What Is Expectancy in Trading?
Expectancy is the average amount a single trade makes or loses once win rate and the size of wins and losses are combined into one number. A system with a high win rate can have negative expectancy, and a system that loses most of its trades can have positive expectancy.
Most traders judge a system by how often it wins. That number on its own cannot tell you whether the system makes money, and treating it as though it can is probably the most expensive habit in retail trading.
How it works
Expectancy is the average profit of one trade. Take every trade a system produced, add the wins, subtract the losses, divide by the number of trades. That is the whole calculation, and the answer is a single number in money or in R.
Written out, it is the win rate multiplied by the average win, minus the loss rate multiplied by the average loss. Two inputs, and neither is meaningful without the other.
Nine wins in every ten can still be a losing system. If nine trades make one unit each and the tenth loses twelve, the win rate is superb and the account is down two units. This is not a contrived case — it is the exact shape of selling premium without a hedge, and of moving a stop to avoid taking a loss.
And three wins in ten can be a strong system, if the wins are large enough. Trend following lives here, which is why it feels so uncomfortable to trade — the experience is mostly losing, and the arithmetic is fine.
The costs come out first
Every trade pays to enter and pays to leave, and that comes out of the average before any edge is counted. On this site’s shared series a round trip costs 0.0098, which is about 2% of the median bar range of 0.493.
That sounds small. Whether it is small depends entirely on how far you were planning to hold, which is the part most cost discussions skip.
A worked example
Here is the calculation on this site’s own measured numbers rather than invented ones.
The base rate. Of 566 ten-bar windows on the shared series, 54% finished higher than they started. Suppose a system captures exactly that — it wins 54% of the time, and the wins and losses are the same size, R.
The gross edge. Win 54% and lose 46% at the same size, and the average trade returns 0.54R − 0.46R = 0.08R. Eight percent of whatever you are risking, per trade, before costs.
The costs. Subtract the round trip: the average trade is worth 0.08R − 0.0098.
The break-even point. Set that to zero and solve. 0.08R = 0.0098 gives R = 0.1225. The median ATR14 on this series is 0.5994, so 0.1225 is about 0.20 ATR.
What that means. At this base rate, a target smaller than roughly a fifth of the median ATR is a losing system — not because the trader executed badly, not because the market changed, but because the arithmetic was negative before the first trade was placed. No amount of discipline fixes it.
And the same edge is fine at a wider target. At 1 ATR the average trade returns about 0.048 gross against 0.0098 of cost — costs take roughly a fifth of the edge and the rest survives. Identical system, identical win rate, opposite outcome, decided entirely by how far the target sits from the entry.
What it cannot tell you
Expectancy says nothing about the order the results arrive in. A positive-expectancy system produces losing runs routinely, and a run of four or six losses is not evidence that anything has broken. Direction runs on this series average 2.01 bars with a longest of 11 — the market clusters, and so do results.
It also says nothing about survival. A system with excellent expectancy will still end an account that sizes every trade at a third of the balance. Expectancy is the edge; position sizing is whether you are still there when the edge shows up.
And it is silent about the path. On this series 95% of bars sat below a prior peak, the deepest drawdown ran 3.76%, and the longest wait for a new high was 73 bars — while the stretch finished +3.61% overall. A positive result and an uncomfortable ride are the normal combination, not a contradiction.
The original data
A round trip on this site’s shared series costs 0.0098, about 2% of the median bar range of 0.493. The median ATR14 is 0.5994. Of 566 ten-bar windows, 54% finished higher.
Put together, those three measurements produce the figure this page exists for: at that base rate the break-even target is 0.1225, or about 0.20 ATR. Below it the expectancy is negative regardless of execution.
That number is specific to this series and these costs. The method is not — run it on whatever you actually trade, with whatever your broker actually charges, and you will get your own floor. Most people have never calculated theirs, which is why “cut your winners short” gets discussed as a psychological failing when a good part of it is a costs problem.
When it fails
The characteristic failure is calculating expectancy over far too few trades. Twenty trades produce a number, the number looks authoritative because it came from arithmetic, and it is almost entirely noise. A system with genuinely positive expectancy can show a negative average over twenty trades without anything being wrong, and a system with no edge at all can show a strong positive one. The sample has to be large enough that a single outlier cannot move the answer, and on most retail trading frequencies that means months rather than weeks.
A second failure is assuming the average loss equals the stop distance. Gaps skip the level, slippage widens it, and the realised average loss is bigger than the planned one — which pushes expectancy down without any change in strategy.
A third is recalculating after every losing run and concluding the edge has gone. That is the one thing the number cannot answer on a small sample, and acting on it converts an ordinary run into a change of system.
A fourth is leaving costs out entirely, which is the single most common way a backtested edge fails to appear in a live account.
And a fifth is treating expectancy as a promise. It is an average over many trades and it makes no claim about the next one, the next ten, or this month. It tells you which direction the arithmetic points, and that is genuinely all it tells you.
Related
Risk management covers position sizing, which decides whether a positive expectancy ever gets collected. Stop loss covers where the loss side of the calculation is actually set. And ATR covers the volatility measure the break-even target above is expressed in.
This is the number that changed how I think about trading more than any indicator did. I spent a long time chasing a higher win rate, which felt like the obvious thing to improve, and the arithmetic simply does not care about it on its own. Once I started measuring average profit per trade instead, a lot of setups I was proud of turned out to be moving money sideways and paying the broker for the privilege.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.