Risk/Reward and Expectancy

The short answer

An R-multiple converts every outcome into a multiple of what you risked, so results from a $50 risk and a $500 risk become directly comparable. Expectancy is the average R across a sample of trades.

Together they settle a question that win rate cannot answer alone: whether a method makes or loses money, and how large the sample needs to be before you can tell.

What 1R is

1R is the distance between your entry and your stop, multiplied by your position size. It is the planned loss — the number the sizing formula was built to fix.

Every result then gets expressed against it:

R-multiple = profit or loss ÷ amount risked on that trade

A trade that risks $200 and makes $400 is +2R. One that risks $200 and loses the full stop is −1R. One closed early for $60 is +0.3R.

The point of the conversion is that it strips out account size and position size. A +2R trade is the same achievement whether the account is $2,000 or $2 million, which means you can pool results across months in which your equity changed and still have a coherent sample. Currency amounts cannot do that.

It also makes a quiet discipline visible. If your losses regularly come in at −1.4R, your stops are not being honoured, or slippage is worse than you assumed. That shows up immediately in R and is invisible in a profit-and-loss column.

Break-even win rate

Any reward-to-risk ratio implies the win rate needed to break even:

break-even win rate = 1 ÷ (1 + reward-to-risk)

Arithmetic only, and it ignores fees. Costs push every figure in the right-hand column upward.

Read this as a constraint rather than a menu. It does not say that a 5:1 method is easier because it only needs to be right one time in six. The ratio and the win rate are linked: targets further from entry are reached less often, so raising the reward-to-risk usually lowers the hit rate. What the table tells you is the minimum you must clear, and whether the method you are actually running clears it.

The risk/reward calculator does this arithmetic for a specific entry, stop and target, which is more useful than the generic table because it uses the levels the market is actually offering.

Expectancy

Expectancy is what you get when you combine the two halves:

expectancy (in R) = (win rate × average win in R) − (loss rate × average loss in R)

The two systems below are invented for teaching. They describe no real strategy, and neither is a claim that any approach is profitable.

System A wins 40% of the time. Winners average +2R, losers average −1R.

(0.40 × 2) − (0.60 × 1) = 0.80 − 0.60 = +0.20R per trade

System B wins 80% of the time. Winners average +0.2R, losers average −1R.

(0.80 × 0.2) − (0.20 × 1) = 0.16 − 0.20 = −0.04R per trade

System B wins twice as often as System A loses, and it still bleeds. This is the single most common way traders misread their own results. The win rate is the number people quote, and it is the number that feels like skill, but on its own it carries no information about whether money is being made.

Now subtract costs. If a round trip costs roughly 0.05R at your venue, System A falls from +0.20R to +0.15R and System B falls from −0.04R to −0.09R. Fees do not change the ranking here, but they routinely turn a marginally positive method into a negative one, which is why the cost of a round trip belongs in the calculation rather than beside it.

What expectancy does not tell you

Four limits, all of which matter more than the formula.

It says nothing about the next trade. Expectancy is a mean. Individual outcomes are drawn from a distribution around it, and in System A above, 60% of them are losses. There is no trade that returns +0.20R.

It says nothing about the path. Two methods with identical expectancy can differ enormously in how they get there. A high win rate with small winners produces a smooth equity curve with rare, deep setbacks; a low win rate with large winners produces long flat stretches punctuated by jumps. Expectancy is blind to that, which is why it has to be read alongside the drawdown arithmetic.

It is an estimate, not a measurement. Expectancy computed from twenty trades tells you almost nothing, because a couple of outliers dominate the average. The smaller the sample, the wider the error around the number, and the estimate from a sample you also used to design the rules is optimistic by construction — the trap described in backtesting and forward testing.

It assumes tomorrow resembles the sample. Expectancy measured in one volatility regime can disappear in another. The number is historical. It is not a property of the strategy the way mass is a property of an object.

Planned R and realised R

Keep these separate in your records.

Planned R is what the trade was designed to return: the distance from entry to target, divided by the distance from entry to stop. Realised R is what actually landed in the account after slippage, fees, and any decision you made mid-trade to exit early or move a stop.

The gap between them is diagnostic. A plan full of 3R setups that produces an average realised win of 0.9R is not a 3:1 system that is unlucky. It is a system where targets are not being reached, or where nerves are closing trades before they get there. Both are fixable; neither gets fixed while the journal records intentions instead of outcomes. Journaling and metrics covers what to log.

What to do with this

Convert your last fifty trades into R-multiples, then compute the two inputs separately: the fraction that won, and the average size of the winners and losers in R.

If the expectancy is negative, you now know which of the two halves is responsible, which is the only thing that tells you what to change. If it is positive, treat it as a provisional estimate on a small sample rather than a result — and then check that your per-trade risk can survive the streaks that the same win rate guarantees.