How do you calculate expected value per trade?

Multiply the win rate by the average win, multiply the loss rate by the average loss, and subtract the second from the first. With a 45% win rate, a $200 average win and a $150 average loss, that is $90.00 - $82.50 = $7.50 per trade before costs.

What is a breakeven win rate?

It is the win rate at which the average wins exactly cover the average losses. It equals the average loss divided by the sum of the average win and the average loss, so a $200 average win and a $150 average loss break even at about 42.86%.

Expected value explained

What expected value is, how to calculate EV per trade from win rate and average win and loss, and how to find the breakeven win rate. Worked examples.

Part of the Statistics for Investors and Traders track on Agenticks. About 10 minutes, written for a intermediate reader.

Read first: Probability basics for trading.

Last reviewed 2026-11-08.

Risk notice. Backtested and hypothetical results are simulated: no trades were placed, the rules were applied to past data with the benefit of hindsight, and they may not reflect liquidity, slippage or every cost. Past results, real or simulated, do not predict future results.

Key takeaways

Expected value is each outcome times its probability, added up: the average result per try over many tries.
Expected value per trade is win rate x average win minus loss rate x average loss.
The breakeven win rate is the average loss divided by the sum of the average win and the average loss.
Trading costs and small errors in the inputs can turn a thin positive edge negative.
A positive expected value describes a long-run average, not the next trade or the next 20.

Expected value, often shortened to EV, is the average result you would get per try if you could repeat the same bet a very large number of times. You find it by multiplying each possible outcome by its probability and adding the results together. It does not tell you what happens next. It tells you what the bet is worth on average, which is what counts once you make it many times. In trading, expected value per trade has its own name: expectancy. The expectancy lesson shows how to read it off a finished backtest. This lesson builds it from the ground up, so you can see exactly where the number comes from and how small changes move it.

Outcome times probability, then add

Expected value = (probability of outcome A x value of A) + (probability of outcome B x value of B) + ... for every possible outcome. Losses go in as negative numbers, and the probabilities must add up to 1.

Start with a simple bet. A friend offers a game: roll one die, and if it shows a six you win $4. Anything else, you lose $1. Is that a good deal? A six comes up 1 time in 6, so the chance of winning is 1/6 and the chance of losing is 5/6. Multiply and add: (1/6 x $4) + (5/6 x -$1) = $4/6 - $5/6 = -$1/6, about -$0.17 per roll. Play once and you might well win. Play 600 times and you should expect to be down roughly $100, give or take the luck of the rolls. The bet looks generous because the win is four times the loss, but the win does not come often enough to pay for all the losses. It would only break even if a six paid $5, because then 1/6 x $5 exactly matches 5/6 x $1.

Worked example: expected value per trade

A hypothetical strategy wins 45% of its trades. Its average win is $200 and its average loss is $150. Illustrative numbers, before costs.

Win rate	45%
Loss rate (100% - 45%)	55%
Expected gain from wins (0.45 x $200)	$90.00
Expected cost of losses (0.55 x $150)	$82.50
Expected value per trade ($90.00 - $82.50)	$7.50
In units of the average loss (R) ($7.50 / $150)	0.05R
Breakeven win rate ($150 / ($200 + $150))	42.86%
Average result over 200 trades (200 x $7.50)	$1,500
Expected value per trade	+$7.50 before costs

Hypothetical figures for illustration only. The calculator below gives the same results with the same inputs.

Set expected value to zero and solve for the win rate, and you get the breakeven win rate: the win rate at which the wins exactly pay for the losses. It equals average loss / (average win + average loss). Here that is $150 / $350 = 42.86%. The strategy wins 45%, only about 2 percentage points above breakeven, and that gap is the whole edge. If its true win rate were 42% instead, the same strategy would lose money: 0.42 x $200 - 0.58 x $150 = $84 - $87 = -$3 per trade. Costs eat the gap from the other side. Suppose commissions and slippage cost $10 a trade, so the average win shrinks to $190 and the average loss grows to $160. Expected value becomes 0.45 x $190 - 0.55 x $160 = $85.50 - $88.00 = -$2.50, and the breakeven win rate rises to $160 / $350 = 45.71%. A small positive edge on paper turned negative once real costs were counted. The fees and costs lesson covers where those costs come from.

