Three numbers tell me most of what a list of trades can: payoff ratio, profit factor and expectancy. In the made-up example below, 20 trades with a 45% win rate earn +0.16R per trade, and taking out the single best trade brings that to exactly zero.
That second fact is why I never read them alone. Below are the definitions, the formulas that link them, 20 invented trades worked through step by step, and the traps.
The six numbers, in plain English
Everything here is in R, the amount a trade planned to risk, the way Van Tharp teaches it. If a trade would lose 10 points of premium at its stop, 1R is 10 points, so a 15-point gain is +1.5R and a full stop is −1R. It compares trades and strategies of different sizes without mentioning money. My monthly scorecard uses a close cousin: the month's average loss.
| Number | What it tells you | Formula |
|---|---|---|
| Win rate (p) | How often trades ended in profit | winning trades ÷ all trades |
| Average win | How big a typical winner was | total of wins ÷ number of wins |
| Average loss | How big a typical loser was, as a positive number | total of losses ÷ number of losses |
| Payoff ratio (b) | How big winners were next to losers | average win ÷ average loss |
| Profit factor | How much was won for each unit lost | total of wins ÷ total of losses |
| Expectancy | What an average trade added | (total of wins − total of losses) ÷ all trades |
Win rate, payoff ratio and profit factor match the definitions on my scorecard. A profit factor above 1 means the winners outweighed the losers. Expectancy answers the question I actually care about: on average, what did one more trade of this kind add, in units of risk?
How they fit together
The three aren't independent. With win rate p and payoff b:
- Expectancy = p × average win − (1 − p) × average loss.
- Profit factor = p × b ÷ (1 − p). Total wins are the number of wins times the average win, total losses the same for losers, so the trade count cancels out.
- Break-even win rate = 1 ÷ (1 + b). At this win rate expectancy is exactly zero and profit factor exactly 1.
| Payoff ratio | Win rate needed to break even, before costs |
|---|---|
| 0.5 | 66.7% |
| 1.0 | 50.0% |
| 1.5 | 40.0% |
| 2.0 | 33.3% |
| 3.0 | 25.0% |
A high win rate with a small payoff can lose, and a low win rate with a big payoff can win. Neither number means much alone. Divide expectancy by the average loss and you get p × (1 + b) − 1: expectancy in average losses, the scorecard's unit.
A worked example: 20 made-up trades
These trades are invented for teaching. They are not from my bot or any real strategy.
| Trade | R | Trade | R | Trade | R | Trade | R |
|---|---|---|---|---|---|---|---|
| 1 | +1.5 | 6 | −1.0 | 11 | −1.0 | 16 | −1.0 |
| 2 | −1.0 | 7 | +3.2 | 12 | +0.5 | 17 | +1.0 |
| 3 | −1.0 | 8 | −0.6 | 13 | −1.0 | 18 | −1.0 |
| 4 | +2.0 | 9 | −1.0 | 14 | +2.4 | 19 | +0.6 |
| 5 | +0.8 | 10 | +1.2 | 15 | −0.4 | 20 | −1.0 |
- Win rate. 9 winners and 11 losers, so 9 ÷ 20 = 45%.
- Total of wins. 1.5 + 2.0 + 0.8 + 3.2 + 1.2 + 0.5 + 2.4 + 1.0 + 0.6 = 13.2R.
- Total of losses. Nine full stops of 1.0R, plus 0.6 and 0.4: 10.0R.
- Averages. Average win = 13.2 ÷ 9 = 1.467R. Average loss = 10.0 ÷ 11 = 0.909R, below 1R because two trades were closed before the stop.
- Payoff ratio = 1.467 ÷ 0.909 = 1.61.
- Profit factor = 13.2 ÷ 10.0 = 1.32. The formula agrees: 0.45 × 1.61 ÷ 0.55 = 1.32.
- Expectancy = (13.2 − 10.0) ÷ 20 = +0.16R per trade. Again: 0.45 × 1.467 − 0.55 × 0.909 = 0.66 − 0.50 = 0.16.
- Break-even win rate = 1 ÷ (1 + 1.61) = 38.3%. The list wins 45%, about 6.7 points above it.
On its face, a modest edge: each trade added about a sixth of its risk.
Same expectancy, three different strategies
Three made-up profiles, each earning +0.12R per trade. Every win is the average win and every loss exactly 1R, so real results would be more spread out.
| Frequent small wins | In the middle | Rare big wins | |
|---|---|---|---|
| Win rate | 70% | 50% | 32% |
| Average win | 0.6R | 1.24R | 2.5R |
| Payoff ratio | 0.60 | 1.24 | 2.50 |
| Break-even win rate | 62.5% | 44.6% | 28.6% |
| Profit factor | 1.40 | 1.24 | 1.18 |
| Expectancy per trade | +0.12R | +0.12R | +0.12R |
| Chance that 5 given trades in a row all lose | 0.2% | 3.1% | 14.5% |
| Trades before the average is 2 standard errors above zero | about 150 | about 350 | about 740 |
- Profit factor isn't edge per trade. All three earn the same, but the frequent winner shows the best profit factor, because the rare-big-win profile has more losing trades to divide by. Across styles, I compare expectancy.
