What the Kelly criterion calculator does
The Kelly criterion, published by John Kelly at Bell Labs in 1956, gives the share of capital to stake on a repeated bet with a known edge so that the bankroll grows as fast as possible over the long run. In trading, the stake is what you lose if the stop-loss is hit: your risk per trade. The calculator turns your win rate and payoff ratio into the Kelly fraction, shows half and quarter Kelly beside it, and converts the fraction you choose into a risk per trade and a dollar amount, with an optional cap.
How to use it
- Enter your win rate in percent, taken from a journal or a backtest with a meaningful number of trades.
- Enter your average win and average loss in the same unit — dollars, pips or R. Only their ratio, the payoff ratio, matters.
- Enter your account balance and the maximum risk per trade you accept. The cap protects you when Kelly asks for more than you would ever risk.
- Choose the fraction of Kelly to apply: full, half or quarter.
The panel shows full, half and quarter Kelly, your suggested risk per trade after the cap, the amount in dollars, the share of the full-Kelly growth rate you keep, and the drawdown ten losses in a row would cause at that risk.
The formula
payoff ratio b = average win ÷ average loss
Kelly fraction f* = W − (1 − W) ÷ b
growth per trade g(f) = W × ln(1 + f × b) + (1 − W) × ln(1 − f)
W is the win rate as a decimal. f* is the risk per trade, as a share of equity, that maximises g(f), the expected logarithmic growth of the account per trade. If f* is zero or negative, the strategy has no edge on these numbers and Kelly says to stay out.
Worked example
A strategy wins 50% of the time and its average win is 1.5 times its average loss:
- Payoff ratio b = 1.5
- Full Kelly: f* = 0.50 − 0.50 ÷ 1.5 = 0.50 − 0.333 = 16.67% of equity per trade
- Half Kelly: 8.33%; quarter Kelly: 4.17%
- Expectancy: 0.5 × 1.5 − 0.5 = +0.25R per trade; break-even win rate 1 ÷ 2.5 = 40%
On a $10,000 account, half Kelly means risking $833 on the next trade. With a 2% cap, the suggested risk becomes $200. What each level keeps of the maximum growth rate, and what ten losses in a row would cost:
| Risk per trade | Share of full-Kelly growth | Drawdown after 10 straight losses |
|---|---|---|
| 16.67% (full Kelly) | 100% | 83.8% |
| 8.33% (half Kelly) | 75% | 58.1% |
| 4.17% (quarter Kelly) | 44% | 34.7% |
| 2% (cap) | 23% | 18.3% |
| 33.3% (double Kelly) | 0% | 98.3% |
At double Kelly the growth rate falls to zero: the account goes nowhere in the long run despite a positive edge, and anything above that shrinks it.
Why most traders use fractional Kelly
Full Kelly is growth-optimal only when its inputs are exact, and in trading they never are:
- Estimates are noisy. A win rate measured on 100 trades can easily be five to ten points away from the true one. Overestimate the edge and full Kelly becomes overbetting.
- The penalty is asymmetric. Half Kelly keeps about three quarters of the growth rate; double Kelly loses all of it. Erring on the small side costs little, erring on the large side costs a lot.
- Drawdowns are deep. In the classic continuous-time model, a full-Kelly bettor has a 50% chance of seeing the account halve at some point; at half Kelly that falls to 12.5%, at quarter Kelly to under 1%.
- Trades are not independent draws. Correlated positions, changing market regimes and losses beyond the stop (gaps, slippage) all make real risk larger than the formula sees.
This is why Kelly is best treated as an upper bound rather than a target. Many traders size from a fraction of it and cap the result, often somewhere between 0.5% and 2% per trade. See what your chosen risk does over a long series of trades with the risk of ruin calculator and the Monte Carlo trading simulator, then turn it into lots with the position size calculator.
Common mistakes
- Treating backtest numbers as exact. Costs, slippage and curve-fitting inflate a backtested edge. Feed Kelly conservative estimates, or the averages from a live journal.
- Mixing units. The average win and average loss must use the same unit, and the loss is entered as a positive number.
- Applying Kelly to each of several correlated trades. Three positions on the same theme behave like one large bet, so their combined risk should respect the fraction.
- Forgetting it is a share of current equity. After a loss the dollar risk shrinks with the account — that is part of the protection, not a mistake to correct.