By Keel Research Team · Updated May 13, 2026
The Kelly criterion is a formula that computes the bet size — as a fraction of bankroll — that maximizes long-run logarithmic growth, given known win probability and win/loss ratio. Used right, it's the mathematical ceiling on aggression. Used naively, it's a great way to blow up an account.
John Kelly Jr. derived the formula in 1956 while working on signal transmission at Bell Labs. The question he was answering was essentially: given a noisy signal with known reliability, what fraction of your wealth should you bet on each outcome to maximize long-run wealth? Ed Thorp later popularized the result in markets — Kelly is the math behind blackjack card counting and a chunk of modern hedge-fund position sizing.
The intuition: bet too small and you leave growth on the table. Bet too big and a losing streak ruins you before edge has time to compound. Kelly threads the needle by setting bet size proportional to edge — bigger bets when you have bigger advantage, smaller bets (or none) when edge is marginal or negative.
For a binary outcome with known parameters:
f* = (b × p − q) / b
p = probability of winning
q = 1 − p
b = avg_win / avg_loss (positive)Worked example. A strategy backtest shows: win rate 55%, average win $150, average loss $100. Then p = 0.55, q = 0.45, b = 1.5. Full Kelly: f* = (1.5 × 0.55 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 = 0.25.
Kelly says bet 25% of bankroll per trade. That's aggressive — over 100 trades, the drawdown variance is enormous. Almost no professional trader actually bets full Kelly.
Full Kelly is growth-optimal under one critical assumption: you know p and b exactly. In real trading, both are estimated from finite samples with significant error. The estimation error compounds badly.
Consider two failure modes:
Half-Kelly addresses both: it captures roughly 75% of full-Kelly long-run growth at roughly 25% of the variance. The asymmetry is favorable — most of the upside, much less of the path pain. Quarter-Kelly is safer still and is the practical floor most traders observe.
Fixed-percent risk (e.g. always risk 1% of account per trade, computed via stop-distance) and Kelly sizing answer different questions:
Best practice: combine them. Use fixed-percent (0.5-1% risk per trade) as the default. Compute Kelly separately. Treat half-Kelly as a ceiling — never risk more than half-Kelly even if fixed-percent suggests a bigger position. This catches edge-aware downsizing in regimes where edge is uncertain.
The Kelly criterion calculator takes win probability, average win, and average loss, then computes full, three-quarter, half, and quarter Kelly fractions. Use Keel backtest results as inputs — every Keel backtest returns win rate, average win, average loss, and total trade count.
If you don't have a backtest yet, build a strategy in the Lab or fork one of the documented templates in the strategies library. The funding carry template includes win-rate data from a real 20-month backtest you can plug into Kelly directly.
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A formula that computes the bet size (as a fraction of bankroll) that maximizes long-run logarithmic growth, given known win probability and win/loss ratio. Developed by John Kelly Jr. in 1956; popularized in financial markets by Ed Thorp.
f* = (b × p − q) / b, where p = probability of winning, q = 1 − p, b = average_win / average_loss. The result f* is the fraction of bankroll to bet on each trade.
Kelly assumes you know p and b exactly. In real trading, both are estimated from finite samples with significant error. Overestimating edge by even 20% can make full Kelly catastrophically aggressive — drawdowns of 50%+ are realistic at full Kelly even with positive expected value. Half-Kelly captures about 75% of full-Kelly long-run growth at roughly 25% of the variance. Quarter-Kelly is safer still. Most professional traders bet between quarter and half.
It means the expected value of the trade is negative — the strategy as described loses money in expectation. Don't bet on it. Re-examine your win-rate and win/loss-ratio estimates. The Kelly math is mechanically suggesting you bet the other side, but practically it means: refine the strategy first.
Fixed-percent (e.g. "always risk 1% of account") is bankroll-relative but ignores the edge of the trade. Kelly is edge-aware — bigger bets when edge is bigger. In practice, Kelly is best used as a ceiling: never risk more than half-Kelly, and use fixed-percent as the default. The position-size calculator implements fixed-percent sizing; the Kelly calculator gives you the edge-aware ceiling.
Backtest your strategy on Keel — every backtest returns win rate, average win, average loss, total trades, and standard error of each metric. Multi-period sub-sample testing (run the strategy on rolling 6-month windows) helps estimate parameter stability before committing live capital at the Kelly-suggested size.
Compute Kelly fractions from win probability and win/loss ratio, with fractional-Kelly options.
Risk-based sizing — fixed % of account per trade. Pairs with Kelly as a complementary ceiling.
The risk metric that Kelly's drawdown variance directly affects.