Kelly Criterion for Prediction Markets: Size Your Bets

Key takeaway: The Kelly Criterion determines the optimal proportion of your capital to wager, accounting for your probabilistic advantage and available odds. Within prediction markets, this framework guards against two critical pitfalls: deploying excessive capital (and facing potential ruin) or deploying insufficient capital (and forgoing achievable returns).

The margin between sustained profitability and financial collapse often hinges on proper position sizing. Introduced by John Kelly, a researcher at Bell Labs, in 1956, the Kelly Criterion is a mathematical framework for identifying the ideal stake magnitude to achieve maximum compounding returns over time. Below we explore its practical application in prediction markets.

The Kelly formula

For binary prediction markets (YES/NO outcomes), the Kelly fraction calculates as follows:

f* = (p * b - q) / b

Where:

f* = proportion of total capital to allocate to the wager
p = your assessed likelihood of a successful outcome
q = likelihood of an unsuccessful outcome (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 event concludes YES. The current market quotation stands at 45 cents (suggesting 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

According to Kelly, commit 27.2% of your capital. If your total capital is $1,000, this translates to a $272 position in this particular trade.

Why full Kelly is dangerous

The Kelly formula presupposes you can pinpoint your true probability with certainty — a condition rarely met in practice. Miscalculating your edge upward results in ruinously large positions. Experienced market participants nearly universally adopt fractional Kelly instead:

Half Kelly (f*/2): The predominant choice among professionals. Surrenders roughly 25% of theoretical maximum growth yet cuts volatility in half
Quarter Kelly (f*/4): A more cautious stance suited to situations where edge estimation carries substantial uncertainty
Capped Kelly: Establishes an absolute ceiling—typically 5-10% of total capital—for any single market position, overriding Kelly's calculation if necessary

Applying Kelly to multi-market portfolios

Once you hold concurrent stakes across numerous prediction markets, individual Kelly allocations require recalibration. The aggregate of all Kelly fractions must remain at or below 1.0 (your entire bankroll). Prudent practitioners maintain cumulative deployment beneath 50% to preserve liquidity for emerging opportunities.

When Kelly does not apply

Kelly's framework depends on reliable probability estimation. Several contexts undermine this assumption:

Situations characterised by extreme ambiguity (unprecedented scenarios lacking historical analogue)
Interdependent markets (such as a presidential election and legislative composition, which are not statistically independent)
Markets where you possess no informational superiority relative to prevailing market consensus

Leverage PolyGram's integrated Kelly Criterion calculator to calibrate position magnitude ahead of each transaction. The suite of risk management tools encompasses payoff visualisations and maximum drawdown assessments. Start trading on PolyGram →