One trade tells you very little about a strategy. Expectancy tells you what the strategy returns on average per trade, measured in units of the risk you take. Measured that way, the same numbers hold on a $10K Classic account and a $100K Direct one.
What you will learn
- How to express any trade result as an R multiple
- The win rate you need to break even at a given reward-to-risk ratio
- How to calculate expectancy from your own results
- What expectancy and losing streaks mean for a challenge target and floor
Measure every trade in R
R is the amount you planned to lose if your stop was hit. On a $10,000 Classic account risking 0.5% a trade, 1R is $50. A trade that makes $90 is +1.8R, a trade stopped out is -1R, and a trade you close early for a $20 loss is -0.4R.
R lets you compare trades across account sizes and risk levels. A 2R win is the same result whether 1R was $50 or $500.
The reward-to-risk ratio is the planned version of the same idea. With a 20-pip stop and a 40-pip target, the trade risks 1R to make 2R, written 1:2.
The break-even win rate
The break-even win rate is the share of trades you must win to finish flat, before costs. Work it out as 1 ÷ (1 + reward-to-risk):
- At 1:1 you need to win 50% of trades.
- At 1:1.5 you need 40%.
- At 1:2 you need 33.3%.
- At 1:3 you need 25%.
A bigger target lowers the win rate you need, but price reaches a distant target less often, so your actual win rate tends to fall as well. Trading costs push every break-even figure slightly higher.
Expectancy: the average result per trade
Expectancy combines how often you win with how much you win and lose:
Expectancy = (win rate × average win in R) minus (loss rate × average loss in R)
Strategy A wins 45% of its trades. The average win is 1.8R and the average loss is 1R. Expectancy is (0.45 × 1.8) minus (0.55 × 1), which is 0.81 minus 0.55, or +0.26R a trade. At $50 per R, that averages $13 a trade.
Strategy B wins 60% of its trades, with an average win of 0.6R and an average loss of 1R. Expectancy is 0.36 minus 0.40, or -0.04R. It wins more often than Strategy A and still loses over time.
Use the averages you actually achieved, from your journal, and not the targets you planned. Trades closed early, partial exits and costs all pull the real average win below the planned one. Lesson 7 shows how to record them. Judge expectancy over a decent sample, such as your last 50 trades, because ten trades can look good or bad by chance alone.
What expectancy means for a challenge target
Divide the target in R by your expectancy and you get the number of trades it takes on average.
On a $10,000 Classic account, the Phase 1 target is $800. At 0.5% risk, 1R is $50, so the target is 16R. At Strategy A's +0.26R a trade, that is about 62 trades on average. On a $10,000 Direct account the target is $1,000, or 20R, which comes to about 77 trades.
There is no time limit, so 62 trades is a perfectly workable number. Doubling your risk to 1% cuts it to about 31 trades, but it also halves the number of straight losses the floor allows, to 10 on Classic and 6 on Direct.
Plan for losing streaks
Expectancy is an average, and the real order of wins and losses swings around it, sometimes for a long stretch. Suppose Strategy A's trades are independent and each one wins 45% of the time. The chance that a given five trades all lose is 0.55 to the power of 5, about 5%. Over 100 trades, the chance of at least one run of five or more losses is about 92%, and of six or more about 73%, even though the strategy has a positive expectancy.
Size your trades so that a long streak fits inside your floor. At 0.5% risk, eight losses in a row cost $400 on a $10,000 account. That sits well inside the Classic floor, $1,000 below the start, and takes you two-thirds of the way to the Direct floor, $600 below it.
A loss also moves the target further away in R. If a Classic $10,000 account drops to $9,500, the Phase 1 target of $10,800 is now $1,300 away. That is 26R at $50, up from 16R, or about 100 trades at +0.26R where 62 would have done.
Check your understanding
1. A strategy wins 35% of its trades, with an average win of 2.5R and an average loss of 1R. What is its expectancy?
(0.35 × 2.5) minus (0.65 × 1) is 0.875 minus 0.65, which gives +0.225R a trade.
2. What win rate do you need to break even at 1:2.5?
1 ÷ 3.5, which is about 28.6%, before costs.
3. On a $25,000 Direct account at 0.5% risk, how many R is the target, and how many R away is the floor?
1R is $125. The 10% target is $2,500, which is 20R. The floor is $1,500 below the start, which is 12R.
Key points
- 1R is the amount you planned to risk. Record every result in R.
- Break-even win rate = 1 ÷ (1 + reward-to-risk), before costs.
- Expectancy = (win rate × average win) minus (loss rate × average loss), in R.
- A high win rate can still give a negative expectancy if the average win is small.
- Even with a positive expectancy, a run of five or six losses is likely over 100 trades at a 45% win rate, so size for it.
Next lesson: Stay inside the daily loss limit and the maximum loss
All trading is simulated. Rewards are based on performance and are not guaranteed.