A 70% Win Rate Still Hands You 4 Losses In A Row, 43% Of The Time Over 100 Trades

4 losses in a row with a 70% win rate.

Your system didn't break. You just met math.

Over 100 trades, there is a 43% chance of at least one streak like that.

Why a streak feels like a signal

Four losses in a row feels like a pattern. It feels like something changed. So the instinct is to fix a rule, tighten a filter, or skip the next setup.

That instinct has a cost. If you change the rules in the middle of a sample, you delete the evidence you were collecting. Here is how to check whether the streak means anything before you touch a thing.

The three checks

Check one: find your real win rate over a decent sample. Count wins and trades from your journal. Use the whole record, not the last month. In the example below the win rate is 70%.

Check two: ask how often a streak this long happens by chance at that rate. For a 70% win rate and a run of 4 losses, the chance of at least one such run is:

20 trades: about 10%

50 trades: 24%

100 trades: 43%

200 trades: 68%

Shortcut for a different win rate or streak length (calculator or spreadsheet):

Count the places a streak could start: trades minus streak length plus 1.

Multiply by (loss rate to the power of streak length) and then by the win rate. That is the expected number of streaks.

Chance of at least one is 1 minus e to the power of minus that number (EXP in a spreadsheet).

At 70% over 100 trades and a run of 4: 97 starting points, times 0.3 to the 4th power (0.0081), times 0.7, gives about 0.55. One minus e to the minus 0.55 is about 42%. The exact figure is 43%.

Check three: decide what counts as unusual before it happens. At a 70% win rate over 100 trades, the chance of at least one run of 4 is 43%, of 5 is 15%, of 6 is 4.8%, of 7 is 1.4% and of 8 is 0.4%. Pick the line you would call surprising, for example anything under 5%, and write it down now, while you are calm. At 70% over 100 trades that line is 6 in a row. Anything shorter is inside what chance produces. Anything longer is a reason to go and read the trades one by one. It is still not a verdict.

A worked example (hypothetical numbers)

Hypothetical journal: 50 trades, 35 wins, so a 70% win rate. Trades 41 to 44 are four losses in a row.

It feels like the strategy died. The check says that over 50 trades at 70%, there is a 24% chance of at least one run of 4 losses. That is about one journal in four. Nothing here is unusual.

Now suppose the rules get changed after trade 44. The next 50 trades are evidence about a different system, and the first 44 can no longer be compared to them. You will not find out whether the original rules worked, because you stopped the test at the first uncomfortable stretch.

Three honest limits

The win rate is an estimate. 35 wins in 50 trades means the true rate could plausibly sit anywhere from about 56% to 81% (95% interval). If it is really 60%, a run of 4 losses in 50 trades has a 54% chance. If it is really 75%, 13%. At 200 trades the same 70% narrows to about 63% to 76%. A bigger sample tightens the check. It never makes it exact.

It assumes the trades are independent. Five short puts on five correlated tech names in one week are closer to one trade than five. If they all lose, that is one loss counted five times, and the table does not apply to it. The streak is telling you about the concentration, not about your edge. Count correlated trades as one when you count win rate and streaks.

A normal streak does not prove the system works. The check only says whether this streak is common. A 70% win rate with losses larger than the wins can still lose money. Win rate and expectancy are different numbers.

After reading this, you can

Work out how often a losing streak of any length should show up at your own win rate, and set the length that would actually mean something before you are in the middle of one.

How many losses in a row before you change your rules, and did you set that number before or after the last streak?

Figures: my own calculation, run-length probabilities for independent trades at a 70% win rate, checked by simulation. The 56% to 81% and 63% to 76% ranges are 95% Wilson intervals. All journal numbers in the worked example are hypothetical.

Stop guessing. Start calculating.

Live to fight another day. 🤙

#options #tradingpsychology #riskmanagement #optionstrading