How long a normal losing streak is: the arithmetic nobody checks

The most expensive decisions in trading tend to be made during losing streaks, and most of them are made because the streak felt abnormal. It usually was not. The arithmetic of consecutive outcomes is unintuitive in a specific direction: runs are longer and more common than people expect, and the expectation gap is what triggers the size increase, the abandoned plan or the revenge trade.

How likely is a run of five losses?

Start with the simplest version. If outcomes are independent and the chance of a loss is q, the chance of five specific consecutive losses is q^5. At q = 0.5 that is 3.1%. That number is where most people stop, and it is the wrong number, because the question is not whether a specific five trades all lost — it is whether any run of five appears somewhere in a longer sequence.

Read the second row again. At an even hit rate, five straight losses somewhere in a hundred trades is the normal case, not the exception. At a 40% hit rate — perfectly workable with an asymmetric payoff — an eight-loss run is more likely than not within 100 trades. Anyone who trades for a year and does not experience this is the statistical anomaly.

Drawdown recovery is not symmetric

The second piece of arithmetic is the one that turns a streak into a structural problem. A percentage loss requires a larger percentage gain to return to the starting point, and the gap widens fast.

The third column is the honest defence. At 1% of equity per idea, the compounding of losses means it takes an implausible run to reach a 20% drawdown. At 5% per idea, the same 20% is roughly four or five losses — a run that the table above says will happen. Risk per trade is not a preference; it is the variable that decides whether a normal streak is an inconvenience or an account event.

Expectancy, and why hit rate alone says nothing

Expectancy per trade is (hit rate x average win) - (miss rate x average loss). A 35% hit rate with an average win three times the average loss produces a positive expectancy; a 70% hit rate with average losses four times the average win does not. Any discussion of a hit rate that omits the payoff ratio is missing the term that determines the sign.

• 35% hit rate, 3R average win, 1R average loss: 0.35 x 3 - 0.65 x 1 = +0.40R per trade.
• 70% hit rate, 1R average win, 4R average loss: 0.70 x 1 - 0.30 x 4 = -0.50R per trade.
• 50% hit rate, 1R win, 1R loss, minus 0.1R of costs: -0.10R per trade.

That third line is where most attention should go. A process with no edge and modest costs is not flat, it is negative, and it declines slowly enough to feel like bad luck for a long time. Costs belong in the expectancy calculation from the first trade, not as an afterthought.

How large a sample has to be

The uncomfortable part. The standard error on a proportion is roughly sqrt(p(1-p)/n). At p = 0.5, a sample of 30 trades has a standard error near 9 percentage points, which means a 95% interval spanning roughly 32% to 68%. A sample of 100 narrows it to about 40% to 60%. A sample of 400 gets to roughly 45% to 55%.

This is the reason a published record with a small denominator deserves scepticism regardless of what it says, and the reason any honest record prints its n next to every number. The same logic applies to your own results: a strong month is not evidence, and neither is a weak one. How to verify a trading track record works through what to demand before treating any published number as information.

What to do with this

1. Write down, before the streak, what run length would genuinely be abnormal for your hit rate. Use the first table.
2. Set risk per idea so that a run of that length is survivable without changing behaviour.
3. Record every outcome so the sample accumulates, using the structure in how to build a trading journal.
4. Judge the process on plan adherence and expectancy, not on the last five results.
5. Re-examine only when the evidence is a change in conditions, not a change in mood.

None of this makes a losing streak pleasant. It makes it expected, which is a different and more useful state to be in — a run you have already priced does not force a decision, and forced decisions are the ones that do lasting damage.