Win rate and expected value
Expected value combines win rate, average gain, and average loss into one number. Only that number tells you whether a strategy holds up.
Expected value answers the question: what does a trade earn me on average, if I do it a thousand times?
The math: win rate times average gain, minus loss rate times average loss. At a 40 percent win rate, a €300 average gain, and a €100 average loss, that's 120 minus 60, so plus €60 per trade.
Forty percent winners sounds like a bad rate, and it's still profitable here. That's the most important sentence in this lesson: being right and making money are two different things.
If expected value is negative, sticking with it doesn't help. Trading more often just accelerates the loss. That's why this calculation comes before any strategy, not after.
Formally, E = p · G − (1 − p) · L, with p the win rate, G the average gain, and L the average loss, each after costs. This expression is the only quantity that determines long-term viability. Win rate and ratio are merely its components.
Two biases matter when estimating from historical data. First, cost capture: spread, fees, and taxes reduce G and increase L, and are often underestimated in backtests. Second, sample size: the standard error of the estimated win rate only falls with the square root of the number of observations, which is why thirty trades don't allow a reliable statement about p.
A positive expected value guarantees no positive outcome over a finite period. Variance determines how long deviations can persist. That's why the combination of positive expected value and limited position size is necessary: the former provides the direction, the latter ensures you stay in long enough for it to assert itself.
Summary
- Expected value equals win rate times gain minus loss rate times loss.
- Being right and making money are two different things.
- Thirty trades tell you statistically nothing about your win rate.
Did you get it?
How is a trade's expected value calculated?
Win rate times average gain, minus loss rate times average loss, each after costs.
What happens with negative expected value if you trade more often?
The loss arrives faster. Frequency amplifies the sign.
Why aren't thirty trades a reliable basis?
Because the standard error of the estimate only falls with the square root of the number of observations.
Related
- Capital preservation before profitStage 2
- Overtrading and revenge tradingStage 2
- The trading journalStage 2