In this guide
Key takeaway: The Kelly Criterion calculates the optimal proportion of your capital to allocate to each trade, determined by your probabilistic advantage and the available odds. Within prediction markets, this formula eliminates two critical pitfalls: deploying excessive capital (which invites bankruptcy) and deploying insufficient capital (which squanders potential returns).
The margin between sustained profitability and financial collapse often hinges on position sizing discipline. The Kelly Criterion — a mathematical framework conceived by John Kelly, a researcher at Bell Labs, in 1956 — establishes the theoretically ideal stake magnitude for achieving maximum compound returns over time. This guide demonstrates its practical application within prediction markets.
The Kelly formula
For a binary prediction market (where outcomes resolve as either YES or NO), the Kelly fraction is expressed as:
f* = (p * b - q) / b
Where:
- f* = proportion of total capital to allocate
- p = your assessed likelihood of a successful outcome
- q = likelihood of an unsuccessful outcome (calculated as 1 - p)
- b = net odds (return divided by initial investment). For a prediction market share trading at price c, b = (1 - c) / c
Worked example
Suppose you assess a 60% probability that an event concludes YES. The prevailing market quotation stands at 45 cents (reflecting an implied 45% 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 total capital. If your account balance is $1,000, this translates to a $272 position in this particular trade.
Why full Kelly is dangerous
The Kelly formula presupposes that you possess perfect knowledge of your true winning probability — a condition that never materialises in practice. Miscalculating your informational edge upward produces severe overexposure. Experienced market participants consistently adopt fractional Kelly approaches instead:
- Half Kelly (f*/2): The industry standard. Surrenders roughly 25% of maximum growth but halves portfolio volatility
- Quarter Kelly (f*/4): A more cautious methodology suited to situations where your edge calculation carries substantial uncertainty
- Capped Kelly: Establishes an absolute ceiling — typically 5-10% of capital per individual market — irrespective of what the Kelly calculation suggests
Applying Kelly to multi-market portfolios
When you maintain concurrent stakes across several prediction markets, the individual Kelly percentages require modification. The aggregate of all Kelly percentages should remain at or below 1.0 (your entire capital base). Practically speaking, restrict cumulative capital deployment to 50% or less, preserving dry powder for emerging opportunities.
When Kelly does not apply
The Kelly formula relies on your capacity to estimate your genuine winning probability with reasonable accuracy. This assumption deteriorates under certain circumstances:
- Situations characterised by fundamental unpredictability (unprecedented events without comparable historical data)
- Markets exhibiting statistical dependence (such as a presidential election outcome and legislative chamber control, which are not autonomous events)
- Markets where your analysis provides no competitive advantage relative to existing market consensus
Leverage PolyGram's integrated Kelly Criterion calculator to determine appropriate position sizes prior to executing any trade. The analytical suite encompasses payoff visualisations and maximum drawdown metrics. Start trading on PolyGram →