What Is the Kelly Criterion?

In short. The Kelly criterion is a formula for the fraction of capital to risk on each bet or trade that maximizes long-run account growth, given a known win rate and payoff. For trading, it is usually written as f = W − (1 − W) / R, where W is the win rate and R is the average win divided by the average loss. Its weakness is the inputs: full Kelly assumes your edge is known exactly, so most traders who use it treat it as a ceiling and size far below it.

Most risk rules for traders start from a fixed number, such as risking 1% of the account per trade. The Kelly criterion starts from the other end. It asks what fraction of capital, given your actual statistics, would grow the account fastest over many trades, and then lets the answer be whatever the math says. That answer is often surprisingly large, and understanding why is the most useful part of learning the formula.

What the Kelly criterion is

The formula comes from John L. Kelly Jr., a researcher at Bell Labs, who published "A New Interpretation of Information Rate" in the Bell System Technical Journal in July 1956. The paper was about information theory, not markets: it showed how a gambler with an informative signal could size bets to grow capital at the fastest possible rate.

Edward O. Thorp later applied the idea to blackjack card counting and then to securities. In his paper on the Kelly criterion in blackjack, sports betting and the stock market, he describes it as maximizing the expected value of the logarithm of wealth, an approach also known as the growth-optimal or geometric-mean strategy. In plain terms: Kelly sizing ignores the average result of a single trade and optimizes the compounded result of a long series of them.

The Kelly formula for trading

For a trade with two outcomes, a win of R times the amount risked or a loss of the amount risked, the Kelly fraction is:

f = W − (1 − W) / R

• f: the fraction of the account to risk on the trade, meaning the amount lost if the stop is hit, not the size of the position.
• W: the win rate, as a decimal (45% = 0.45).
• R: the payoff ratio, average win divided by average loss, which is the same as the average winning R-multiple when losses are close to 1R.

The first point matters more than it looks. A Kelly result of 10% does not mean a position worth 10% of the account. It means a stop placed so that a loss costs 10% of the account. The position itself is then calculated from the stop distance, exactly as in standard position sizing.

All figures are our own calculations from the formula. Two things stand out. First, a strategy with zero expectancy gets a Kelly fraction of zero, and a negative result means the formula says not to take the trade at all. Second, perfectly ordinary statistics produce full Kelly sizes of 10-20% per trade, many times larger than the 0.5-2% that most risk rules allow.

Why full Kelly is too aggressive for most traders

Leonard MacLean, Edward Thorp and William Ziemba summarize the trade-off in their review of the good and bad properties of the Kelly criterion. The main advantage is that it maximizes the long-run growth rate of wealth. The main disadvantage is that the suggested bets can be very large, so Kelly can be very risky in the short term.

The table below uses the 45% win rate and 2.0 payoff ratio from above, where full Kelly is 17.5%. It compares long-run growth per trade with the drawdown from five losses in a row, which is far from rare: at a 45% win rate, a run of five or more losses appears in about 92% of 100-trade sequences, assuming independent trades.

These are our own calculations for this example, not data from real accounts. The pattern matches the research: half Kelly keeps roughly three quarters of the growth while cutting the drawdown sharply. MacLean, Thorp and Ziemba reproduce a blackjack example in which the chance of doubling a bankroll before halving it rises from about 0.67 at full Kelly to about 0.89 at half Kelly, with relative growth of about 0.75.

The asymmetry runs the other way above Kelly. Betting more than the Kelly fraction adds risk and lowers growth at the same time. The same paper notes that for processes close to continuous time, betting twice the Kelly amount brings growth down to about the risk-free rate, meaning no extra growth for all the added risk. In the example above, 2x Kelly (35% per trade) keeps only about 6% of the growth rate while five losses take the account down by about 88%.

The input problem: your edge is an estimate

Kelly assumes the win rate and payoff ratio are known. In trading they never are; they are estimates from a finite journal, and they drift as markets change. MacLean, Thorp and Ziemba stress that Kelly calculations are extremely sensitive to errors in the estimated mean return and recommend reducing bet size to stay on the safe side.

Sample size shows how wide the uncertainty is. The table below takes a measured win rate of 45% with a 2.0 payoff ratio and shows the range of one standard error around it:

Even with 200 trades, the "correct" Kelly size could plausibly be half or double another reasonable estimate, and this ignores any change in the payoff ratio. If the true win rate is 40% but the journal shows 45%, a trader sizing at the measured 17.5% is betting 1.75 times the true Kelly of 10%. In our calculation, that cuts the long-run growth rate roughly in half compared with sizing correctly, while exposing the account to much deeper drawdowns.

How traders use the Kelly criterion in practice

In practice, the Kelly criterion is more useful as a sanity check than as a sizing rule:

1. Measure the inputs on a real sample: win rate and payoff ratio from at least 100 closed trades taken under the same rules, after fees and slippage.
2. Calculate full Kelly: if the result is zero or negative, the problem is the strategy, not the size.
3. Take a fraction and apply a hard cap: the Kelly literature commonly discusses half and quarter Kelly; many traders go further and cap risk at the limit their account rules allow.
4. Recalculate on a schedule: update the inputs at a fixed review, not after a hot or cold streak.

The cap often matters more than the fraction. On a prop firm account with, for example, a 10% maximum loss limit, a single loss at full Kelly in the 17.5% example would end the account. In that setting, the useful reading of Kelly is the opposite of "bet more": if your fixed 1% risk is already far below a quarter of Kelly, the sizing is not what is holding back results. The broader framework for those limits is in our guide to risk management for traders.

Where the formula breaks down

The simple trading version of Kelly rests on assumptions that real trading rarely meets:

• Two fixed outcomes: real trades produce a spread of R-multiples, including partial wins and losses larger than 1R from gaps or slippage.
• Independent trades: correlated positions open at the same time act like one larger bet, so applying Kelly to each one separately overstates the safe size.
• A stable edge: win rates and payoffs change with market regimes, so last quarter's inputs may not describe next quarter.
• Unlimited time: Kelly's advantage is asymptotic. MacLean, Thorp and Ziemba point out that it can take a very long time for one strategy to reliably outperform another, and any strategy can have a poor result over a finite series.

None of this makes the formula useless. It means the output describes the best case for your statistics, and the real answer sits below it.

What to log so the inputs are real

A Kelly calculation is only as good as the journal behind it. The fields that matter are:

• Planned risk and actual result in R for every trade, so the payoff ratio comes from real exits, not targets.
• Fees and slippage, recorded separately, because they shrink the payoff ratio and with it the Kelly fraction.
• Setup or strategy tag, since two setups with different statistics have different Kelly fractions and should not be blended.
• Streak data, such as the maximum consecutive losses, to check the drawdown a given risk level would have produced.

This article is for educational purposes only and is not financial or investment advice. The formulas and examples are illustrative and are not recommended position sizes. Trading, especially with leverage, carries a high risk of losing some or all of your capital, and statistics from past trades do not guarantee future results.

A trading journal that records risk, R-multiple and setup on every trade, together with a performance dashboard that shows win rate and average win and loss over time, gives you the inputs a Kelly check needs from real data rather than memory.