Key takeaway: The Kelly Criterion provides a mathematical framework to determine how much of your total funds should be allocated to each bet, accounting for your competitive advantage and the available odds. In prediction markets, it shields you from two critical pitfalls: wagering excessively (which can lead to total loss) and wagering insufficiently (which leaves potential gains unrealised).
The ability to determine appropriate position sizes separates successful market participants from those who deplete their capital. The Kelly Criterion — a mathematical approach created by John Kelly, a researcher at Bell Labs in 1956 — establishes the theoretically ideal stake amount for achieving the strongest possible returns over extended periods. This guide explains how to implement it within prediction markets.
The Kelly formula
For a binary prediction market (where outcomes are YES or NO), the Kelly fraction is calculated as:
f* = (p * b - q) / b
Where:
- f* = proportion of total funds to allocate
- p = your assessed likelihood of success
- q = likelihood of failure (calculated as 1 - p)
- b = net odds (return relative to stake). For a market share trading at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% probability that an event settles as YES. The current market quotation stands at 45 cents (suggesting the market assigns 45% probability).
- p = 0.60, q = 0.40
- b = (1 - 0.45) / 0.45 = 1.222
- f* = (0.60 * 1.222 - 0.40) / 1.222 = (0.733 - 0.40) / 1.222 = 0.272
The Kelly formula recommends allocating 27.2% of your capital. If your account holds $1,000, this translates to a $272 position in this particular trade.
Why full Kelly is dangerous
The Kelly formula operates under the assumption that you possess precise knowledge of your true probability — an assumption that rarely holds in practice. Misjudging your informational advantage results in excessive position sizing and potential ruin. Experienced market traders routinely employ fractional Kelly approaches:
- Half Kelly (f*/2): The standard choice among professionals. Surrenders roughly 25% of theoretical maximum returns while cutting volatility in half
- Quarter Kelly (f*/4): A more cautious strategy suitable when your probability estimates carry substantial uncertainty
- Capped Kelly: Establishes a ceiling of 5-10% of total capital per individual market, irrespective of what the Kelly calculation suggests
Applying Kelly to multi-market portfolios
When you maintain concurrent stakes across several prediction markets, each market's Kelly fraction requires recalibration. The aggregate of all Kelly fractions across your portfolio must remain at or below 1.0 (representing your entire bankroll). As a practical guideline, maintain cumulative positions below 50% of available capital, preserving liquidity for emerging opportunities.
When Kelly does not apply
The Kelly framework depends on your capacity to reliably estimate underlying probabilities. Multiple scenarios undermine this foundational requirement:
- Situations characterised by substantial unknowns (unprecedented circumstances lacking comparable historical data)
- Markets exhibiting interdependence (such as a presidential election and subsequent legislative composition, which are not independent outcomes)
- Markets where you possess no informational advantage relative to prevailing market consensus
Leverage PolyGram's integrated Kelly Criterion calculator to optimise your position sizing ahead of each transaction. The comprehensive risk management suite encompasses payoff visualisations and maximum drawdown assessments. Start trading on PolyGram →