Expected value, losing streaks and decisions under uncertainty
A trade does not need to win most of the time to have positive expected value. It needs a payoff that compensates for its probability of loss, and position sizing that can withstand an unfavourable run.
Desk insight. A higher win rate can still produce a lower expected return. Payoffs and costs complete the calculation.
A prediction is a statement about one outcome: “the euro will rise this week”. A probability is a statement about a distribution: “this setup rises six times in ten, and the winners are twice the size of the losers”. The first invites pride. The second invites arithmetic.
The problem with predictions
A prediction makes every trade a test of whether you were right. Being wrong then feels personal, and people defend personal things.
That is where the damage starts. Stops are moved because the forecast “has not played out yet”. Losers are held because closing them would be an admission. Winners are cut early to lock in proof of being right.
A trader thinking in probabilities has nothing to defend. A loss was always one of the listed outcomes. It was priced in before the order was sent.
Expected value puts the payoff in context
The core idea fits on one line.
Expected value = (probability of winning x average win) - (probability of losing x average loss)
A positive estimate suggests an edge only if the inputs are reliable and costs are included. It does not guarantee a profit over a finite sample, and an edge can disappear when conditions change.
Two examples show why win rate alone misleads. Results are measured in R, where 1R is the amount risked per trade.
Expected value before trading costs
With the stated assumptions and before costs, Strategy A has positive expectancy despite losing more often. Strategy B has negative expectancy despite its higher win rate. Win rate alone cannot tell you which process is stronger.
One trade means almost nothing
A casino does not know whether the next hand will win. It does not care. It knows the edge, and it knows the number of hands will be large.
The result of a single trade is mostly noise. An edge only appears over dozens or hundreds of repetitions. This is why professionals standardise their setups. A hundred versions of the same bet can be measured. A hundred unrelated bets cannot.
Small position sizes help preserve capital through the sample needed to evaluate a strategy. They reduce the risk of ruin; they cannot guarantee survival or prove that an edge exists.
Losing streaks are part of the maths
Assuming independent trades and a constant 40 percent win rate, the chance that a specified block of five trades all lose is 0.6^5 = 7.776 percent, or about 8 percent. Across a hundred trades there are many opportunities for a losing run, but overlapping runs are not independent and several streaks are not guaranteed.
A trader who knows this in advance stays calm at loss number five. A trader who does not concludes the system is broken, abandons it, and starts another just before its own losing streak.
Desks size their risk around the streak they expect. If ten losses in a row is plausible, the risk per trade must be small enough to survive ten.
Scenarios instead of forecasts
Ask a macro trader what happens after a central bank meeting and you will rarely get one answer. You get a table.
Illustrative central bank scenarios
The numbers are illustrative. The trader then asks which outcome the market is underpricing. The trade may be on the 30 percent case, not the most likely one, because the payoff there is largest relative to its odds.
This is a strange idea at first. A good trade can be one you expect to lose more often than not.
Decisions and outcomes are different things
Poker players call it “resulting”: judging a decision by how it turned out. A reckless bet that wins is still reckless.
Professional reviews separate four cases.
Decision quality and outcomes
A good decision can lose, and a poor decision can win. Review rule adherence separately from the result, then revisit the strategy over a meaningful sample. A losing trade should not automatically trigger a rule change, but it should still be recorded and examined.
Updating as evidence arrives
Probabilities are not fixed at entry. New information changes them, and position size should follow.
If the reason for a trade weakens, a professional cuts the position before the stop is hit. If the evidence strengthens, the position may grow. The view is held loosely and revised often.
A predictor does the reverse. Evidence against the forecast is explained away, and evidence for it is collected.
Confidence is not a probability
Feeling 90 percent sure is not the same as being right nine times in ten. Most people who track their forecasts find their strong convictions are right far less often than they felt.
Keep score. Record probability estimates before outcomes are known, then compare similar estimates with observed frequencies. Fifty observations can begin a review; larger samples are needed for reliable calibration.
Putting it into practice
- Define each setup precisely enough that it can be counted.
- Record every trade in R, not in money.
- After thirty trades of one setup, begin an exploratory review of win rate, average win and average loss. Treat the sample as provisional and continue collecting data.
- Work out the expected value. If it is negative, stop trading that setup.
- Estimate plausible losing streaks and stress the account against worse ones. Size risk to preserve room for model error.
- Before each trade, list two or three scenarios with rough odds.
- Grade every trade on whether the rules were followed, separately from the result.
Key takeaway. Markets do not reward being right. They reward taking favourable bets repeatedly and surviving the unfavourable results in between.
The useful shift is from defending a forecast to managing a repeatable process. Losing outcomes belong inside that process from the start.
Part 5 of 15 in the series Institutional Trading. Next: The Difference Between Finding a Trade and Manufacturing One.
Independent educational commentary, not investment advice. References to firms do not imply affiliation or endorsement. Figures in examples illustrate a method, not a recommended allocation or a promised outcome. Trading leveraged products carries a high risk of loss.
