The math of losing streaks

Nothing tests process thinking like a losing streak. The natural reading of six or eight losses in a row is "something is broken," and the natural response is to change something: the system, the size, the market. This lesson shows what streaks actually look like for a profitable system, so that when yours arrives you recognise it as weather rather than as a verdict.

The basic arithmetic

Take a system with a 45% win rate, which is a perfectly good win rate for a strategy with winners larger than losers. The probability of any single trade losing is 55%. Because trades are (roughly) independent, the probability of a specific sequence of eight consecutive losses is:

0.55⁸ ≈ 0.0084

About 0.8%, or one in 120. That sounds rare, and if you only ever took eight trades it would be.

Why streaks are more common than that

The 0.8% is the probability that a particular window of eight trades all lose. But a trader takes hundreds of trades, and a streak can start on any of them. The right question is: over a sample of N trades, what is the probability that at least one run of eight consecutive losses occurs somewhere?

That calculation is a little more involved, but the results for a 55% loss rate are:

Read the row for 200 trades, which is roughly a year for a trader taking one trade a day. A five-loss streak is essentially guaranteed. A six-loss streak happens in more than nine years out of ten. An eight-loss streak is a coin flip. A ten-loss streak has a one-in-five chance.

None of these streaks means the system has stopped working. They are what a 45% win rate looks like when it is working exactly as designed.

Key idea: At a 45% win rate, a streak of eight consecutive losses has roughly a 50% chance of appearing somewhere in 200 trades. It is not evidence that the system is broken. It is the system.

What the streak costs

Eight losses at 1R each, with 1R at 1% of the account, is a drawdown of about 7.7% (compounding slightly reduces it from a flat 8%). Unpleasant, recoverable, and well within what a positive-expectancy system earns back over the following fifty trades.

Eight losses at 3% each, which is where many under-capitalised traders actually sit, is a drawdown of over 21%. Recoverable in arithmetic, much harder in practice, because at −21% the trader is deep in the loss region of the value function and the cascade from Module 2 is waiting.

The streak is inevitable. Whether it is survivable is a sizing decision made before it arrives.

Higher and lower win rates

The table changes with win rate but the lesson does not.

• A 60% win-rate system (loss rate 40%) has about a 7% chance of an eight-loss run in 200 trades. Rarer, but a 60% system with small winners has other risks, and a five-loss run is still common.
• A 30% win-rate trend-following system (loss rate 70%) has a 98% chance of an eight-loss run in 200 trades and will see runs of twelve or fifteen. Trend followers who do not know this quit right before the trade that pays for the year.

Know your system's loss rate and compute your own table. The streak length you should expect at least once a year is your "normal" streak, and it should produce no reaction at all.

The trap in the middle of a streak

Streaks are dangerous less because of the money than because of what they do to judgement. Around loss five or six, three thoughts arrive:

"The system is broken." Possible, but the math says a six-loss streak is a normal event, so the streak alone is not evidence. The evidence would be a change in the A-trade expectancy over a full block of 50 to 100 trades. Check that, and if it is intact, the streak is noise.

"I should size down until it turns." This feels prudent and it is a form of fear tilt. If the streak is noise, sizing down means being small when the winners arrive, which is what turns a break-even stretch into a losing one. Sizing changes happen at the monthly review, based on blocks, never mid-streak.

"I should size up because a win is due." Gambler's fallacy. The eighth trade wins 45% of the time, exactly like the first.

The correct response to a streak inside the expected range is the boring one: same setups, same size, same rules, and the streak ends when it ends.

When a streak is a signal

A streak becomes evidence when it is outside the expected range for your sample size and the A-trade expectancy over the last full block has dropped. A ten-loss streak in a 60% system is a one-in-forty event; combined with a falling block expectancy, it justifies pausing and reviewing the strategy. A ten-loss streak in a 30% system is Tuesday.

Even then, the response is a review with the platform closed, not a change at the screen.

Try it: Find your system's win rate from your last 100 A-graded trades. Compute the probability of a single run of six, eight and ten losses (loss rate to the power of six, eight, ten). Then, from the table above, estimate how likely each is to appear somewhere in a year of your trading. Write the answer in the journal as "My normal worst streak is __ losses." When it arrives, you will already have met it.

Recap

• At a 45% win rate, any specific eight-trade window all losing has about a 0.8% probability, but over 200 trades an eight-loss streak somewhere has roughly a 50% chance.
• Five- and six-loss streaks are near-certain over a year for most systems; ten-loss streaks are common for low-win-rate trend systems.
• The cost of a streak is set by sizing decided beforehand: eight losses at 1% is under 8%, at 3% it is over 21%.
• Mid-streak thoughts ("it's broken," "size down until it turns," "a win is due") are all bias; the answer is same setups, same size, same rules.
• A streak is only evidence when it is outside the expected range and A-trade expectancy over a full block has dropped; review with the platform closed.