Kelly Criterion Calculator

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula developed by John Kelly at Bell Labs in 1956. Originally created for optimizing telephone signal noise, it was quickly adopted by gamblers and later by professional traders and investors. The formula calculates the optimal percentage of capital to risk on each bet or trade to maximize long-term wealth growth.

The brilliance of Kelly is that it balances risk and reward optimally. Bet too little and you leave money on the table. Bet too much and you risk ruin. Kelly finds the mathematical sweet spot for compounding growth.

How to Use This Calculator

Enter your historical win rate percentage
Enter your average profit on winning trades
Enter your average loss on losing trades
Review Full, Half, and Quarter Kelly percentages
Check your Expected Value per trade

The Kelly Criterion Formula

Kelly Criterion Formula

Kelly % = W − ((1 − W) ÷ R)

W Win rate (wins ÷ total trades)

R Win/Loss ratio (avg win ÷ avg loss)

Half Kelly Divide result by 2 for safety

Why Use Half Kelly?

While full Kelly maximizes theoretical growth, most professional traders use half Kelly (50% of the full Kelly percentage) because:

Reduces portfolio volatility and drawdowns by 50%
Still achieves 75% of full Kelly's growth rate
More forgiving of estimation errors in win rate
Provides psychological comfort during losing streaks
Real-world win rates are harder to estimate than theoretical

Expected Value and Edge

The Expected Value (EV) shown in this calculator represents your average profit per trade. A positive EV indicates you have an edge over the market. Remember: Kelly only works when you have a genuine edge. Without positive expected value, no position sizing strategy can make a losing strategy profitable.

Frequently Asked Questions

What if Kelly gives a negative number?

A negative Kelly means you have no edge - your expected value is negative. You should not take this trade. Either pass on it entirely or work to improve your strategy until you have a positive edge before risking capital.

Can Kelly be over 100%?

Mathematically yes, which would suggest using leverage. However, this is extremely risky and not recommended. Most professional traders cap Kelly at 20-25% maximum regardless of what the formula suggests, as real-world outcomes have more variance than theory predicts.

How accurate does my win rate need to be?

Kelly is very sensitive to win rate estimates. Small errors in win rate can lead to significantly wrong position sizes. Use at least 30-50 trades of data for estimation, and consider using half or quarter Kelly to provide a margin of safety for estimation errors.

Should I use Full, Half, or Quarter Kelly?

Half Kelly is the most popular choice among professionals. It provides 75% of full Kelly's growth with 50% less volatility. Quarter Kelly is even more conservative, suitable for uncertain edges or risk-averse traders. Full Kelly is rarely used due to extreme volatility.

Does Kelly work for investing, not just trading?

Yes, Kelly principles apply to investing too, though the inputs are different. For long-term investing, you'd estimate expected return and volatility rather than win rate and win/loss ratio. Many legendary investors like Warren Buffett and Charlie Munger have advocated Kelly-inspired concentration.