Technical analysisModule 5, lesson 28 of 32
Expectancy, losing streaks and risk of ruin
How expectancy combines win rate and the size of wins and losses, how long losing streaks can be by chance, and how risk per trade drives the chance of ruin.
In this lesson
- Calculate expectancy from win rate, average win and average loss.
- Explain why a high win rate does not guarantee profits.
- Estimate how long losing streaks can be by chance.
- Explain how risk per trade affects drawdowns and the risk of ruin.
Builds on
- Risk/reward and position size per tradeExpectancy combines the risk/reward of trades with how often they win.
- Probability and expected valueExpectancy is the expected value of a trade, explained there.
On this page
In simple terms
Traders often judge a method by its win rate: the share of trades that make money. But win rate alone says little. What matters is how much you win when you win and how much you lose when you lose. Expectancy combines all three into the average result per trade.
This lesson also shows two uncomfortable facts: losing streaks are longer than most people expect, and the amount risked per trade decides whether a trader survives them.
Expectancy
expectancy per trade = (win rate × average win) − (loss rate × average loss)
It is the expected value of a trade. Calculate it after costs.
Worked example: Two made-up strategies
| Strategy X | Strategy Y | |
|---|---|---|
| Win rate | 40% | 70% |
| Average win | ₹9,000 | ₹2,000 |
| Average loss | ₹4,000 | ₹6,000 |
| Expectancy: win × avg win − loss × avg loss | 0.4 × 9,000 − 0.6 × 4,000 = +₹1,200 | 0.7 × 2,000 − 0.3 × 6,000 = −₹400 |
Strategy X loses more often than it wins, but makes money on average. Strategy Y wins most of the time, but loses money on average, because its occasional losses are large. Many traders prefer strategies like Y, because frequent small wins feel good, until the large losses arrive.
Strategies like Y often come from taking profits quickly and letting losses run, the opposite of the exit discipline in the entry and exit planning lesson.
Expectancy needs a large, honest sample
A win rate and average win and loss measured on 15 trades are mostly luck. Expectancy estimated from a small sample, or from a backtest full of the biases described in the backtesting module, can easily be positive by chance when the true figure is negative. Treat any expectancy as an estimate with wide uncertainty.
Losing streaks
Even a strategy with positive expectancy will have runs of losses. They are longer than intuition suggests.
Worked example: How long can a losing streak be?
Suppose each trade has a 60% chance of losing, independently of the others. A computer simulation of many sets of 100 trades shows, roughly:
| Chance of at least one streak of 6 or more losses in 100 trades | about 88% |
|---|---|
| Chance of at least one streak of 8 or more losses in 100 trades | about 50% |
| Typical longest losing streak in 100 trades | about 8 |
These are results of chance alone, with nothing wrong with the strategy. A trader who expects at most three or four losses in a row will abandon a working method, or raise their risk to "win it back", at exactly the wrong moment.
Risk per trade and drawdowns
A drawdown is a fall from a peak in capital. How deep a losing streak takes you depends on how much you risk per trade.
Worked example: Ten losses in a row at different risk levels
Each loss takes the stated percentage of current capital.
| At 1% per trade: 1 − 0.99^10 | about 9.6% drawdown |
|---|---|
| At 2% per trade: 1 − 0.98^10 | about 18.3% drawdown |
| At 5% per trade: 1 − 0.95^10 | about 40.1% drawdown |
Recovering from a 40% drawdown needs a gain of about 67%, as the loss recovery calculator shows.
Risk of ruin
Risk of ruin is the chance of losing so much capital that you cannot continue, or will not. It depends on expectancy, the variability of results, and risk per trade. Two points matter:
- With negative expectancy, ruin is only a matter of time, whatever the position size.
- With positive expectancy, high risk per trade can still cause ruin, because a normal losing streak can wipe out the capital before the edge has time to work.
That is why risk per trade is usually kept small, and why sizing matters as much as the method.
Why it matters
These calculations explain why so many traders lose money despite "winning most of the time", why losing streaks feel shocking, and why the size of each bet decides survival. They also show why SEBI's studies found most individual traders lost money over the periods studied: costs and small or negative edges, combined with large position sizes, are a dangerous mix, as the investing compared with trading lesson discusses.
Limitations
Real trades are not independent coin tosses: losses can cluster when market conditions change. Expectancy and win rates change over time and are uncertain. The streak and drawdown figures here come from simple models with made-up assumptions; real results can be worse.
Common mistakes
- Judging a strategy by win rate alone.
- Estimating expectancy from a handful of trades.
- Underestimating losing streaks.
- Raising risk per trade after losses to win them back.
Try it yourself
- From a journal or a list of paper trades, calculate win rate, average win and average loss after costs.
- Calculate expectancy per trade.
- Find the longest losing streak in your record, and work out the drawdown it would cause at 1%, 2% and 5% risk per trade.
- Write down the risk per trade that would let you survive a streak twice as long without abandoning the plan.
Key takeaways
- Expectancy is the average result per trade = win rate × average win − loss rate × average loss, after costs.
- A strategy that wins 70% of the time can still lose money if its losses are much larger than its wins.
- Losing streaks are longer than intuition suggests. With a 60% chance of losing each trade, a streak of eight or more losses somewhere in 100 trades happens about half the time.
- Risk per trade decides how deep drawdowns get. Ten losses in a row cost about 10% at 1% risk per trade, but about 40% at 5%.
- Risk of ruin, the chance of losing so much that you cannot continue, rises sharply with risk per trade, even when expectancy is positive.
Check your understanding
Try the numbers yourself
- Position size and risk/reward calculatorHow many shares can I hold so a stop-loss costs only what I planned?
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Terms used in this lesson
- Expectancy
- The average result per trade, equal to win rate times average win minus loss rate times average loss, after costs.
- Risk of ruin
- The chance of losing so much capital that a trader cannot, or will not, continue.
- Drawdown
- The fall in value of an investment or index from its most recent peak, usually expressed as a percentage.
- Expected value
- The average result of a decision if it could be repeated many times, found by weighting each outcome by its probability.
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This lesson is general education, not investment advice. Examples use made-up or clearly dated figures to explain ideas; they are not recommendations. Read the disclaimer.