Trading Psychology · Intermediate · 5 min
Thinking in probabilities
You can calculate the expected value of a simple trading rule and explain why single trades say little about whether the rule works.
Seventy percent rain
A weather forecast says there is a 70% chance of rain, and the day stays dry. Was the forecast wrong? Not necessarily. Out of ten such days, three should stay dry.
Most people find this easy to accept for weather and hard to accept for their own trades. A losing trade feels like a mistake, a winning one like proof. Both reactions skip the most important question: what happens over many trades?
Lose more often, still positive
No trade outcome is certain. A trading rule does not predict the next trade. At best, it gives you a set of possible outcomes, each with a rough chance, based on how similar trades have played out before.
The tool for judging such a rule is the expected value: the average result per trade you would get over a large number of trades. For a simple rule with one size of win and one size of loss:
Expected value = chance of a win × average win − chance of a loss × average loss.
Results are often measured in R, the amount risked on a trade. A loss of the full risk is −1R, a win of twice the risk is +2R.
Take a fictional rule that wins 40% of the time with +2R and loses 60% of the time with −1R:
- 0.4 × 2 = 0.8
- 0.6 × 1 = 0.6
- Expected value = 0.8 − 0.6 = +0.2R per trade, before costs.
This rule loses more often than it wins, and it is still positive on average. The reverse is also possible: a rule that wins 80% of the time can be negative if its few losses are large enough.
Two consequences follow. First, a single trade tells you almost nothing about a rule. Second, losing streaks are built in. With a 60% chance of losing, four losses in a row have a chance of about 13% at any given point. Over hundreds of trades, they are almost certain to happen.
Twelve wins, eighteen losses
Here is a fictional series of 30 trades from the rule above, risking 1% of a 10,000 account each time.
- 12 trades win +2R, 18 lose −1R. That is a total of +6R, exactly what the expected value of +0.2R per trade predicts.
- Along the way, the balance drops by about 4% from its high, after a run of losses.
- At the end, the account stands at 10,584.
A trader judging the rule after trades 6, 7 and 8, three losses in a row, might have dropped it. A trader judging it after trades 14 and 15, two wins in a row, might have doubled the size. Both would have reacted to noise.
Real results will never match the expected value this neatly. Thirty trades is still a small sample, and costs reduce the result.
Common mistakes
- "This trade will work." You can only know the chances, never the next outcome.
- Judging a rule after a few trades. Small samples swing widely by chance.
- Looking only at the win rate. Without the size of wins and losses, it says nothing about profit.
- Expecting a win after losses. Past trades do not change the chance of the next one.
The takeaway
Each trade is one draw from many possible outcomes. Only many trades show what a rule is really worth.
Check yourself
Quick quiz
4 questions. Instant feedback, nothing is saved.
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1Tap the largest drop in this series of trades.
Tap the chart.
Even a rule that gains over time has stretches where it loses. Drops like this are part of the distribution, not proof that it stopped working.
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2A rule wins 40% of the time with a gain of 2R and loses 60% of the time with a loss of 1R. What is its expected value per trade?
0.4 × 2 − 0.6 × 1 = 0.8 − 0.6 = +0.2R per trade, before costs.
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3The same rule loses four trades in a row. What does that tell you?
With a 60% chance of losing, four losses in a row have a chance of about 13% at any given point, so they happen regularly.
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4Which statement shows probabilistic thinking?
Probabilistic thinking talks about frequencies over many cases, not certainty about one trade.
of 4 correct.