Trade Expectancy Formula: How to Calculate Expected Value per Trade

Trade expectancy estimates the average amount a trading strategy could gain or lose per trade based on its win rate, average win and average loss.

The basic trade expectancy formula is:

Trade expectancy
= (Win rate × Average win)
− (Loss rate × Average loss)

For a strategy with:

Win rate: 50%
Average win: $200
Average loss: $100

The calculation is:

Trade expectancy
= (50% × $200) − (50% × $100)
= $100 − $50
= +$50 per trade

A positive result means the inputs imply a positive average outcome before any costs not included in the calculation. It does not mean each trade will earn $50, and it does not guarantee that future performance will match the historical sample.

Calculate expectancy with the BasisPilot Trade Expectancy Calculator →

Trade expectancy is the probability-weighted average outcome of a repeated trading process.

It combines four components:

1. Percentage of trades that win
2. Average amount won on winning trades
3. Percentage of trades that lose
4. Average amount lost on losing trades

The result can be expressed as:

• dollars per trade;
• account percentage per trade;
• R-multiples per trade;
• points, ticks or another consistent unit.

For example:

Expectancy: +$50 per trade

means the selected inputs imply an average result of $50 across a sufficiently large number of comparable trades.

It does not mean:

• the next trade should earn $50;
• every group of ten trades will earn $500;
• losses cannot occur;
• the strategy will continue to behave the same way;
• the estimate includes costs that were omitted;
• historical or hypothetical results guarantee future performance.

Expectancy is an average, not a schedule of returns.

The standard formula is:

Expectancy
= (Probability of win × Average win)
− (Probability of loss × Average loss)

Because:

Loss rate
= 1 − Win rate

the formula can also be written as:

Expectancy
= (Win rate × Average win)
− ((1 − Win rate) × Average loss)

The average loss should be entered as a positive magnitude.

Correct input:

Average loss: $100

Not:

Average loss: -$100

The subtraction is already included in the formula. Entering a negative average loss and subtracting it again would incorrectly turn the loss into a gain.

Assume a trading record contains 100 completed trades:

Winning trades: 45
Losing trades: 55
Average winning trade: $240
Average losing trade: $120

Step 1: Calculate win rate

Win rate
= Winning trades ÷ Total trades
= 45 ÷ 100
= 45%

Step 2: Calculate loss rate

Loss rate
= Losing trades ÷ Total trades
= 55 ÷ 100
= 55%

Or:

Loss rate
= 1 − 45%
= 55%

Step 3: Calculate the weighted average win

Win contribution
= 45% × $240
= $108

Step 4: Calculate the weighted average loss

Loss contribution
= 55% × $120
= $66

Step 5: Calculate expectancy

Expectancy
= $108 − $66
= +$42 per trade

Step 6: Check against the total result

Gross profit from winning trades:

45 × $240
= $10,800

Gross loss from losing trades:

55 × $120
= $6,600

Net result:

$10,800 − $6,600
= $4,200

Average result:

$4,200 ÷ 100 trades
= $42 per trade

Both methods produce the same expectancy.

Dollar expectancy can be useful when trade size is consistent. Expectancy in R is often more useful when position sizes vary.

What is R?

One R represents the initial planned risk on a trade.

If the maximum planned loss is $100:

1R = $100

A $200 winning trade is:

+$200 ÷ $100
= +2R

A $75 losing trade is:

-$75 ÷ $100
= -0.75R

Expectancy in R

Assume:

Win rate: 40%
Average winner: 2.5R
Average loser: 1R

Expectancy
= (40% × 2.5R) − (60% × 1R)
= 1.00R − 0.60R
= +0.40R per trade

If the trader risks $100 per trade:

Dollar expectancy
= 0.40R × $100
= $40 per trade

If the risk amount changes to $250:

Dollar expectancy
= 0.40R × $250
= $100 per trade

The strategy’s expectancy in R remains 0.40R, while the dollar expectancy changes with position size.

Why R can be useful

R-multiples normalize results by initial risk. This makes it easier to compare trades with:

• different entry prices;
• different stop distances;
• different share quantities;
• different dollar risk amounts.

R still depends on accurate records. If the initial risk, fees or actual exits are recorded inconsistently, the calculated expectancy can be misleading.

Trading costs reduce the average result and can turn a slightly positive gross expectancy into a negative net expectancy.

Potential costs include:

• commissions;
• regulatory and exchange fees;
• bid-ask spread;
• slippage;
• stock-borrow fees;
• margin interest;
• platform or data fees;
• currency conversion costs.

