In this guide
Key takeaway: The Kelly Criterion determines the optimal proportion of your capital to allocate to each bet, accounting for your edge and available odds. In prediction markets, it safeguards against two critical pitfalls: deploying excessive capital (jeopardising your entire stake) and deploying insufficient capital (forgoing potential gains).
How you allocate capital across trades separates successful market participants from those who deplete their funds. The Kelly Criterion — a mathematical framework established by John Kelly, a researcher at Bell Labs, in 1956 — calculates the theoretically optimal stake size for achieving maximum compound growth over time. This guide shows how to implement it within prediction markets.
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 assessed likelihood of success
- q = likelihood of failure (1 - p)
- b = net odds (payout / stake). For a prediction market share trading at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% probability that an outcome materialises. The current market quotation stands at 45 cents (suggesting a 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
According to Kelly, you should commit 27.2% of your capital. If your account holds $1,000, this translates to a $272 position in this market.
Why full Kelly is dangerous
The Kelly formula presumes you possess perfect knowledge of your true probability — a condition that never materialises in practice. Miscalculating your advantage by overestimating it produces severe overbetting and potential ruin. Experienced market participants consistently adopt fractional Kelly instead:
- Half Kelly (f*/2): The industry standard. Surrenders roughly 25% of theoretical growth but cuts volatility in half
- Quarter Kelly (f*/4): Prudent strategy when confidence in your edge remains limited
- Capped Kelly: Enforce a ceiling—never exceed 5-10% of total capital on any single market, irrespective of what Kelly prescribes
Applying Kelly to multi-market portfolios
Once you hold stakes across numerous prediction markets concurrently, the individual Kelly allocations require recalibration. The aggregate of all Kelly fractions must remain at or below 1.0 (your entire bankroll). In real-world trading, restrict cumulative exposure to 50% or less, preserving capital for emerging opportunities.
When Kelly does not apply
Kelly presupposes you can reliably quantify your true probability. Several contexts undermine this assumption:
- Outcomes surrounded by fundamental uncertainty (unprecedented scenarios lacking historical data)
- Interdependent markets (a presidential election and legislative control are statistically linked, not separate)
- Markets where you possess no informational advantage relative to prevailing market consensus
PolyGram offers an integrated Kelly Criterion calculator to determine position sizes before executing any trade. The analytics suite encompasses payoff visualisations and maximum drawdown metrics. Start trading on PolyGram →