WhitmanTrading

Kelly Criterion Calculator

The Kelly criterion gives the fraction of capital that maximises 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.

Full Kelly fraction 25.00%
Half Kelly, which most people use 12.50%
Full Kelly in money 2500.00
Half Kelly in money 1250.00

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.

Runs entirely in your browser. Nothing you type is sent anywhere or stored.

How the number is built

A candlestick chart with a series of sized positions marked.
The fraction that maximises growth over many repetitions. Illustrative chart - not real market data.

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.

The first half of a price series with wins and losses marked.
Both inputs have to be measured, not estimated. Illustrative chart - not real market data.

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.

The second half of a price series with a position scaled to the account.
The answer is a share of capital, not a lot count. Illustrative chart - not real market data.

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

A candlestick series swinging violently across a range.
Full Kelly produces drawdowns almost nobody tolerates. Illustrative chart - not real market data.

Kelly maximises 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 this site’s shared series has direction runs averaging 2.01 bars with a longest run of 11 across 286 runs.

A section of the price series with a reduced position size.
Half Kelly is the size most practitioners actually trade. Illustrative chart - not real market data.

Half Kelly is the common compromise and the trade is favourable. 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

A window of price bars where an assumption proves wrong.
An overestimated win rate produces an oversized position. Illustrative chart - not real market data.

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 long-horizon candlestick view of a declining position.
A negative answer means the correct size is zero. Illustrative chart - not real market data.

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

A candlestick chart annotated with the round-trip cost of a switch.
Costs come out of the edge before the formula sees it. Illustrative chart - not real market data.

Costs are subtracted from the edge, not from the result. On this site’s shared series a round trip measures about 2% of the median bar range of 0.493 — so a payoff measured before costs overstates the edge, and therefore the fraction. The figures are in research/series-measurements.json.

A candlestick chart with a volume histogram beneath it.
It also assumes you can always get the fill you modelled. Illustrative chart - not real market data.

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 research/search-study-corpus.jsonl, 2 have an instruction-shaped title about the Kelly criterion, at a median of 96,269 views across 2 channels — and 0% are calculator-shaped. Risk of ruin appears in 2 at 23,415 and position sizing in 195 at 1,738. The counts come from site/rank_tools2.py, which deduplicates by video id.

A candlestick series with several gaps, the largest of them marked.
A gap breaks the assumption the derivation rests on. Illustrative chart - not real market data.

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.

A stretch of price bars cut short at a decision point.
The formula says twenty-five percent. Take it? Illustrative chart - not real market data.

The answer to the question on that chart 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.

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.

What I actually do

I treat this as a ceiling rather than a recommendation. If my sizing is well under half Kelly I am probably being reasonable; if it is anywhere near full Kelly I have either found something extraordinary or, far more likely, I have overestimated my win rate. The second explanation has been right every time I have checked.

— Michael Whitman

This page is educational, not financial advice. Test every idea on your own charts before risking money.