Expected value in trading: how to calculate and trust expectancy
Expectancy is the average net result per trade: win rate times average win minus loss rate times average loss, after costs. With 40% winners averaging $300 and 60% losers averaging $150, it is 0.40 × $300 − 0.60 × $150 = $30 per trade before costs. It is only an estimate. Trust it when it rests on many trades, stays positive on unseen data and fits a drawdown you can live through.
By Soren Huang · Published · updated · Editorial policy
Contents
- What is expected value in trading?
- How do you calculate expectancy from your trades?
- How do win rate and payoff ratio work together?
- What happens to expectancy after costs?
- How many trades do you need before you trust expectancy?
- Why can a positive expectancy stop working?
- How do you check expectancy with drawdown and out-of-sample tests?
- Frequently asked questions
- References
What is expected value in trading?
Expected value in trading, or expectancy, is the average amount a strategy made or lost per trade. You calculate it as win rate times average win minus loss rate times average loss, after costs. Trust it only when it comes from many trades, stays positive out of sample and survives the drawdowns it implies.
Expectancy is the average net result of one trade, measured in money, points or ticks. Think of a casino. The casino knows its edge on every bet because the rules of the game fix it. A trader has no rule book. You only have a list of past trades, and expectancy is your best estimate of the edge hidden in that list. Expectancy moves with every exit rule, so where you place a stop loss changes this number directly.
How do you calculate expectancy from your trades?
Multiply the share of winners by the average win, multiply the share of losers by the average loss, and subtract the second from the first. You can do this by hand from any trade list, or enter the numbers in the win rate and expectancy calculator.
The formula is:
Expectancy = W × AW − L × AL
- W is the win rate. Win rate is the share of all trades that closed with a profit, for example 0.40 for 40%.
- AW is the average winning trade, in money or points.
- L is the loss rate, the share of all trades that closed with a loss. If you have no break-even trades, L is simply 1 − W.
- AL is the average losing trade, written as a positive number.
There is a quick way to check your result. Take the total net profit of all trades and divide it by the number of trades. You get the same number, because the formula is just the average trade split into its winning and losing parts. Break-even trades count in the number of trades with a result of zero.
Hypothetical example
A strategy has 100 trades. 40 are winners with an average of $300. 60 are losers with an average of $150. Expectancy = 0.40 × $300 − 0.60 × $150 = $120 − $90 = $30 per trade. Check: total profit is 40 × $300 − 60 × $150 = $12,000 − $9,000 = $3,000, and $3,000 ÷ 100 trades = $30.
How do win rate and payoff ratio work together?
Neither win rate nor payoff ratio means anything alone; expectancy is positive only when the two together clear the break-even line. Payoff ratio is the average winning trade divided by the average losing trade. A strategy that wins only 30% of the time can have positive expectancy if its winners are large enough. A strategy that wins 70% of the time can lose money if its losers are large.
The table shows the win rate a strategy needs just to break even, before costs, for each payoff ratio.
| Payoff ratio (average win ÷ average loss) | Win rate needed to break even |
|---|---|
| 0.5 | 66.7% |
| 1.0 | 50.0% |
| 1.5 | 40.0% |
| 2.0 | 33.3% |
| 3.0 | 25.0% |
The example strategy has a payoff ratio of 2.0 ($300 ÷ $150) and a win rate of 40%. It needs 33.3% to break even, so its margin is about 7 percentage points. That margin is what you are really measuring. A small margin can disappear with a small change in costs or market behavior.
What happens to expectancy after costs?
Costs come off every trade, so they lower the average win, raise the average loss and push the break-even win rate up. Use only the net expectancy, after commission, fees and slippage, when you judge a strategy. Slippage is the difference between the price a backtest assumes and the price you actually get.
Hypothetical example
Take the strategy above and assume costs of $20 per round trip (entry plus exit), for commission, fees and slippage together.
| Before costs | After costs | |
|---|---|---|
| Average win | $300 | $280 |
| Average loss | $150 | $170 |
| Payoff ratio | 2.00 | 1.65 |
| Win rate needed to break even | 33.3% | 37.8% |
| Expectancy per trade | $30 | $10 |
Costs take two-thirds of the edge. The win rate is still 40%, but the strategy now clears its break-even line by only about 2 percentage points.
Two habits help here. First, compare the gross expectancy with the round-trip cost. If the cost is a large part of the average trade, a slightly worse fill will remove the edge. Second, rerun the test with double the slippage and see whether expectancy stays positive. The article on trading costs in backtests explains how to estimate commission and slippage for futures. The slippage setting in the backtesting of AlphaPrime (Valynox) is where the doubled figure goes, and every candidate in that run then pays the same doubled cost before its expectancy is read.
How many trades do you need before you trust expectancy?
Enough trades that the uncertainty around the average is clearly smaller than the average itself; with a few dozen trades it almost never is. Each trade result is noisy. The average of noisy numbers is also noisy, and it only settles down as the number of trades grows.
Standard deviation is a measure of how far individual trade results typically spread around the average. The uncertainty of the expectancy estimate is roughly the standard deviation divided by the square root of the number of trades. In practice, four times as many trades halves the uncertainty. Nine times as many trades cuts it to one third.
Hypothetical example
The strategy has an expectancy of $30 per trade and a standard deviation of $300 per trade. A rough range that should contain the true expectancy about 95 times in 100 is the estimate plus or minus two uncertainties.
