In this guide
Key takeaway: The Kelly Criterion is a mathematical framework that determines the optimal percentage of your total funds to allocate to each bet, taking into account your competitive advantage and the available odds. For those participating in prediction markets, this approach eliminates two critical pitfalls: deploying excessive capital (which threatens total loss) and deploying insufficient capital (which forgoes potential gains).
How you allocate capital across individual trades separates sustained profitability from financial collapse. The Kelly Criterion — a mathematical framework created by John Kelly, a scientist at Bell Labs, in 1956 — calculates the theoretically optimal allocation to maximise compound returns over time. This guide shows how to implement it within prediction markets.
The Kelly formula
In a binary prediction market (where you choose between YES or NO outcomes), the Kelly fraction follows this equation:
f* = (p * b - q) / b
The variables are defined as:
- f* = percentage of total bankroll to allocate
- p = your personal assessment of winning likelihood
- q = assessment of losing likelihood (calculated as 1 - p)
- b = net odds (return divided by initial investment). When buying a prediction market share at price c, then b = (1 - c) / c
Worked example
Suppose you assess a 60% likelihood that an event will resolve YES. The current market valuation stands at 45 cents (suggesting 45% likelihood according to market participants).
- 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, allocate 27.2% of your capital. If your total capital is $1,000, this equals a $272 position in this opportunity.
Why full Kelly is dangerous
The Kelly Criterion relies on the assumption that you can determine your true probability with precision — an assumption rarely met in practice. Miscalculating your actual advantage results in severe overallocation. Experienced market participants almost universally adopt fractional Kelly instead:
- Half Kelly (f*/2): The industry standard. Surrenders roughly 25% of theoretical maximum returns whilst cutting volatility in half
- Quarter Kelly (f*/4): A more cautious strategy when your probability estimates carry significant uncertainty
- Capped Kelly: Establish a ceiling (typically 5-10% of total capital) as the maximum allocation to any single market, overriding Kelly calculations if necessary
Applying Kelly to multi-market portfolios
When you maintain simultaneous stakes across numerous prediction markets, each market's individual Kelly allocation requires recalibration. The combined total of all allocations must remain at or below 1.0 (your entire bankroll). Practically speaking, restrict cumulative allocation to 50% or less, preserving capital for emerging opportunities.
When Kelly does not apply
The Kelly Criterion depends on reliable probability estimation. Several circumstances undermine this requirement:
- Situations characterised by radical uncertainty (unprecedented events lacking comparable historical data)
- Markets exhibiting statistical dependence (such as a presidential election and subsequent legislative control, which move together)
- Markets where you possess no analytical advantage relative to prevailing market consensus
PolyGram provides an integrated Kelly Criterion calculator for determining position sizes ahead of each transaction. The analytics suite encompasses payoff visualisations and maximum drawdown monitoring. Start trading on PolyGram →