Kelly Criterion Position Calculator

How to use this tool

The Kelly criterion answers a precise question: in a repeated bet where the win rate is p and the net odds are b (you win b units for every 1 lost), what fraction of the bankroll should you risk per bet to maximise the long-run compound growth rate? The answer is f = (bp − q) / b, with q = 1 − p.

Concrete example: 100 backtested trades, win rate 55%, average win-to-loss ratio 1.5 (so b = 1.5). Plug it in: f = (1.5 × 0.55 − 0.45) / 1.5 = 0.25. The math says 25% of capital per trade is optimal — but that's the mathematical optimum, not the realised-trading optimum.

In live trading Kelly has three uncomfortable problems: (1) your estimates of p and b are always noisy; (2) crypto P/L isn't normally distributed and has fat tails; (3) full Kelly drawdowns are punishing (theoretical max drawdown above 60%). The practical rule is quarter-Kelly — roughly half the drawdown, about 75% of the long-run growth rate. This calculator flags quarter-Kelly as the recommended size.

The math behind it

p = win rate (0 ≤ p ≤ 1)
q = 1 − p = loss rate
b = net odds (win b units vs lose 1)

Expected value E = bp − q
Kelly fraction f = (bp − q) / b = E / b

When f ≤ 0, expected value is non-positive — don't take the trade.
When f > 1, math suggests leverage (not recommended in practice).

Half Kelly = 0.5 × f
Quarter Kelly = 0.25 × f

That's the binary-outcome Kelly. If your strategy returns are continuous (variable P/L per trade), there's a log-return maximisation variant — but for the vast majority of trend, grid, or arb strategies, binary Kelly is a good ceiling reference.

Common mistakes

"Full Kelly is optimal, so I should use full Kelly." Mathematically yes; in practice no. The formula assumes you know p and b exactly. Real p estimates can be off by 5–10 percentage points. Edward Thorp — the person who pioneered practical Kelly use — never went above half-Kelly himself.

"I feel like my win rate is 70%, so Kelly says 60%." Kelly is extremely sensitive to the win-rate input. "Feeling" isn't p. A sample under 100 trades barely produces a usable estimate. If your win rate hasn't been stress-tested by a real backtest, default to quarter-Kelly or lower.

"Kelly is all you need for position sizing." No. Kelly only answers "what's the maximum I should put on each trade". It doesn't answer "should I take this trade", "where do I stop", "how do I diversify". It's a ceiling, not a strategy.