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Number of Occurrences

ES: Número de Ocurrencias PT: Número de Ocorrências

Why a strategy with positive expectancy needs repetitions before the edge shows up, and what that implies for the size of each position.

The problem it solves

A strategy can have positive mathematical expectancy and still produce a long losing streak. That is not a flaw in the strategy: it is the definition of randomness. If a trade wins 70% of the time, the probability of losing three in a row is 2.7%, which sounds negligible until you remember that across a hundred trades that event will occur several times. Number of occurrences is the explicit recognition of this fact: a strategy’s statistical edge only materialises in aggregate, and aggregate requires repetition. Someone trading five times a year with a 5% edge per trade is not exploiting that edge, they are submitting to noise.

La misma ventaja converge según el número de ocurrencias EV 1 – 25 operaciones domina el ruido 25 – 100 la señal empieza a verse 100 – 400 converge a la esperanza error estándar ∝ 1 / √n → para reducir la dispersión a la mitad hay que cuadruplicar las operaciones

The law of large numbers, in practice

The mathematical foundation is the law of large numbers: as the number of independent trials grows, the observed mean converges toward the theoretical expectancy. What matters to a trader is how fast it converges. The standard error of the mean decreases with the square root of the number of observations, which means that halving the dispersion of your result requires quadrupling your trades. At 25 trades, the band of plausible outcomes around your expectancy is still enormous; at 100 it narrows by half; at 400 to a quarter. That square-root relationship is why desks that live on a small edge trade often and small, rather than rarely and large.

Independence: the condition almost nobody meets

The law of large numbers requires trials to be independent, and that is where most portfolios fail. Selling twenty strangles on the same day across twenty different technology names is not twenty occurrences: in a market selloff they all move together and it is in practice one occurrence repeated twenty times. Correlation destroys statistical diversification without showing up in the count. To accumulate genuine occurrences you must spread across three dimensions at once: time — staggered entries across different weeks — underlying — sectors and asset classes with low correlation — and structure — not the entire book carrying the same Greek profile.

The direct consequence for position size

If the edge needs repetitions, each repetition must be small enough that no single one can prevent the next. This is the most important connection and the most ignored: number of occurrences and position sizing are the same problem seen from two sides. Risking 20% of the account per trade guarantees that a perfectly ordinary run of four losses leaves you without capital to keep trading, and at that point your strategy’s positive expectancy becomes irrelevant because you will never reach the aggregate where it shows up. The usual references — risking 1% to 3% of capital per trade, 5% at the very outside — do not come from a preference for caution but from the arithmetic of surviving long enough for the law of large numbers to work in your favour.

How to apply it when building a plan

Operationally the idea translates into three concrete decisions. First, define an evaluation horizon in trades, not months. A plan is not judged by "how March went" but by "how the last hundred trades went"; the calendar is an arbitrary unit that injects noise. Second, prefer expirations and structures that allow rotation. Tying capital up in a single twelve-month position produces one occurrence a year; the same capital in 30-to-45-day structures produces eight or ten. Third, log every trade with its thesis and outcome, because without a log there is no aggregate to evaluate — only memories, and memories are biased toward the recent and the painful.

Frequently Asked Questions

How many trades do I need to know whether my strategy works?
There is no magic number, but below 30–50 trades almost any result is compatible with chance, and below 100 the uncertainty about your true expectancy remains large. The smaller the edge you claim, the more sample you need: detecting a 20% edge takes few observations, detecting a 3% edge takes hundreds. And the sample only counts if the trades were reasonably independent of each other.
Doesn’t trading more frequently increase commissions and slippage?
Yes, and that is the real limit of the idea. Number of occurrences improves the statistical reliability of your edge, but every trade pays transaction costs. The correct conclusion is not "trade as much as you can" but "trade at the maximum frequency at which your edge remains positive after costs". If your gross expectancy per trade is $8 and the round trip costs you $6, you do not have a strategy — you have a donation to your broker.
How do I know whether my positions are genuinely independent?
Beta-weight the portfolio against a benchmark index and look at aggregate delta. If doing so reveals that your fifteen "diversified" positions add up to exposure equivalent to buying several hundred shares of the index, they are not diversified: you have one directional bet sliced into fifteen tickets. It is the fastest diagnostic available, and it is usually uncomfortable the first time.
Does this mean the analysis of each individual trade does not matter?
On the contrary: it matters because it determines the expectancy that later aggregates. What number of occurrences discards is the emotional expectation attached to any single trade — the feeling that this one in particular has to work out. Each trade should be selected with judgement and executed well; but once open, its individual result is noise, and treating it as decisive leads to managing it badly.
Does it apply equally to directional strategies and premium selling?
It applies to any strategy with a statistical edge, but it is especially critical in premium selling because the outcome distribution is asymmetric: many small wins and a few large losses. That shape requires more occurrences to converge than a symmetric distribution, and it punishes excessive size far more harshly, because the left tail that can appear at any moment is exactly what takes you out of the game.