Expected value per trade

Change the win rate, the average win and the average loss and watch the expected value and the breakeven win rate move. The defaults are the hypothetical strategy above, not typical results for any market.

Two strategies can have the same expected value and feel nothing alike. Strategy A wins 80% of the time, with a $50 average win and a $175 average loss: 0.80 x $50 - 0.20 x $175 = $40 - $35 = $5 per trade. Strategy B wins only 30% of the time, with a $250 average win and a $100 average loss: 0.30 x $250 - 0.70 x $100 = $75 - $70 = $5 per trade. Same $5 edge, different ride. A wins four trades in five, but one loss wipes out three and a half wins, and its breakeven win rate is $175 / $225 = 77.78%, so a small slip in its win rate erases the edge. B loses most of the time, and five losses in a row at a 70% loss rate happen 0.7 x 0.7 x 0.7 x 0.7 x 0.7 = 16.8% of the time for any five particular trades. Expected value tells you the average. It does not tell you which ride you can actually sit through.

Positive expected value is not a promise

A positive expected value describes the average over many trades. Over 20 trades, a strategy with a +$7.50 edge can easily be down, because each trade swings by $150 or more while the edge is a few dollars. The probability lesson showed how often streaks happen; an edge needs a large number of trades to show through them.

Every number in the formula is an estimate. The win rate and the average win and loss come from past trades, so they carry every weakness of a small or biased sample. A strategy that sits only slightly above breakeven is the most fragile kind, because a small error in any input flips the sign. That gives two simple questions to ask of any expected value. How far above breakeven is it? And how many trades is the estimate built on? The edge, expectancy and variance lesson puts those questions together with the swings you will see along the way.

Expected value: The average result per try over many repetitions
Breakeven win rate: The win rate at which wins exactly pay for losses
Loss rate: 100% minus the win rate
Expected value in R: Expected value divided by the average loss

You can work out what a bet is worth

You can now compute expected value for a bet and for a trade, find the breakeven win rate, and explain why costs and small samples matter so much.

Check your understanding

A bet pays $9 with probability 0.1 and loses $1 with probability 0.9. What is its expected value?: $0, it is a fair bet. 0.1 x $9 = $0.90 and 0.9 x -$1 = -$0.90. They cancel, so the average result per bet is zero.
A strategy's average win is $300 and its average loss is $100. What is its breakeven win rate?: 25%. Average loss / (average win + average loss) = 100 / 400 = 25%.
A strategy wins 45% of the time, with an average win of $200 and an average loss of $150. What is its expected value per trade before costs?: +$7.50. 0.45 x $200 = $90.00 and 0.55 x $150 = $82.50. $90.00 - $82.50 = $7.50.
Why can a strategy with a positive expected value still be down after 20 trades?: Because 20 trades is a small sample, and normal swings can be far larger than a small average edge. An edge of a few dollars per trade sits under swings of hundreds of dollars per trade. It needs many trades to show through.

Common questions

How do you calculate expected value per trade?: Multiply the win rate by the average win, multiply the loss rate by the average loss, and subtract the second from the first. With a 45% win rate, a $200 average win and a $150 average loss, that is $90.00 - $82.50 = $7.50 per trade before costs.
What is a breakeven win rate?: It is the win rate at which the average wins exactly cover the average losses. It equals the average loss divided by the sum of the average win and the average loss, so a $200 average win and a $150 average loss break even at about 42.86%.

Terms defined in this lesson

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Agenticks Learn is general education. It is not financial, investment, tax or legal advice, it does not take your situation into account, and nothing on it is a recommendation to buy, sell or hold any security or to open any account. Examples use illustrative numbers. Investing involves risk, including losing money you put in, and past performance does not predict future results. Tax rules and limits change; the official sources linked in each lesson are the final word.