Investor.gov advises that fees and expenses reduce investment returns and should be considered when evaluating performance claims. FINRA similarly notes that trading and account costs can materially affect returns.

Method 1: subtract average cost per trade

If the same estimated cost applies to every completed trade:

Net expectancy
= Gross expectancy − Average cost per trade

Example:

Gross expectancy: +$50
Average cost per trade: $12

Net expectancy
= $50 − $12
= +$38 per trade

Method 2: use net average wins and losses

Assume:

Gross average win: $200
Gross average loss: $100
Round-trip cost per trade: $10
Win rate: 50%

Net winning outcome:

Net average win
= $200 − $10
= $190

Net losing outcome:

Net average loss
= $100 + $10
= $110

Net expectancy:

(50% × $190) − (50% × $110)
= $95 − $55
= +$40 per trade

This matches:

Gross expectancy: $50
Minus average cost: $10
Net expectancy: $40

Costs can remove a small edge

Assume:

Win rate: 48%
Average win: $110
Average loss: $100

Gross expectancy:

(48% × $110) − (52% × $100)
= $52.80 − $52.00
= +$0.80 per trade

With $4 of average costs:

Net expectancy
= $0.80 − $4.00
= -$3.20 per trade

The strategy changes from slightly positive to negative.

This is especially important for frequent trading, small average price moves or strategies with narrow gross margins.

The break-even win rate is the win rate at which expectancy equals zero.

Before costs:

Break-even win rate
= Average loss
÷
(Average win + Average loss)

Assume:

Average win: $200
Average loss: $100

Break-even win rate
= $100 ÷ ($200 + $100)
= 33.33%

Break-even rate with equal trading costs

If the same average cost applies to every trade:

Break-even win rate
= (Average loss + Cost)
÷
(Average win + Average loss)

Using:

Gross average win: $200
Gross average loss: $100
Average cost: $10

Break-even win rate
= ($100 + $10)
÷
($200 + $100)
= 36.67%

The denominator remains $300 because the cost reduces a winning outcome by $10 and increases a losing outcome by $10.

The same result can be calculated with net outcomes:

Net win: $190
Net loss: $110

Break-even win rate
= $110 ÷ ($190 + $110)
= 36.67%

Break-even table before costs

A lower break-even win rate does not automatically indicate a better strategy. Larger theoretical targets may be reached less frequently, while tight stops may increase the loss rate.

Profit factor and expectancy both use winning and losing results, but they express the outcome differently.

Profit factor formula

Profit factor
= Gross profit ÷ Gross loss

Using rates and average outcomes:

Profit factor
= (Win rate × Average win)
÷
(Loss rate × Average loss)

From the earlier 100-trade example:

Gross profit: $10,800
Gross loss: $6,600

Profit factor
= $10,800 ÷ $6,600
= 1.64

Expectancy formula

Expectancy
= Net profit ÷ Number of trades

From the same record:

$4,200 ÷ 100
= $42 per trade

Key difference

A profit factor above 1 and a positive expectancy generally describe the same gross direction, provided the calculations use the same trades and cost treatment.

However, expectancy is often easier to connect to position risk:

+0.20R expectancy

means the sample produced an average result of 0.20 times the initial risk per trade.

Profit factor does not show trade frequency

Two strategies can have the same profit factor but different practical outcomes.

Profit factor alone does not describe frequency, capital capacity, drawdown or consistency.

A planned risk-reward ratio describes one setup’s potential payoff. Trade expectancy describes the average result of repeated trades.

Planned risk-reward

Entry: $50
Stop: $47
Target: $56

Risk: $3
Reward: $6
Reward-to-risk: 2.00

Expectancy also needs probability

At a 30% win rate:

(30% × 2R) − (70% × 1R)
= -0.10R

At a 40% win rate:

(40% × 2R) − (60% × 1R)
= +0.20R

The planned payoff is identical, but the expectancy changes because the win rate changes.

A favorable risk-reward ratio is therefore not enough to establish a positive edge.

Review the relationship between payoff and break-even win rate →

An expectancy estimate is calculated from a sample of trades. A small or unrepresentative sample can change sharply when only one or two outcomes are added.

One trade has a large effect in a small sample

In 20 trades:

One trade = 5% of the sample

In 100 trades:

One trade = 1% of the sample

If a 20-trade record has 12 winners:

Win rate
= 12 ÷ 20
= 60%

One additional losing trade changes it to:

12 ÷ 21
= 57.14%

The observed win rate falls by 2.86 percentage points after one trade.