- 100 trades: uncertainty $30, range about −$30 to +$90. Zero is inside the range.
- 400 trades: uncertainty $15, range about $0 to +$60. Zero is at the edge.
- 900 trades: uncertainty $10, range about +$10 to +$50. Zero is outside the range.
Treat these ranges as a best case. They assume each trade is independent of the others. Real trades often cluster: winners come in trending months and losers come in choppy ones. When results are correlated like this, the true uncertainty is larger than the simple calculation shows. Lo (2002) makes the same point for the Sharpe ratio, a related measure.
Why can a positive expectancy stop working?
A past expectancy describes the history you tested, and several common forces make it larger in the backtest than it will be later.
- Selection from many variants. If you tested many parameter sets and kept the best one, part of its expectancy is luck. The more variants you try, the more luck the winner contains. Bailey, Borwein, López de Prado and Zhu (2014) show how testing many configurations produces strong backtests that fail on new data. White (2000) and Harvey and Liu (2015) describe ways to correct for this.
- Market change. Volatility, liquidity and the behavior of other traders shift over the years. An edge from one period can fade in the next.
- Costs that change. Wider spreads or worse fills in live trading cut directly into a thin edge.
- A few outsized trades. If one or two large winners carry the total, the expectancy rests on events that may not repeat.
- Data errors. Bad ticks, missing bars or a rule that uses information it could not have known at the time inflate the average trade.
To test whether a few outsized trades carry the result, remove the largest winner and recalculate. To catch data errors, check the bars for gaps and bad ticks before trusting the average.
Hypothetical example
The 100-trade strategy made $3,000 in total. Its best trade made $900. Without it, the total is $2,100 over 99 trades, or about $21 per trade. The edge shrinks but survives. If the expectancy had turned negative, the whole result would depend on one trade.
How do you check expectancy with drawdown and out-of-sample tests?
Use expectancy as one number among several: drawdown tells you whether you can survive the path, and out-of-sample data tells you whether the edge was real. Drawdown is the fall of the equity from its highest point to a later low. Out-of-sample data is data that was not used to build or tune the strategy.
Two strategies can have the same expectancy and very different paths. A low win rate means long losing streaks, even with a positive edge.
Hypothetical example
With a 60% loss rate, the chance that eight losses in a row start at any given trade is about 1.7%. Over 500 trades, you should expect roughly three such streaks. Eight losses of $150 each is a $1,200 drawdown. At $30 per trade, it takes about 40 average trades to earn that back.
Measure drawdown in units of the average trade, as in the example. You can get the maximum drawdown from an equity series with the drawdown calculator. Then run these checks in order:
- Net expectancy against cost. Confirm the expectancy is positive after costs and stays positive with double slippage.
- In-sample against out-of-sample. Compare expectancy on the data used to build the strategy with expectancy on later data. Some drop is normal. A collapse toward zero means the build fitted noise. Walk-forward analysis repeats this comparison across many windows.
- Period by period. Calculate expectancy for each year. A strategy that earns most of its total in one year is fragile.
- Long against short. Calculate expectancy for long and short trades separately. If one side is negative, the strategy may be riding one market direction.
- Drawdown in average trades. Divide the maximum drawdown by the net expectancy. Decide in advance whether you could keep trading through that many trades of recovery.
In AlphaPrime, the Performance Report shows equity, drawdown, the trades, periodic performance and long and short analysis, which covers the inputs for steps 3 to 5. Strategy validation includes walk-forward analysis and lets you apply your own thresholds to every candidate.
What this means if you use AlphaPrime: read the net average trade together with its drawdown, its yearly results and its out-of-sample results. Judge each strategy by whether all of these agree, not by expectancy alone.
Frequently asked questions
What is the expectancy formula in trading?
Expectancy equals win rate times average win minus loss rate times average loss. For 40% winners averaging $300 and 60% losers averaging $150, it is $120 − $90 = $30 per trade. Total net profit divided by the number of trades gives the same number.
What is a good expectancy for a trading strategy?
There is no fixed good value, because expectancy depends on the contract and the trade size. Judge it against two things: the round-trip cost, which should be a small part of the gross average trade, and the average loss. Expressing expectancy as a fraction of the amount risked per trade makes strategies on different markets comparable.
How many trades do you need to calculate a reliable expectancy?
It depends on how much individual trades vary. The uncertainty of the average falls with the square root of the number of trades, so four times as many trades halves it. With a few dozen trades, the range around the average usually still includes zero.
Is a high win rate better than a high payoff ratio?
Neither is better by itself; only their combination decides expectancy. A 30% win rate with a payoff ratio of 3 has positive expectancy before costs, while a 70% win rate with a payoff ratio of 0.3 does not. Low win rates bring longer losing streaks, so check the drawdown as well.
What is the difference between expectancy and profit factor?
Expectancy is the average net result per trade. Profit factor is the total of all winning trades divided by the total of all losing trades. Both come from the same trade list, but expectancy is in money or points per trade, while profit factor is a ratio without units.
References
- Bailey, D. H., Borwein, J., López de Prado, M., & Zhu, Q. J. (2014). Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance. Notices of the American Mathematical Society, 61(5), 458–471.
- White, H. (2000). A Reality Check for Data Snooping. Econometrica, 68(5), 1097–1126.
- Harvey, C. R., & Liu, Y. (2015). Backtesting. The Journal of Portfolio Management, 42(1), 13–28.
- Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal, 58(4), 36–52.