Trading expectancy calculator

How do you calculate trading expectancy?

Trading expectancy is the average result of one trade. Multiply the win rate by the average win, subtract the loss rate multiplied by the average loss, then subtract what each trade costs: expectancy = (win rate x average win) - (loss rate x average loss) - costs per trade.

With the default inputs, 45% of trades win an average of $300 and the other 55% lose an average of $200. The winners contribute 0.45 x $300 = $135 per trade and the losers take away 0.55 x $200 = $110, so the average trade makes $25 before costs. Take off $10 of commission, spread and slippage and it is $15 after costs. Over 100 trades that adds up to $1,500, after paying $1,000 in costs along the way.

The bar chart in the result shows those four pieces side by side: what the wins add, what the losses and the costs subtract, and the net figure left over.

What is expectancy in R multiples?

R is the amount you risk on a trade, the loss you take if the stop is hit. Stating results in R strips out position size, so a record built on $50 risks can be compared with one built on $5,000 risks.

Expectancy in R = expectancy in money / 1R. The default trader risks $200 per trade, so $15 after costs is 15 / 200 = 0.075R per trade, and the average win of $300 is 1.5R. Over 100 trades, 0.075R adds up to 7.5R. If the same trader later risks $400 a trade on the same rules, the figure in R stays 0.075 while every money figure doubles.

The amount at risk and the average loss are often close but not equal, because some losing trades are closed before the stop. That is why the calculator asks for 1R separately instead of assuming it equals the average loss.

How do trading costs change expectancy?

Costs come off every trade, winners and losers alike, so they cut expectancy one for one. On the default inputs the edge before costs is $25 a trade:

Costs also raise the win rate needed to break even. Without costs, a $300 average win against a $200 average loss breaks even at 200 / (300 + 200) = 40%. With $10 of costs the break-even win rate is (200 + 10) / (300 + 200) = 42%, because each trade now has to cover its costs as well as the losers. A small edge feels this most: at a 50% win rate with a $220 average win and a $200 average loss, the $10 before costs becomes -$5 after $15 of costs, and the break-even win rate rises to 51.19%.

Calculating expectancy from your own trade record

The From your trade record tab takes four numbers a trade journal or a broker statement export can give you: the count of winning trades, the count of losing trades, the total made on the winners and the total lost on the losers. The calculator turns them into averages first.

In the default record, 22 trades won a total of $7,700 and 28 lost a total of $5,600. The win rate is 22 / 50 = 44%, the average win $7,700 / 22 = $350 and the average loss $5,600 / 28 = $200. Expectancy before costs is $42 a trade, the same as the $2,100 net result divided by 50 trades, and $32 after $10 of costs. Multiplied over 100 trades, those averages give $3,200.

Fifty trades is a small record. Each trade is 2 points of win rate: had one of the 22 winners been a loser instead, at the same averages, expectancy before costs would fall from $42 to $31. Add trades to the record before treating the figure as settled.

Same expectancy, very different trading

Expectancy hides the shape of the results. The default inputs, a 45% win rate with a $300 average win and a $200 average loss, average $25 a trade before costs. A record that wins 70% of the time but averages only $100 per win against $150 per loss also averages $25, since 0.7 x 100 - 0.3 x 150 = 25.

The two give the same total over many trades, but they feel different along the way. The first loses more often and depends on its larger winners; the second wins often and has only 10 points of win rate between its record and break-even. The win rates either side of yours are in the table under the result.

Expectancy worked in pounds and dirhams

The formula is identical in every currency, and the calculator never converts between them.

• Pounds. A 38% win rate, an average win of £450, an average loss of £180 and £6 of costs per trade. Before costs: 0.38 x 450 - 0.62 x 180 = £59.40. After costs: £53.40 a trade. With 1R at £150 that is 0.356R, and 200 trades total £10,680. The payoff ratio is 2.5, so the record breaks even at 28.57% before costs and 29.52% after.
• Dirhams. A 55% win rate, an average win of AED 900, an average loss of AED 1,000 and AED 40 of costs. Before costs: AED 495 - AED 450 = AED 45. After costs: AED 5 a trade, or 0.005R with 1R at AED 1,000. Across 50 trades the costs come to AED 2,000 and the net total to AED 250. The break-even win rate is 52.63% before costs and 54.74% after, so the record sits barely above it.

How to calculate trading expectancy in Excel

If each row of a sheet holds one trade's result after costs, with losses as negative numbers in F2:F101, expectancy is simply the average of the column: =AVERAGE(F2:F101). The average of every result, winners and losers together, is the same number as win rate x average win - loss rate x average loss. Divide by your 1R to get it in R: =AVERAGE(F2:F101)/200 for a $200 risk.

To see the parts, Microsoft documents COUNTIF(range, criteria) and AVERAGEIF(range, criteria, [average_range]). The count of winners is =COUNTIF(F2:F101,">0"), the average win =AVERAGEIF(F2:F101,">0") and the average loss =AVERAGEIF(F2:F101,"<0"), which comes back negative. With averages typed in instead, a win rate in B2, average win in C2, average loss in D2 and costs in E2, the formula is =B2*C2-(1-B2)*D2-E2.

How each input moves the expectancy

• Win rate. Each point of win rate is worth 1% of the average win plus the average loss. With $300 and $200, 5 points moves expectancy by $25 a trade: on the default inputs it runs from -$35 at 35% to $65 at 55% after costs.
• Average win. Raising it by $10 adds the win rate times $10, so $4.50 a trade at 45%.
• Average loss. Cutting it by $10 adds the loss rate times $10, $5.50 a trade at 45%. At win rates below 50%, a smaller average loss is worth more per dollar than a larger average win.
• Costs. Each dollar of cost takes exactly one dollar off every trade.
• 1R. Changes only the figure in R, never the money.
• Number of trades. Multiplies the expectancy. It does not make a result more likely.

Common mistakes, and what expectancy leaves out

• Leaving out costs. On the default inputs, costs take $10 of a $25 edge, 40% of it.
• Mixing gross and net. If your totals already include commission, set costs to zero or they are counted twice.
• Counting break-even trades as wins. Decide where scratch trades go and keep to it, since they move the win rate.
• Trusting a short record. A few dozen trades can show a positive average by chance.
• Reading the total as a forecast. The total over 100 trades is the average multiplied by 100. Real results arrive in streaks and can be negative over any stretch.

The calculator also leaves out tax, financing charges on positions held overnight, and the order of wins and losses. For what a run of losses does to an account, see the drawdown recovery calculator; for sizing a trade from an edge, the Kelly criterion calculator.

Glossary

Expectancy: the average result of one trade, in money or in R. Win rate: winning trades divided by all trades. Average win and average loss: the total of each kind of trade divided by how many there were. Payoff ratio: average win divided by average loss. 1R: the amount risked on a trade. R multiple: a result divided by 1R. Costs per trade: commission, spread and slippage for opening and closing one trade. Break-even win rate: the win rate at which expectancy is zero.

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