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R and expectancy: why your win rate means nothing
"I am right 70% of the time" says nothing at all. Profitability is set not by the share of wins but by the product of two numbers.
While results are measured in dollars, trades cannot be compared: one was $500, another $3000, and "plus a hundred" means something entirely different in each. You need a unit that is the same across all trades. That unit exists and is called R.
What R is
R is your risk in that particular trade — the one you set when entering. If you risked $50, then R = $50. A trade closed for $150 profit earned +3R. A trade stopped out lost −1R. Always −1R, whatever the sum: that is the whole point of the unit.
The same run in two measurements
In dollars: −40, +180, −55, +90, −45, +260, −50. Hard to read anything, the sizes differ. In R (risk was 1% throughout): −1, +3.5, −1, +1.8, −1, +5.2, −1. Now everything is visible: four losses at exactly −1R (so the stops worked) and three wins of 1.8, 3.5 and 5.2. Net +6.5R over seven trades. And that is comparable with any other period and any other account.
Why win rate is useless
Two systems. The first is right 70% of the time but takes +0.5R on a win and loses −1R on a loss. The second is right 35% of the time but takes +4R and loses −1R. The first sounds far better. Compute: the first gives 0.7×0.5 − 0.3×1 = +0.05R per trade; the second, 0.35×4 − 0.65×1 = +0.75R. The second is fifteen times more profitable while being wrong two times out of three.
Everything in R. The result is how many R you earn per SINGLE trade on average. Above zero the system is profitable; below zero it is not, however many correct entries it contains. This is the only number worth computing about your own trading.
What it takes to be profitable
| Avg win | Win rate needed | Comment |
|---|---|---|
| +1R | above 50% | hard: almost no margin |
| +2R | above 33% | the working zone |
| +3R | above 25% | you may be wrong three times in four |
| +5R | above 17% | rare entries, large moves |
Cutting winners and holding losers
The most widespread habit on the market, and it breaks expectancy precisely. Someone closes a win at +0.5R "before it is taken away" and holds a loss hoping it comes back, closing at −2R. Their win rate is excellent — say 65%. Compute: 0.65×0.5 − 0.35×2 = −0.375R per trade. They are right two times out of three and steadily lose money. No amount of analysis fixes this, because the problem is not in the analysis.
How many trades before you know anything
Expectancy is a statistical quantity, and over ten trades it means nothing: variance swamps any effect. The minimum for a rough estimate is forty to fifty trades; for a confident conclusion, a hundred. Everything you believe about your system after ten trades is an opinion about randomness, not about the system.
The trade journal in your account computes the result of every trade, so you can work out your expectancy by hand: add all results in R and divide by the number of trades. If you have no journal yet, run fifty trades in paper trading at constant risk and one appears by itself.
About the account and journalCompute your expectancy
Take your last fifty trades — your own or from paper trading. Convert each to R: divide the result by the risk that was set in it. Add them up and divide by fifty. That number says more about your trading than anything you believe about it. Separately, check that all losses are exactly −1R: if there are −2R and −3R among them, your stops are not working, and that must be fixed before anything else.
Win rate 40%, average win +2.5R, average loss −1R. Is the system profitable?
0.4 × 2.5 − 0.6 × 1 = 1.0 − 0.6 = +0.4R per trade. Yes, and noticeably so: a hundred trades give +40R. At 1% risk per trade that is +40% on the deposit — while being wrong six times out of ten.
Why can you not judge a system on its last ten trades?
Because on such a sample randomness outweighs the effect. A system with +0.4R expectancy easily shows a loss over ten trades, and a losing one shows a profit. You would be deciding about the system while looking at noise. Below forty trades there is nothing to conclude; a hundred is where confidence begins.