In this guide
Key takeaway: The Kelly Criterion determines the optimal proportion of your capital to allocate to each wager, accounting for your statistical advantage and available odds. In prediction markets, it guards against two critical pitfalls: wagering excessively (which jeopardises your entire stake) and wagering conservatively (which sacrifices potential returns).
How you allocate capital across trades separates sustained profitability from financial collapse. The Kelly Criterion — a mathematical framework introduced by John Kelly, a researcher at Bell Labs, in 1956 — delivers the theoretically optimal wager magnitude for achieving maximum compounded returns. This guide explains its practical application within prediction markets.
The Kelly formula
For a two-outcome 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 a successful outcome
- q = likelihood of an unsuccessful outcome (1 - p)
- b = net odds (return / investment). 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 as YES. The market quotes 45 cents (reflecting 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
The Kelly formula recommends committing 27.2% of your capital. If your account holds $1,000, you would deploy $272 on this position.
Why full Kelly is dangerous
The Kelly formula presupposes you possess exact knowledge of your true probability — a condition rarely met in practice. Miscalculating your edge upward results in excessive position sizing and potential ruin. Experienced market participants consistently employ fractional Kelly:
- Half Kelly (f*/2): The industry standard. Trades away roughly 25% of theoretical growth for a 50% reduction in portfolio swings
- Quarter Kelly (f*/4): A prudent approach when your edge assessment carries substantial uncertainty
- Capped Kelly: Establish an absolute ceiling — typically 5-10% of account balance — on any single market exposure, overriding Kelly's recommendation if necessary
Applying Kelly to multi-market portfolios
When you maintain concurrent stakes across several prediction markets, each market's individual Kelly fraction requires recalibration. The aggregate of all Kelly fractions must remain at or below 1.0 (your entire capital base). Practically speaking, maintain total deployed capital below 50% to preserve dry powder for emerging opportunities and unexpected market moves.
When Kelly does not apply
The Kelly framework relies on your capacity to estimate your true probability with reasonable accuracy. Several contexts undermine this assumption:
- Outcomes characterised by extreme novelty (unprecedented scenarios lacking historical data)
- Interconnected markets (such as political markets where election results and legislative control move in tandem)
- Markets where your analysis offers no genuine informational advantage relative to prevailing prices
Leverage PolyGram's integrated Kelly Criterion calculator to determine appropriate position sizes ahead of each transaction. The analytics suite encompasses payoff visualisations and maximum drawdown calculations. Start trading on PolyGram →