Lessons › Advanced track › Expectancy: what a trade is worth on average

World 10 · Advanced track · lesson 6 · level 4

Expectancy: what a trade is worth on average

Expectancy tells you how much you make or lose per trade on average, and only a number that stays positive after costs is worth trading.

In one line

A 70% win rate that loses money, and a 40% win rate that makes it. How?

Explained simply

Expectancy is like working out a game's average score per turn. Winning often doesn't help if each win is tiny and each loss is huge. You multiply how often you win by how much you win, subtract how often you lose times how much you lose, and see whether the answer is above zero.

The lesson

Expectancy = (win rate x average win) - (loss rate x average loss), usually measured in R, the amount risked per trade. A strategy that wins 40% of the time with average wins of 2R and average losses of 1R has an expectancy of 0.4 x 2 - 0.6 x 1 = +0.2R per trade before costs. Costs and slippage must come out of it, and a small edge can disappear after them. Expectancy only means something over many trades, because a handful of trades is mostly luck.

A worked example

Illustrative example: Strategy A wins 40% at 2R and loses 60% at 1R: 0.4 x 2 - 0.6 x 1 = 0.2R per trade. Strategy B wins 70% at 0.3R and loses 30% at 1R: 0.7 x 0.3 - 0.3 x 1 = -0.09R. Strategy C wins 50% at 1R and loses 50% at 1R: 0.5 x 1 - 0.5 x 1 = 0R. Costs of 0.1R per trade turn A into 0.2 - 0.1 = 0.1R, so over 100 trades A's expected total is 100 x 0.1 = 10R. At a 3R reward, the break-even win rate is 1 / (1 + 3) = 0.25, or 25%.

The same idea at four levels

1. Beginner. Expectancy is your average result per trade over many trades.
2. Foundation. The formula is win rate x average win - loss rate x average loss.
3. Intermediate. Win rate alone misleads: 70% wins at 0.3R and 30% losses at 1R gives 0.7 x 0.3 - 0.3 x 1 = -0.09R per trade.
4. Advanced. Subtract costs per trade in R, since a +0.2R edge with 0.1R of costs is only +0.1R, and remember that the break-even win rate for a reward of R against a risk of 1 is 1 / (1 + R).
5. Expert. Multiply by the number of trades for the expected total and expect a wide band around it, like this lesson's strategy averaging +10R over 100 trades while totals from about -5R to +25R are common.

Mistakes to avoid

• Judging a strategy by its win rate alone.
• Trusting an expectancy worked out from a handful of trades.
• Forgetting to subtract costs and slippage from expectancy.

Goal of this lesson: Calculate expectancy in R and use it to compare strategies.