In this guide
Key takeaway: The Kelly Criterion determines the optimal percentage of your bankroll to wager by weighing your edge against the available odds. Within prediction markets, it guards against two critical pitfalls: staking excessively (courting financial ruin) and staking insufficiently (forfeiting potential gains).
The margin separating a successful trader from financial collapse often hinges on bet sizing discipline. Introduced by Bell Labs mathematician John Kelly in 1956, the Kelly Criterion is a formula that computes the theoretically ideal stake magnitude for optimising wealth expansion over time. Below is its application 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 bankroll 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 settles YES. The market quotes 45 cents (reflecting 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 formula recommends deploying 27.2% of your bankroll. If you hold $1,000, this translates to a $272 position.
Why full Kelly is dangerous
The Kelly formula presumes you possess perfect knowledge of your true probability — an assumption that rarely holds in practice. Misjudging your genuine advantage triggers severe overexposure. Seasoned professionals adopt fractional Kelly instead:
- Half Kelly (f*/2): The industry standard. Surrenders roughly 25% of theoretical growth whilst cutting volatility in half
- Quarter Kelly (f*/4): Prudent strategy when edge confidence is low
- Capped Kelly: Enforce a ceiling of 5-10% per market, overriding Kelly output if necessary
Applying Kelly to multi-market portfolios
Once you operate across several prediction markets concurrently, individual Kelly allocations require recalibration. The aggregate of all Kelly fractions must remain at or beneath 1.0 (your full capital). Practically speaking, restrict combined exposure to 50% so you retain dry powder for emerging opportunities.
When Kelly does not apply
The formula hinges on accurately estimating your true probability. Several circumstances undermine this assumption:
- Situations marked by extreme ambiguity (unprecedented scenarios lacking historical data)
- Interdependent markets (a presidential election and legislative control are not independent wagers)
- Markets where your analysis yields no advantage relative to prevailing consensus
Leverage PolyGram's integrated Kelly Criterion calculator to determine position sizing ahead of each trade. The analytics suite encompasses payoff visualisations and drawdown metrics as well. Start trading on PolyGram →