- Rare big wins are harder to sit through. Five losses in a row is ordinary.
- And harder to prove. More spread means about five times as many trades as the frequent winner before the average means anything.
Small samples: one trade can be the whole edge
Back to the 20 trades. Take out trade 7, the +3.2R winner. Total wins fall to 10.0R, the same as total losses. Profit factor goes from 1.32 to 1.00, and expectancy from +0.16R to zero. One trade in 20 was the entire edge.
Add a single +5R winner instead, and profit factor jumps to 1.82 and expectancy to +0.39R. The strategy didn't change. One trade did.
A rough guide to trusting an average is its standard error: the standard deviation of the results divided by the square root of the number of trades. Here the standard deviation is 1.36R, so the standard error is 1.36 ÷ √20 = 0.30R, and the +0.16R average is only about half a standard error from zero. The usual rough band of two standard errors either side runs from about −0.45R to +0.77R: a losing strategy, a flat one and a very good one all fit.
Halving the error takes four times the trades. If the spread stayed at 1.36R, a +0.16R average would need about 290 trades to sit two standard errors above zero. That assumes independent trades, and same-day trades often aren't, so treat it as a floor. The backtesting guide explains why separate days matter more than trade counts.
Costs, partial exits and uneven trade counts
Costs come straight off expectancy. Charges and slippage are paid on every trade, so in R they come off every result. In the example, 0.1R of cost per trade takes expectancy from +0.16R to +0.06R and profit factor from 1.32 to 1.11. At 0.2R, expectancy is −0.04R and profit factor 0.93. The strategy now loses.
How big is 0.2R? My cost guide works out that one lot of a ₹100 Nifty option needs about 1 point to cover charges, and about 2 with a little slippage. If 1R is 10 points, those 2 points are 0.2R. If 1R is 30 points, they're about 0.07R and the example keeps +0.09R. Tight stops make the same cost a bigger slice of R.
Partial exits change the counting. Suppose a strategy closes half the position whenever a trade reaches +1R. Ten made-up trades: 4 hit the stop at −1R, and 6 reach +1R and close half. Of those 6, 3 close the rest at +2R and 3 at +0.2R. Measure each record against the whole trade's risk, so half a position at +1R is +0.5R.
| Counted per trade | Counted per record | |
|---|---|---|
| Rows | 10 trades | 16 records |
| Win rate | 60% | 75% |
| Average win | 1.05R | 0.53R |
| Payoff ratio | 1.05 | 0.53 |
| Profit factor | 1.58 | 1.58 |
| Expectancy | +0.23R per trade | +0.14R per record |
Same trades, same +2.3R in total. Splitting made the win rate look better and the payoff worse, and spread the expectancy over more rows. Only profit factor, a ratio of totals, didn't move. That's why my scorecard says exactly what a record is.
Uneven trade counts. Two made-up results, both with the example's spread of 1.36R:
- +0.40R per trade over 25 trades: 10R in total, standard error 0.27R. Two standard errors (0.54R) is bigger than the average itself.
- +0.15R per trade over 400 trades: 60R in total, standard error 0.07R. The average clears two standard errors (0.14R).
The first looks better per trade, but I can't tell it apart from zero. The second has much stronger evidence, though it pays costs 16 times as often. And count every version you tried: the best of 25 versions of one idea is partly the luckiest.
How I use the three together
When I read a backtest, a paper run or my own scorecard, I go in this order:
- Trade count first. How many trades, on how many separate days? A few dozen is a story, not a result.
- Win rate next to payoff. How far does the win rate sit above the break-even rate for that payoff? A few points is thin.
- Expectancy in R, after costs. If what's left is close to zero, I treat it as zero.
- Profit factor, with and without the best trades. If removing one or two winners takes it to 1, the edge lives in a handful of trades.
- Standard error. Standard deviation ÷ √n shows whether the average stands out from nothing.
After that come the questions about how trades behaved, which I cover in how I analyse my trading bot's trades.
None of these numbers says anything certain about the next trade. They describe trades that already happened. Read together, they tell me how much that list deserves to be believed, and that's all I ask of them.
Sources
- Van Tharp Institute: Tharp Think trading concepts (R, R-multiples and expectancy)
- FXStreet Learning Center: revenue statistics (averages, profit factor, payoff ratio)
- FXStreet Learning Center: stability statistics (win rate and the expectancy formula)
- Babypips: payoff ratio
- Option Alpha: profit factor
- Wikipedia: standard error (standard error of the mean)
- The trades and strategy profiles in this guide are made up. All figures are my own calculations.
This guide is about testing methods, for information only. It is not investment advice or a recommendation to trade any strategy. I am not registered with SEBI as an investment adviser or research analyst.