With a larger sample, one result has less influence, although a larger sample does not remove bias or guarantee future stability.

There is no universal minimum sample

The useful sample size depends on:

• trade frequency;
• strategy type;
• holding period;
• market regime;
• number of instruments;
• variation in trade outcomes;
• presence of rare large wins or losses;
• whether the rules changed during the sample.

A sample can be large but still misleading if it includes:

• only one favorable market period;
• cherry-picked trades;
• changing entry or exit rules;
• excluded losses;
• different position-sizing methods;
• unrealistically favorable fills;
• look-ahead bias;
• survivorship bias.

Separate development and evaluation samples

When possible, avoid evaluating a strategy only on the same historical data used to create it.

A stronger process distinguishes between:

Development sample
Used to form or refine the rules.

Evaluation sample
Used to test the rules without further adjustment.

Live sample
Actual trades executed under current conditions.

Repeatedly modifying the rules to fit the evaluation period can recreate the same hindsight problem.

The CFTC warns that hypothetical trading results can benefit from hindsight and may not accurately account for liquidity or the financial and behavioral impact of real losses. NFA disclosures similarly emphasize that hypothetical trading does not involve actual financial risk.

Positive expectancy does not mean wins and losses will alternate smoothly.

Assume:

Win rate: 40%
Average win: 2R
Average loss: 1R
Expectancy: +0.20R

The loss rate is 60%. The probability of five losses in a specific sequence, assuming independent trades with an unchanged loss probability, is:

0.60^5
= 7.776%

The probability of five consecutive losses occurring somewhere across a long series is higher than the probability for one specific five-trade block.

A positive-expectancy strategy can therefore experience:

• multiple consecutive losses;
• extended drawdowns;
• temporary negative performance;
• realized results below the estimated average;
• large variation around the expected value.

Expectancy should be evaluated alongside:

• maximum drawdown;
• longest losing streak;
• outcome dispersion;
• position risk;
• number of simultaneous positions;
• correlation between trades;
• liquidity and gap risk.

Expectancy is not the same as account growth

Multiplying expectancy by the number of trades gives a linear average estimate:

Projected average result
= Expectancy per trade × Number of trades

But actual account growth can differ because of:

• changing position size;
• compounding;
• drawdowns;
• variable risk;
• overlapping positions;
• capital limits;
• skipped trades;
• changing market conditions.

Do not present a linear expectancy projection as a forecast or guaranteed account balance.

Expectancy can be expressed as a percentage of the amount risked or of account equity.

Percentage of risk

Expectancy per risk unit
= Expectancy ÷ Planned risk amount

If:

Expectancy: $40
Planned risk: $200

Expectancy
= $40 ÷ $200
= 0.20R

Percentage of account

If the account is $20,000:

$40 ÷ $20,000
= 0.20% of account per trade

This does not mean the account should grow by exactly 0.20% after each trade.

If the strategy risks a changing percentage of current equity, future results become path-dependent. The order of wins and losses affects the ending balance.

Real records may include trades that are neither clear winners nor full losses.

Break-even trades

A trade with a net result of zero can be handled as a separate category:

Expectancy
= (Win rate × Average win)
− (Loss rate × Average loss)
+ (Break-even rate × 0)

Because the break-even contribution is zero, it does not change the arithmetic, but the rates must still sum to 100%.

Small gains and small losses

A trade should generally be classified by its net realized result after costs, not by whether the price briefly moved in the planned direction.

Partial exits

For a trade with multiple exits, calculate one combined net result for the full trade:

Total trade result
= Sum of realized gains and losses
− Total costs

Then include that full-trade result in the average win or average loss.

Do not count each partial fill as a separate strategy trade unless that is the consistent unit used throughout the dataset.

1. Entering average loss as a negative number

The formula already subtracts the loss. Use a positive loss magnitude.

2. Using planned winners instead of realized winners

A planned 3R target is not an average 3R win if most trades exit at 1R.

3. Ignoring fees and slippage

A small gross edge may disappear after costs.

4. Using win rate alone

A high win rate can coexist with negative expectancy when occasional losses are much larger than typical wins.

5. Using profit factor alone

Profit factor does not show the average dollar or R result per trade, trade frequency or drawdown.

6. Treating a small sample as stable

A handful of trades can produce a highly unstable estimate.

