In this lesson
- understand why a high win rate does not mean profit
- calculate a strategy's expected value in R
- find out how long losing streaks are normal
"My strategy has a 70% win rate!" Sounds great. But without a second number it means nothing at all. This lesson is about telling whether a way of trading has any chance of working.
Two numbers, not one#
Every strategy is described by two numbers:
- the win rate – what percentage of trades end in profit,
- the average win and the average loss – in the R-multiples from the last lesson.
Only together do they give the expected value – how many R you make or lose on one trade on average:
Expected value = win rate × average win − loss rate × average loss
Two examples#
Strategy A: a 40% win rate, wins of +2R, losses of −1R. 0.4 × 2 − 0.6 × 1 = +0.2R per trade. Most trades end in a loss, and yet the strategy is positive on average.
Strategy B: a 70% win rate, wins of +0.4R, losses of −1R. 0.7 × 0.4 − 0.3 × 1 = −0.02R per trade. Seven trades out of ten work out – and you still lose in the long run.
And that is before costs. If fees and slippage cost, say, 0.1R per trade, strategy A makes +0.1R and strategy B ends at −0.12R.
A positive expected value is rare
The numbers above are an example of the calculation, not a promise. Most people who trade do not have a positive expected value after costs – that is why most of them lose. Finding out whether you have one takes a long time and costs money.
Losing streaks are normal#
Even a strategy with a positive expected value has long losing streaks. With a 40% win rate over 100 trades:
- 5 losses in a row happen almost certainly (in 98% of cases in a simulation),
- 8 losses in a row in roughly every second case,
- 10 losses in a row in roughly every fifth.
That is why you risk 1% and not 10%. And that is why a streak of five losses on its own does not mean the strategy does not work.
How many trades you need#
After ten trades you know nothing – luck decided. After fifty you have a first idea. A more reliable picture comes from a hundred or more trades under the same rules. Anyone who changes strategy after every three losses will never find out whether any of them worked.
Common myths#
- "I win 7 out of 10, I am good." It depends on how much you win and how much you lose.
- "Five losses in a row – the strategy is broken." With a 40% win rate that is common.
- "I am up for the month, it works." A month is too short to prove anything – it may have been luck.
Summary
- The win rate without the size of wins and losses says nothing.
- Expected value = win rate × average win − loss rate × average loss (in R).
- Costs reduce the expected value of every trade.
- Long losing streaks are normal; you only know something about a strategy after a hundred trades.