Kelly Criterion Calculator
The Kelly criterion gives the fraction of capital that maximizes the long-run growth rate, calculated from a win rate and a payoff ratio. It is mathematically optimal for growth and produces drawdowns most people cannot sit through, which is why practitioners commonly trade a half or a quarter of it.
The optimal fraction, and the fraction people use
Defaults are a win rate of 55% with a payoff of 1.5 to 1, on a 10,000 account.
A negative answer is not a small position — it means the inputs describe a strategy with no edge, and the correct size is zero. The formula assumes your win rate and payoff are known rather than estimated, which is the assumption that fails first.
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Covered on this page: TradingView.
How the number is built
Two measured quantities produce one fraction. The formula asks how often you win and how much bigger a win is than a loss, and returns the share of capital that grows the account fastest.
f = W − (1 − W) ÷ R
where W is the win rate and R is the average win divided by the average loss.
Both inputs come from a record, not from an opinion. A win rate you feel is right is the single most common way this calculation goes wrong.
A worked example
Take the defaults: a win rate of 55% with a payoff of 1.5 to 1.
The loss rate is 45%, and 0.45 ÷ 1.5 = 0.30.
So f = 0.55 − 0.30 = 0.25 — twenty-five percent of the account.
On 10,000 that is 2,500 at risk on a single trade.
That figure is correct and almost nobody trades it. It is roughly twelve times the 2% most risk frameworks recommend, and the reason is not that the formula is wrong.
Why nobody uses the full number
Kelly maximizes the growth rate and says nothing about the path. Risking a quarter of the account per trade means a run of three losses removes more than half of it, and at the default win rate of 55% a run of three or more losses somewhere in a hundred trades is close to certain.
Half Kelly is the common compromise and the trade is favorable. Because the growth curve is flat near its peak, halving the fraction gives up roughly a quarter of the growth rate while cutting the volatility of the equity curve by about half.
Quarter Kelly gives up more growth again and is what a lot of professional risk management resembles in practice, without anybody calling it that.
The inputs are the weak point
The formula is exact and your inputs are estimates. Overstate the win rate by five points and the recommended fraction moves a long way, in the direction that hurts.
On the defaults, 55% and 1.5 gives 25%. At 50% and 1.5 it gives 16.67%. At 45% it gives 8.33%. A five-point error in one input changes the answer by a third.
And overestimating is the normal direction of error, because a strategy is usually measured on the sample that made you notice it.
A negative result is the most useful output the formula produces. It does not mean bet small in the other direction; it means the win rate and payoff you entered describe a losing strategy, and no position size fixes that.
What the formula ignores
Costs are subtracted from the edge, not from the result. Every trade pays the bid-ask spread — so a payoff measured before costs overstates the edge, and therefore the fraction.
It assumes losses are bounded at the size you chose. In a market that gaps, they are not, and the whole derivation rests on that assumption holding.
Reading it as a ceiling
The useful discipline is to compute Kelly and then check how far below it you are sitting. A strategy sized at 2% of the account against a Kelly figure of 25% is at eight percent of the optimum, which is a deliberately conservative place to be and a defensible one.
A position sized above half Kelly deserves a second look at the inputs rather than at the position. Either the edge is genuinely exceptional, or the win rate came from a sample small enough that the estimate is doing the work.
The original data
Of the 24,971 unique videos in the finance search study this site keeps, 2 have Kelly in the title, at a median of 96,269 views across 2 channels. Position sizing appears in 195 at 1,738, and only 33% of those titles are instruction-shaped.
Two videos at a 96,269 median against 195 position-sizing videos at 1,738. The formula that actually answers “how much” has almost no coverage, and the topic that does has fifty times less audience per video.
The question: The formula says twenty-five percent. Take it?
The answer is no, and the reason is not caution. Kelly is optimal for an infinitely repeated bet with known probabilities, and you have neither. Your win rate is an estimate from a finite sample and your payoff will change with conditions — so the honest use of the number is as a ceiling that tells you when you have gone too far, not as a target to reach.
When it fails
The case that ruins people is an edge that decays while the position size stays sized for it. The win rate was real when it was measured, conditions changed, and Kelly has no mechanism for noticing — it keeps returning a large fraction from stale inputs while the strategy quietly stops working. Sizing from a formula fed by history is only safe if the history is recalculated.
The second failure is estimating the win rate from a small sample. It takes hundreds of trades to distinguish a real edge from noise.
A third is using pre-cost figures. Costs come out of the edge first.
A fourth is treating a negative answer as a small position. It means zero.
A fifth is applying it to several correlated positions at once. They are one bet, not three.
And a sixth is trading full Kelly on borrowed conviction. The drawdowns are the reason.
Related
Position sizing is the practical alternative, where the stop sets the size. Expectancy is where the payoff input comes from. And risk of ruin is what the fraction is really being chosen against.
Treat this as a ceiling rather than a recommendation. Sizing well under half Kelly is probably reasonable; sizing anywhere near full Kelly means either something extraordinary has been found or, far more likely, the win rate has been overestimated. The second explanation is usually the right one.
— Michael Whitman
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