The formula
Expectancy combines how often you win with how much you win compared with how much you lose. Written in R, where 1R is the amount you risk on a trade:
Expectancy (R) = win rate × average win (R) − (1 − win rate) × 1R
A trader who wins 45% of trades with an average winner of 1.5R makes 0.45 × 1.5 − 0.55 × 1 = +0.125R per trade. Multiply by the risk per trade to get dollars: at $200 risk, that is $25 per trade on average.
| Win rate | 0.8R winners | 1R winners | 1.5R winners | 2R winners | 3R winners |
|---|---|---|---|---|---|
| 35% | -0.37R | -0.30R | -0.13R | +0.05R | +0.40R |
| 40% | -0.28R | -0.20R | +0.00R | +0.20R | +0.60R |
| 50% | -0.10R | +0.00R | +0.25R | +0.50R | +1.00R |
| 60% | +0.08R | +0.20R | +0.50R | +0.80R | +1.40R |
The table shows why win rate on its own tells you almost nothing. A 60% win rate with 0.8R winners and a 35% win rate with 2R winners have almost the same edge. The row you sit on is decided by your strategy; the column by how you manage exits. Most traders who "improve their win rate" by taking profit early simply move one column to the left.
From expectancy to a prop firm target
In a challenge, expectancy answers a practical question: how many trades will this edge need to reach the target? Divide the target by your dollar expectancy. The smaller the edge, the more trades you need, and the more trades you take, the more chances a losing streak has to reach the breach line first.
| Win rate / avg winner | Per trade | Per 100 trades | Trades to $3,000 |
|---|---|---|---|
| 40% / 2R | $50 | $5,000 | 60 trades |
| 45% / 1.5R | $31 | $3,125 | 96 trades |
| 50% / 1.2R | $25 | $2,500 | 121 trades |
| 55% / 1R | $25 | $2,500 | 120 trades |
| 60% / 0.8R | $20 | $2,000 | 151 trades |
Two traders with the same $25 per trade reach the target in about the same number of trades, but not with the same comfort. The 55% / 1R trader sees fewer long losing streaks than the 40% / 2R trader, so the same size is safer for the first. That is where risk of ruin comes in: expectancy tells you the direction, risk of ruin tells you whether you survive the trip.
How to measure yours
Use real trades, not backtest hopes, and at least 100 of them. Log each result in R, include commissions, and recompute monthly. A trading journal that calculates expectancy automatically, and feeds it into the simulator, removes the guesswork. Compare the figure with the table above, then check what win rate you need for the firm you plan to trade.
FAQ
What is a good expectancy for a prop firm trader?
Anything reliably above zero after costs is an edge. Many consistent traders sit around +0.1R to +0.3R per trade. What matters is that it holds over a large sample, at least 100 trades, not a good week.
Can I pass a challenge with positive expectancy and still fail?
Yes. Positive expectancy only means you win on average over many trades. If your size is too big for the drawdown, a normal losing streak can end the challenge before the edge shows.
Should I measure expectancy in dollars or in R?
In R. It lets you compare trades and accounts of any size, then convert to dollars by multiplying by your risk per trade.
Do commissions change expectancy?
Yes. Subtract average costs per trade from the result. For scalpers with small targets, commissions can turn a positive edge negative.