The Kelly Criterion is a mathematical formula that calculates the percentage of capital you should risk on each trade to maximize long-term account growth. It was developed by John Kelly at Bell Labs in 1956, originally for signal processing, and later applied to gambling and investing by Ed Thorp. For traders, it answers: given my win rate and average R:R, what's the optimal bet size?

The Formula

Kelly % = W − [(1 − W) ÷ R]

Where:

  • W = Win rate (as a decimal — 0.55 for 55%)
  • R = Average win ÷ Average loss (the reward-to-risk ratio)

Example: Win rate 55%, average win/loss ratio 1.5 (risking $100 to make $150).

Kelly % = 0.55 − [(1 − 0.55) ÷ 1.5] = 0.55 − [0.45 ÷ 1.5] = 0.55 − 0.30 = 0.25 = 25%

The Kelly formula says risk 25% of your capital on each trade. Immediately, you should see why applying this directly would be catastrophically volatile. A single 25% loss leaves you with 75% of your capital. Three consecutive losses leave you with 42%. Even with a 55% win rate, the drawdowns at full Kelly are psychologically and financially ruinous for most traders.

Full Kelly vs Fractional Kelly

Professional traders almost never use full Kelly. The standard approach is to use a fraction:

  • Half Kelly (0.5×): Risk 12.5% in the example above. Roughly 75% of the long-term growth rate of full Kelly, but with about half the variance. The best balance for most systematic traders.
  • Quarter Kelly (0.25×): Risk 6.25%. Very conservative, suitable for strategies with high uncertainty in the edge estimate.
  • Fixed fraction (1–2%): What most discretionary traders use. Not mathematically derived from Kelly, but close to quarter-Kelly for many typical trading edges and far more psychologically manageable.

Why Fractional Kelly Is Better in Practice

Kelly assumes you know your exact win rate and R:R. In practice, both are estimates. Your win rate varies over time. Your R:R is an average of a distribution, not a fixed number. Errors in these inputs directly affect the Kelly output — and overestimating your edge at full Kelly leads to extreme overbetting.

Kelly also maximizes terminal wealth in the long run, which means it accepts very large short-term drawdowns as mathematically acceptable. For most real traders, a 40% drawdown — even on the path to superior long-run returns — will cause them to abandon the strategy. Fractional Kelly trades off some theoretical maximum return for a dramatically smoother equity curve.

When Kelly Is Useful

Even if you don't use Kelly as your position-sizing rule, it's valuable as a ceiling check: if your proposed risk per trade exceeds the Kelly fraction, you are mathematically overbetting your edge. A negative Kelly output (which occurs when R × W < 1 − W) signals that the strategy has no positive edge — you should not be trading it at any size.

Use the Kelly Criterion Calculator to check whether your current risk per trade is above or below what the Kelly formula recommends for your historical win rate and R:R.