Fractional Kelly — Definition | Polymarket Trade
Fractional Kelly is a scaled-down Kelly bet (e.g., half or quarter Kelly) that reduces variance and drawdown while maintaining positive expected value. It trades maximum theoretical growth for steadier, more stable returns.
In depth
Fractional Kelly refers to a conservative variant of the Kelly criterion, where instead of betting the full amount suggested by the Kelly formula, a trader bets a smaller fraction—most commonly one-half (half-Kelly) or one-quarter (quarter-Kelly). The core idea is simple: the Kelly criterion tells you the theoretically optimal bet size to maximize long-term wealth growth. But that optimality assumes you have infinite bankroll, perfect information, and can tolerate the volatility that comes with maximum growth. In practice, most traders and investors face constraints. Fractional Kelly scales down the bet size proportionally, reducing portfolio swings and drawdown magnitude while still leveraging positive expected value. If full Kelly suggests risking 10% of your bankroll on a trade, half-Kelly means risking 5%, and quarter-Kelly means 2.5%. The math is straightforward, but the psychological and practical benefits are profound.
The Kelly criterion itself was derived by J.L. Kelly Jr. in 1956 as a formula for optimal wagering in favorable games. In prediction markets, where traders have edge (better information, sharper models), Kelly provides a mathematically sound answer to the critical question: how much should I bet? However, Kelly's assumptions rarely hold perfectly. Markets move, correlations shift, and edge estimates contain error. Overconfidence in your models leads to overbetting—and if your estimate is even slightly wrong, full Kelly can lead to catastrophic losses. Fractional Kelly emerged as a practical compromise between theory and reality. It acknowledges that traders nearly always underestimate their uncertainty. By using half-Kelly or quarter-Kelly, a trader retains most of the growth benefit (half-Kelly gives roughly 75% of full Kelly's long-term growth, but with far less drawdown) while adding a substantial safety margin. In prediction markets like Polymarket, where markets can move 20-30% in hours and liquidity can dry up unexpectedly, fractional Kelly is far more common than full Kelly among professional traders.
On Polymarket, a trader who has done the analytical work to identify an edge—say, believing a market is mispriced and has 55% true probability when the market quote is 45%—must still decide position size. If the trader's model suggests risking 10% of bankroll on a full Kelly bet, they might instead risk 5% (half-Kelly) or even 2.5% (quarter-Kelly). This decision isn't about abandoning the trade; it's about prudent position sizing. Polymarket's order book depth can vary dramatically, and slippage on larger orders is real. A trader using fractional Kelly can enter and exit positions with less market impact, preserve capital for future opportunities, and sleep better knowing that even if their edge estimate is 30% off, they won't face a portfolio-crippling drawdown. Many sophisticated traders maintain a "Kelly profile"—a spreadsheet or mental model of their edge on markets they follow—and then apply a fractional multiplier (like 0.5 for half-Kelly) to all position sizes. This discipline, enforced consistently, separates traders who survive decades from those who blow up after one bad run.
One misconception is that fractional Kelly is "conservative" in the sense of being timid or suboptimal. In fact, given real-world estimation errors and market friction, fractional Kelly often outperforms full Kelly on a risk-adjusted basis over long periods. Another pitfall is using fractional Kelly inconsistently—applying it to some positions but not others, or changing the fraction based on recent wins or losses. This weakens the risk-management benefit. A third mistake is confusing fractional Kelly with simply "betting less." Kelly sizing is dynamic: if your edge grows (say, you gather stronger signal), your Kelly bet size should increase. Fractional Kelly means scaling that entire function down, not capping it at a fixed amount. Finally, some traders treat Kelly as gospel and ignore other constraints—like minimum viable order size on Polymarket, regulatory position limits, or correlation with other holdings. Kelly tells you the math-optimal bet, but you must layer in practical constraints and diversification to avoid concentration risk.
Understanding fractional Kelly requires familiarity with the Kelly criterion itself, which requires understanding edge and odds. You'll also encounter related ideas: the concept of drawdown (the peak-to-trough decline in your portfolio), which fractional Kelly specifically aims to minimize; optimal f, another bet-sizing method from trading literature; and position concentration, which fractional Kelly indirectly constrains by keeping position sizes smaller. In prediction markets, where markets can be illiquid and mispricings are often small (2-5% edges are excellent), fractional Kelly acts as a built-in guard against overconfidence. It lets you pursue your edge while acknowledging the uncertainty you face. Many of the most successful prediction-market traders use half-Kelly or quarter-Kelly as a standing discipline, not because they lack confidence, but because they understand that surviving for decades requires compounding slowly and avoiding catastrophic losses far more than it requires maximizing any single year's returns.
Example
Suppose a trader on Polymarket has a model estimating 55% true probability for a candidate when the market quotes 48%, suggesting a 7% edge. Full Kelly might recommend a $400 position from a $10,000 bankroll, but using half-Kelly, the trader places $200 instead. This smaller position still captures most of the expected profit if the model is correct, while cutting maximum drawdown in half if the estimate proves too optimistic.