What Is the Kelly Criterion? The Sizing Math, Honestly

The Kelly criterion is a formula for how much of your capital to commit to a bet, given an edge, in order to maximise the long-run growth rate of that capital. It comes out of information theory and gambling mathematics, and within its own assumptions it is provably optimal. It is also one of the most misunderstood tools in trading, because the assumptions are where all the danger lives.

The idea

There is a real trade-off in sizing. Bet too little of your capital on a genuine edge and you grow slower than you could. Bet too much and volatility eats your compounded return, because losses hurt geometric growth more than equivalent gains help it, and beyond a point you risk ruin outright. Between too-timid and too-aggressive there is a single fraction that maximises long-run growth, and the Kelly criterion is the formula that identifies it from your edge and your payoff.

Why full Kelly is more violent than it sounds

The growth-optimal fraction is aggressive. Sizing at full Kelly produces an equity curve with enormous swings, where drawdowns of half your capital are ordinary features of the path rather than rare accidents. The math is optimising the long-run growth rate and is completely indifferent to how uncomfortable the journey is. This is why practitioners who use Kelly at all almost always use a fraction of it, half-Kelly or less, deliberately giving up a little growth in exchange for a far smoother ride. The full-Kelly number is better understood as a ceiling than a target.

The assumption traders cannot satisfy

Kelly takes your true probability of winning and your true payoff as exact inputs. In a casino game those are known. In trading they are not: you have estimates drawn from a limited and noisy sample of past trades, and those estimates are usually optimistic, because the strategy was often chosen partly because it looked good on that very sample. Feed Kelly an overstated edge and it confidently instructs you to bet too much. This matters because the penalty is asymmetric: betting somewhat under Kelly costs you a little growth, while betting over Kelly degrades growth quickly and, far enough over, guarantees ruin. Since the normal error is to overestimate your own edge, the normal error also pushes you to the dangerous side of the curve.

Correlation breaks it further

Kelly assumes each bet is independent and repeated. Real trades are frequently correlated, and never more so than in a crash, when positions that looked separate all move together. Correlated bets sized as if they were independent stack far more risk than the formula accounts for, so the same number that is optimal for independent bets is an overbet for correlated ones.

What to actually take from it

The Kelly criterion is best treated as a way of thinking and an upper bound, not a dial you set your size to. Its most useful lesson is not the formula at all: it is that the cost of overbetting an edge you have overestimated is far worse than the cost of underbetting an edge that is real. Since almost everyone overestimates their edge, almost everyone's honest conclusion from Kelly is to size below what their assumed edge suggests. And the input that decides all of it, your true edge, is precisely the thing that has to be measured carefully rather than assumed, which is the whole point of our case study.