The formula, in R terms
Expectancy is the average result you expect per trade, given a win rate and a payoff. Write it as the win rate multiplied by the average win, minus the loss rate multiplied by the average loss. The cleanest unit is R, where one R is the amount you risk on the trade, so a win that returns twice the risk is 2R and a full stop out is minus 1R. Using R removes position size from the question entirely and makes two systems comparable even if one is traded at ten times the size of the other. Expressed that way the formula collapses to something you can hold in your head: multiply each outcome by how often it happens, add the results, and the total is expectancy per trade. Positive means the process adds value over many repetitions. Zero means you are paying costs for entertainment. Negative means the activity is a transfer, and no amount of discipline in execution reverses the sign.
Worked example one, a low win rate system
Define a system that wins 40 per cent of its trades for 2R and loses the other 60 per cent for 1R. Expectancy is 0.4 multiplied by 2, which is 0.8, minus 0.6 multiplied by 1, which is 0.6. The answer is 0.2R per trade. Check it the long way to be sure. Over 100 trades you would expect 40 wins at 2R, which is 80R, and 60 losses at 1R, which is 60R. The net is 20R across 100 trades, and 20 divided by 100 is 0.2R per trade. Both routes agree. Notice what this system feels like from the inside. Six trades out of ten end in a loss, so a losing run of three or four is ordinary and tells you nothing about whether the edge has gone. Anyone judging this system by how often it is right will abandon it, which is why the arithmetic has to be written down before the drawdown arrives rather than during it.
Worked example two, a high win rate system and the cost line
Now define the opposite shape: a system winning 70 per cent of its trades for 0.5R and losing 30 per cent for 1R. Expectancy is 0.7 multiplied by 0.5, which is 0.35, minus 0.3 multiplied by 1, which is 0.30. The answer is 0.05R per trade. It wins far more often and earns a quarter of what the first system earns. Then apply costs, which the formula above ignored. Suppose spread and slippage together amount to 0.1R per trade, a figure you would measure from your own fills rather than assume. Subtract it. The first system falls from 0.2R to 0.1R, so costs have halved the edge. The second falls from 0.05R to minus 0.05R and is now a losing system that will still feel pleasant, because seven trades in ten are winners. This is the most common way a comfortable method quietly loses money, and the reason cost per trade belongs in the calculation from the start.
The breakeven win rate for any payoff
Rearranging the formula gives a result worth memorising. Set expectancy to zero and the required win rate is one divided by one plus the payoff. At a payoff of 1R you need 1 divided by 2, which is 50 per cent. At 1.5R you need 1 divided by 2.5, which is 40 per cent. At 2R you need 1 divided by 3, which is 33.3 per cent. At 3R, 1 divided by 4, which is 25 per cent. At 4R, 20 per cent. Two things follow. First, the curve is steep at the left and flat at the right, so moving a payoff from 1R to 2R relieves far more pressure on the win rate than moving it from 3R to 4R. Second, every one of these figures is before costs, so the real requirement is always higher than the table says. Use the numbers to sanity check a plan, not to justify stretching target and stop distances beyond what the market actually offers.
Expectancy per unit of time, not only per trade
Per trade expectancy ignores how long a trade ties up attention and capital, and that omission can reverse a comparison. Take the 0.2R system from earlier and suppose it produces four trades a week. Weekly expectancy is 0.2 multiplied by 4, which is 0.8R. Now imagine a far more selective method with an expectancy of 0.5R per trade that only triggers once a week. Weekly expectancy is 0.5R. The per trade figure favours the second method by a wide margin and the weekly figure favours the first. Neither comparison is wrong, they answer different questions, and the right one depends on whether your constraint is opportunities or attention. There is a counterweight worth stating. More trades means more cost, more chances to deviate from the plan, and more exposure to execution error, which is part of the case for taking fewer trades. Calculate both figures and decide deliberately rather than by habit.
Why the average win is the unstable part
Expectancy has four inputs and they are not equally reliable. The win rate settles down reasonably quickly, because it is a proportion and each trade contributes one unit of information. The average loss is usually the steadiest input of all, since a stop defines it and most losses land near that stop. The average win is the problem. If profits are taken at varying distances, or if a small number of trades run a long way, the average win is dominated by a handful of results and will swing with each new outlier. Replace one 2R winner with a 6R winner in a short record and expectancy jumps, with nothing having changed about the method. Two defences help. Report the median alongside the mean so you can see how much of the edge sits in the tail, and report expectancy with and without the largest single winner. If removing one trade turns the system negative, you do not have a measured edge, you have one good trade and a story.
The honest limit of a measured expectancy
Expectancy calculated on the same data that chose the rules is not an estimate of anything, it is a description of that history. The arithmetic is still correct and the conclusion does not transfer. The number only begins to mean something when it comes from trades the rules had not seen, recorded in advance rather than remembered, and even then it arrives with an error wide enough to include zero until the sample is large. Treat the figure as provisional, recompute it as the record grows, and expect it to fall rather than rise as costs and real fills enter. Keep it on the same page as the trade count, because an expectancy without a denominator is a decoration. Pair it with a realistic view of risk to reward, log every trade as it happens on the live chart, and let the number earn trust slowly instead of granting it at the start.
FAQ
Is a positive expectancy enough to trade a system?
Not on its own. Expectancy describes the average and says nothing about the path, so a positive system can still produce a drawdown you cannot hold or a losing run that breaks your discipline. You also need a position size that survives the bad stretch and a sample large enough to trust the figure.
Should I include costs inside the expectancy figure?
Yes, and ideally measure them from your own fills rather than assume a number. Report the gross figure if you like, but the net one is what decides whether the activity makes money. A thin edge can be entirely consumed by spread and slippage while the gross figure still looks respectable.
Why use R instead of currency amounts?
Because R removes position size, which lets you compare periods when you traded different amounts and stops a single large trade from dominating the average. Currency figures mix the quality of the system with the aggressiveness of the sizing, so a change in either moves the number and you cannot tell which.
Can a system with a 30 per cent win rate be good?
It can, if the payoff is large enough to clear the breakeven requirement with room to spare after costs. At a payoff of 3R the breakeven win rate is 25 per cent, so 30 per cent leaves a margin. The difficulty is behavioural rather than mathematical, since most people cannot sit through the losing runs that shape implies.
How often should I recalculate it?
Often enough to keep it current and not so often that you react to noise. Recomputing after every trade invites tinkering. A fixed interval, perhaps monthly or every fifty trades, keeps the figure useful while making it obvious when a change is just the normal wobble of a small sample rather than a real shift.
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