Kelly criterion calculator for position sizing

How Kelly sizing works

The Kelly criterion answers one question: what fraction of a bankroll maximises its long-run growth rate, given a repeated bet with a known edge. It does not maximise expected profit — that answer is always to bet everything — and it does not minimise risk. It maximises the expected logarithm of wealth, which is the quantity that governs compounding, and that choice is what makes it useful and what makes it dangerous.

The formula

net odds       b = (1 − c) / c
full Kelly     f* = (p·b − (1 − p)) / b = (p − c) / (1 − c)
stake          k · f* · bankroll
expected value stake · (p − c) / c
log growth     g = p·ln(1 + f·b) + (1 − p)·ln(1 − f)
drawdown       P(wealth ever reaches α·W₀) ≈ α^(2/k − 1)

For a binary contract the formula simplifies pleasantly. Buy a share at price c that pays 1 if the outcome happens; the net odds are b = (1 − c)/c, and the general Kelly fraction collapses to (p − c)/(1 − c). The numerator is the raw edge in probability points. The denominator is what you lose per share if you are wrong. Written this way the behaviour is obvious: the same edge justifies a much larger stake at a high price than at a low one, because the downside per share is smaller.

That is also where the trouble starts. Full Kelly accepts a great deal of variance to buy the last increment of growth. Under the continuous-time approximation, a strategy sized at the full Kelly fraction has roughly an even chance of the bankroll halving at some point along the way, and a one-in-ten chance of reaching a tenth of where it started. Those are not tail scenarios; they are the ordinary behaviour of the strategy the formula recommends.

The second problem is worse and less discussed. Kelly assumes p is known. In a prediction market p is your estimate, and the size it recommends is very sensitive to it: because the recommended fraction moves faster than the edge, an estimate a few points too high produces a stake well above the true optimum. Overbetting and underbetting are not symmetric. Half the optimal size costs you a quarter of the growth rate; twice the optimal size costs you all of it. Uncertainty about p therefore argues for sizing down, always.

This is why fractional Kelly is the practical form. Under the standard quadratic approximation, applying a multiplier k scales the growth rate by k(2 − k), so half Kelly keeps about three quarters of the growth. The drawdown risk falls far faster: the chance of ever halving the bankroll drops from one in two to one in eight. That is not a close decision, and it is why full Kelly is mostly theoretical.

What the formula assumes

The formula also assumes bets are taken one at a time and resolve independently. Real books are neither. Several positions on correlated outcomes behave like one larger position, and sizing each one at its own Kelly fraction quietly builds a bet several times bigger than any of them. If your positions share a driver — the same election, the same macro print, the same token — the sizes here need to be reduced further, and the correct joint calculation is not this one.

There are prediction-market specifics the formula knows nothing about. Resolution can be ambiguous or disputed, so the payout is not always the binary the formula assumes. Liquidity is finite: the stake the calculator recommends may not be fillable at the price you entered, and filling it will move the price against you. Capital is locked until resolution, so a position that is right but slow has a cost the formula never sees.

Used properly, the output is an upper bound to argue with, not an instruction. If the recommended stake makes you uncomfortable, ask which input you do not believe — usually the probability.

Questions

Why is the recommended stake smaller than my intuition?

Usually because Kelly divides the edge by what you lose when you are wrong, and on a cheap contract that loss is nearly the whole stake. It is also because you probably applied a fraction below 1. The full-Kelly figure is shown beside the recommendation so you can see the gap the fraction created.

What fraction of Kelly should I use?

There is no single right answer, but the shape of the trade-off is clear: growth falls slowly as you size down, and drawdown risk falls quickly. Between a quarter and a half of full Kelly is where most practitioners settle. The less confidence you have in your probability estimate, the further down you should be.

Is the chance of halving a real prediction?

No. It is a continuous-time approximation that assumes the edge is real, constant, and repeated indefinitely with no fees. Its value is comparative: it tells you how much more drawdown one fraction accepts than another. Read the column, not the digit.

Can the calculator tell me whether my estimate is good?

It cannot, and that is the input everything depends on. Kelly takes your probability as given. If your estimates are systematically optimistic, the formula will faithfully convert that optimism into oversized positions.

Background

What this calculation is actually measuring

The calculator does the arithmetic. The guide explains the mechanism underneath it: where the number comes from, what has to be true for it to hold, and the point at which it stops describing the market in front of you. If you are going to act on a figure this page produced, that is the page to read first.