In this guide
Key takeaway: The Kelly Criterion determines the optimal proportion of your capital to allocate to each bet, accounting for your statistical advantage and available odds. In prediction markets, this approach guards against two critical pitfalls: wagering excessively (risking total loss) and wagering conservatively (forgoing potential returns).
The ability to determine appropriate stake sizes separates consistently profitable market participants from those who deplete their capital. The Kelly Criterion — a mathematical framework developed by John Kelly, a researcher at Bell Labs, in 1956 — establishes the theoretically optimal wager magnitude for achieving sustainable wealth accumulation. This guide explains its implementation within prediction market contexts.
The Kelly formula
For a binary prediction market (YES/NO), the Kelly fraction is:
f* = (p * b - q) / b
Where:
- f* = proportion of capital to allocate
- p = your calculated likelihood of success
- q = likelihood of failure (1 - p)
- b = net odds (payout / stake). For a prediction market share at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% probability that an event concludes YES. The current market quotation stands at 45 cents (suggesting 45% implied 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 committing 27.2% of available funds. If your account holds $1,000, you would position $272 in this opportunity.
Why full Kelly is dangerous
The Kelly formula presupposes absolute certainty regarding your true probability — a condition that never materialises in practice. Miscalculating your genuine advantage produces severe overexposure. Seasoned market professionals adopt fractional Kelly strategies:
- Half Kelly (f*/2): The predominant choice among traders. Surrenders roughly 25% of theoretical maximum gains whilst cutting volatility in half
- Quarter Kelly (f*/4): Prudent methodology when your edge assessment carries substantial uncertainty
- Capped Kelly: Establish an upper limit of 5-10% per single market, overriding Kelly calculations when they exceed this threshold
Applying Kelly to multi-market portfolios
When maintaining concurrent stakes across numerous prediction markets, individual Kelly percentages require recalibration. The aggregate of all Kelly percentages must remain at or below 1.0 (representing your full capital). Realistically, maintain cumulative deployment beneath 50% to preserve capital for emerging opportunities.
When Kelly does not apply
The Kelly Criterion relies on your capacity to quantify your true probability with precision. Multiple circumstances undermine this assumption:
- Situations characterised by radical unpredictability (unprecedented circumstances lacking comparable historical data)
- Interdependent markets (such as a referendum outcome and subsequent legislative composition, which are not autonomous)
- Markets where your analytical perspective aligns with prevailing consensus forecasts
Leverage PolyGram's integrated Kelly Criterion calculator to calibrate position sizes prior to executing any trade. The analytical suite encompasses payoff visualisations and volatility measurement tools. Start trading on PolyGram →