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Expected value is the average. Margin decides whether you are still trading when a bad run arrives. Read how a margin call works.
What is included
- The calculator, with your own numbers
- The formula written out
- A worked example you can reproduce
- Where grid, martingale and DCA bots break the maths
Who it is for
- People running or testing a trading bot
- Anyone sizing a position or checking costs
- Readers learning how the numbers work
- Not advice, and not for placing trades
Key facts
- Expected value (EV) is the average result of one trade over many trades: win rate times average win, minus loss rate times average loss, minus costs.
- Break-even win rate = (average loss + cost) / (average win + average loss). Below it, the strategy loses on average.
- A positive EV does not mean every trade wins, and it says nothing about how deep the losing runs get.
- Changing position size changes how bumpy the path is. It does not change the sign of the average.
- The inputs are yours. Every example number on this page is made up and is not a result from any bot or strategy.
How the calculator works
It takes the four numbers every strategy report has and combines them the way an average works: each outcome counts in proportion to how often it happens.
Break-even win rate = (average loss + cost) / (average win + average loss)
Profit factor = (win rate x average win) / (loss rate x average loss)
Use the average win and average loss from a backtest or a trade journal, and count every cost: spread, commission, swap and slippage. Leave costs out and the result is a number nobody will ever be paid.
A worked example
Take a made-up strategy that wins 45 percent of the time, wins $120 on average and loses $80 on average, with $2 of costs per trade. The wins are worth 0.45 x 120 = $54.00 per trade and the losses cost 0.55 x 80 = $44.00, so before costs it makes $10.00 and after costs $8.00. Over 100 trades the average is $800. That is a long-run average. Any single run of 100 trades can land well above or below it.
Why costs matter more than they look
In that example costs are only $2, yet they take 20 percent of the $10 edge. At $5 per trade they take half of it, and at $10 per trade the strategy has an expected value of zero. Strategies that trade often feel the effect most, because the cost is paid on every trade while the edge per trade stays small.
Where bots break the maths
Grid, martingale and recovery bots raise the win rate by design: they win a small amount very often and take a large loss rarely. The win rate looks excellent. The expected value does not follow it.
Try 90 percent wins, a $10 average win, a $100 average loss and a $1 cost. The wins add $9.00 per trade, the losses take $10.00 and costs take $1.00, so the strategy loses $2.00 on every trade on average. It will still show a long winning streak on the chart, which is why the average has to be checked and not the streak.
How many trades before you can trust the win rate?
You never know the true win rate. You estimate it from trades, and the estimate is loose when there are few of them. With a true 50 percent win rate, the range that covers about 19 of 20 samples is wide:
| Trades in the sample | Win rate could look like |
|---|---|
| 30 | 32% to 68% |
| 100 | 40% to 60% |
| 300 | 44% to 56% |
| 1,000 | 47% to 53% |
Normal approximation for independent trades, 95 percent range, rounded. A strategy tested on 30 trades has not been tested.
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FAQ
Frequently Asked Questions
What is a good expected value?
Anything above zero after all costs is positive, but size matters against the cost and the risk. An edge of a few cents per trade can vanish when spread widens. Test whether it holds on data the strategy has not seen.
Does a positive expected value mean the bot is safe?
No. Expected value is an average. A strategy can have a positive average and still suffer a losing run that empties the account first. Drawdown and margin decide that, not the average.
Where do I get the average win and average loss?
From a backtest report or your own trade journal. Use net figures after spread, commission and swap, and use enough trades that the averages are stable.
Why is my break-even win rate above 50 percent?
When the average win is smaller than the average loss, or costs are large, you need to win more than half your trades just to stay level. Many grid and martingale bots sit in this position.
Are the numbers on this page real?
Example numbers are made up to show how the maths works, and the page says so. A figure only counts as exact when the page says it was calculated on a stated date. Nothing you enter in a calculator leaves your browser.
Can I use this to decide whether to run a bot?
It can show whether a bot's numbers hold together and how much an account can lose. It cannot say what the market will do, and it is not advice. Use it to ask better questions, then read the terms of your own broker or exchange.
Is this financial advice?
No. It is a calculator and general education. It does not consider your situation, and the numbers it returns are only as good as the numbers you enter.
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