%

For a $1000 bankroll, half-Kelly on a strong +15pp edge is $125. Quarter-Kelly is $63. Both are aggressive but recoverable from a few losses.

Rule of thumb for prediction markets: - Strong edge (>10pp), high confidence: 5-8% of bankroll - Medium edge (5-10pp), reasonable confidence: 2-5% of bankroll - Marginal edge (3-5pp), low confidence: 1-2% of bankroll - Below 3pp edge: don't trade

For more on identifying genuine edge before sizing, see our guide on [how to find +EV markets on Polymarket](/blog/how-to-find-ev-markets-polymarket).

## When Kelly Breaks Down

Kelly assumes: - You know the true probability (you don't, you estimate it) - Outcomes are independent (often aren't in correlated markets) - You can replay infinitely (you can't — bankroll matters) - Bets are sized continuously (in reality, minimum order sizes matter)

For prediction markets, the biggest issue is your estimate's uncertainty. If your AI probability model has ±10pp variance around its estimates, full Kelly suicides because you'll dramatically over-bet on overconfident predictions.

The solution: shrink your edge estimate before computing Kelly. If your raw edge says 12pp, treat it as 6pp for sizing purposes. This naturally implements quarter-Kelly without needing to remember the math.

## Practical Workflow

For each potential trade:

**Step 1**: Compute your edge in percentage points (your prob - market prob).

**Step 2**: Halve it. Conservative estimate adjustment.

**Step 3**: Apply Kelly formula with the halved edge.

**Step 4**: Cap at 5% of bankroll regardless. No single trade ruins you.

**Step 5**: Round down to fit minimum order size.

Example: $5000 bankroll, market at $0.30, you estimate 45%. Edge = 15pp. Halved = 7.5pp.

f* = (0.45 × (0.70/0.30) - 0.55) / (0.70/0.30) = (0.45 × 2.33 - 0.55) / 2.33 = (1.05 - 0.55) / 2.33 = 0.214

Kelly says 21.4%. Halved already by adjusting probability. Cap at 5%: $250.

If minimum order is $1, you buy 833 shares of YES at $0.30. Total cost $250. Max payout if resolved YES: $833. Profit potential: $583.

## Sizing for Multiple Correlated Bets

If you have 10 open Polymarket positions, they're not independent. They might: - All resolve around the same event - Share underlying drivers (sentiment, news) - Have correlated price movements

True Kelly for correlated bets is complex. Pragmatic rule: never have more than 20% of bankroll in active positions total, regardless of individual Kelly recommendations. If 4 positions each say "bet 8%", scale them down so the total stays under 20%.

For copy-trading multiple whales, see our [whale tracking strategies guide](/blog/polymarket-whale-tracking-strategies) — same principle applies.

## When To Bet More Than Kelly Says

Almost never. The temptation to "double down" because you're confident is the path to ruin.

Legitimate exceptions: - You have professional-level edge you've validated over 500+ trades - The bet is small in absolute dollars (under 1% of your net worth) - You can afford to lose 100% of the position with no lifestyle change

For most retail traders, sizing below Kelly is correct. Survival beats theoretical max growth every time.

## What About Kelly for Continuous Outcomes?

Some Polymarket contracts have ranges (e.g., "Tweet count will be between X and Y"). Kelly extends to continuous distributions but the math gets messy. Practical approximation: break the outcome into discrete bins, apply binary Kelly to each bin you think is mispriced, sum the recommended position sizes.

For most retail traders, sticking to binary markets is simpler and clearer.

## Real-World Adjustments

Theoretical Kelly assumes: - Zero costs (Polymarket: zero trading fees, but gas if no Builder Program) - Perfect fills at quoted price (reality: slippage on illiquid markets) - Continuous re-balancing (impossible — minimum order sizes)

For each trade, subtract estimated costs from expected payout before computing Kelly. A 5pp edge that becomes 4pp after gas+slippage might still be worth trading at quarter-Kelly. A 5pp edge that becomes 2pp isn't.

For more on minimizing costs, our [gas fees and Builder Program guide](/blog/gas-fees-builder-program-polymarket) covers the setup.

## Position Sizing Calculator (Quick Reference)

Given bankroll B and edge e (in percentage points): - 3pp edge: bet 1% of B - 5pp edge: bet 2% of B - 7pp edge: bet 3% of B - 10pp edge: bet 5% of B (cap) - 15pp edge: bet 5% of B (cap, but verify edge twice) - 20pp+ edge: 5% of B and check your work — edge this big usually means you're missing something

These approximations include the half-Kelly adjustment plus a hard 5% cap. They work for typical prediction market situations without requiring on-the-fly math.

## Common Sizing Mistakes

**Doubling down after losses**: increases position size to "recover". Mathematically guarantees bankruptcy on a losing streak.

**Confidence-based sizing**: "I'm 90% sure" → bet bigger. Confidence is a feeling. Edge is a number.

**Recency bias**: After a few wins, increase size. After losses, decrease. This kills compounding — you bet less when winning, more when losing.

**Ignoring correlation**: 5 positions all on the same election are one position dressed up as five. Total exposure matters.

**Not adjusting for uncertainty**: If your model has high variance, your edge has high variance, and Kelly should be smaller.

## Bottom Line

Kelly Criterion isn't a magic formula. It's a framework for thinking about position sizing rigorously. Most retail traders skip this entirely — they size based on conviction or hunch. That's why most retail traders lose money over time.

Use half-Kelly or quarter-Kelly. Cap at 5% per trade. Never exceed 20% total exposure. Account for correlation. Adjust for your model's uncertainty.

The math is simple. The discipline is hard. The traders who survive long enough to get rich are the ones who size small enough to stay in the game during inevitable losing streaks.

For an end-to-end strategy that combines position sizing with edge identification, our [+EV trading guide](/blog/what-is-positive-ev-trading) walks through the full framework.