7. Combining unrelated strategies

Mixing short-term momentum, long-term trend and mean-reversion trades into one expectancy figure can hide meaningful differences.

8. Mixing gross and net data

Do not use net average wins with gross average losses, or include costs twice.

9. Excluding open or failed trades selectively

The dataset should follow a consistent inclusion rule.

10. Assuming independence

Trades may share the same market exposure, sector, signal or volatility regime. Correlated losses can cluster.

11. Projecting expectancy as guaranteed income

Expected value is a probability-weighted estimate, not a promised return.

12. Ignoring strategy changes

If entry, exit or position-sizing rules change, older trades may no longer represent the current process.

A consistent workflow is:

1. Define what counts as one completed trade.
2. Record entry and exit executions.
3. Include commissions, spread and other direct costs.
4. Calculate the net result of each trade.
5. Separate positive and negative results.
6. Calculate win rate and loss rate.
7. Calculate average net win and average net loss.
8. Apply the expectancy formula.
9. Calculate profit factor and break-even win rate.
10. Review results by strategy, instrument and market regime.
11. Update the estimate as new comparable trades are added.
12. Compare planned R with realized R.

Useful fields include:

Trade date
Strategy
Direction
Instrument
Initial risk
Net result
Result in R
Fees
Planned stop
Actual exit
Planned target
Exit reason

Avoid recording only the winning or losing label. The size of each outcome is essential to expectancy.

What is a good trade expectancy?

There is no universal expectancy that makes a strategy good. A positive net expectancy is mathematically preferable to a negative one, but it must be considered with sample quality, drawdown, capacity, costs, trade frequency and the risk taken to produce it.

Is 0.20R expectancy good?

It means the inputs or historical sample imply an average gain of 0.20 times the initial risk per trade. Its practical value depends on whether the estimate is stable, net of costs and achievable with acceptable drawdown.

Can a strategy with a low win rate have positive expectancy?

Yes. A low win rate can be offset by average winners that are substantially larger than average losses.

Example:

Win rate: 35%
Average win: 3R
Average loss: 1R

Expectancy
= (35% × 3R) − (65% × 1R)
= +0.40R

Can a high-win-rate strategy have negative expectancy?

Yes. Frequent small wins can be outweighed by occasional large losses.

Example:

Win rate: 80%
Average win: $50
Average loss: $250

Expectancy
= (80% × $50) − (20% × $250)
= $40 − $50
= -$10 per trade

What is the difference between expectancy and expected return?

Trade expectancy is the average outcome per trade under the selected inputs. Expected return may refer to a percentage return over a period or on invested capital. The terms should not be treated as interchangeable without defining the denominator and time period.

What is the difference between expectancy and profit factor?

Expectancy is the average net outcome per trade. Profit factor is total gross profit divided by total gross loss.

Should fees be included?

Yes, when the goal is to estimate net trading expectancy. Costs can materially change the result.

How many trades are needed to calculate expectancy?

The formula can be calculated from any non-empty sample, but a very small sample is highly sensitive to individual outcomes. There is no universal minimum that guarantees reliability.

Does positive expectancy guarantee profit?

No. Outcomes vary, estimates can be wrong, conditions can change and a positive-expectancy process can experience losing streaks or long drawdowns.

Should break-even trades count?

They can be included as a separate zero-result category. Ensure that win, loss and break-even rates sum to 100%.

Can I multiply expectancy by trades per month?

You can calculate a simple average scenario:

Monthly average scenario
= Expectancy per trade × Trades per month

But it should not be presented as a forecast. Trade availability, costs, compounding and actual outcomes may differ.

• Investor.gov: Investor Bulletin — Performance Claims
• Investor.gov: How Fees and Expenses Affect Your Investment Portfolio
• FINRA: Fees and Commissions
• FINRA Rule 2270: Day-Trading Risk Disclosure Statement
• CFTC: Commodity Trading Systems Sold on the Internet
• NFA Compliance Rule 2-29: Communications With the Public and Promotional Material

The formulas in this guide describe mathematical averages based on user-provided or historical inputs. They do not estimate whether a strategy will continue to produce the same win rate, average win or average loss.

Historical and hypothetical results can be affected by hindsight, selection bias, liquidity assumptions, omitted costs and changes in market conditions. Actual trading also involves financial and behavioral pressures that a simulation may not reproduce.

BasisPilot provides educational calculations and does not provide personalized investment, tax, legal or trading advice.