R-Multiples and Expectancy: The Only Two Numbers a Trading Record Needs

Dollars hide the only thing worth comparing

A profit figure tells you what happened. It does not tell you what you paid for the chance.

This is Van Tharp's opening move in Trade Your Way to Financial Freedom, and it is the one idea from the book that has spread everywhere since. Convert every result into a multiple of the risk you accepted before entry. That unit is called R.

What the conversion buys you is comparability. Trades of different sizes, in different instruments, at different account balances, all become the same kind of number — and a run of them becomes a distribution you can actually reason about.

Defining 1R precisely, because a vague R is worthless

1R is the distance from your entry to your stop, multiplied by your position size. Nothing else. Not the amount you had in the account, not the notional value of the position, and not what you ended up losing if you moved the stop.

• Entry $50, stop $48, 100 shares → 1R = $200.
• Exit at $54 → +$400 → +2R.
• Exit at $47 because you widened the stop → −$300 → −1.5R, and that half-R is the record of a rule you broke.
• No stop at all → no R, and no way to evaluate the trade later. This is the real reason the method insists on one.

Expectancy: the average, and what it is for

Expectancy = the mean R across all your trades. Above zero, the method makes money over enough repetitions. Below zero, it does not, whatever last month looked like.

The record above sums to +7R over 20 trades, so expectancy is +0.35R. That is the whole calculation. It says: on average, each trade returns 0.35 times whatever you chose to risk on it. Risk $200 a trade and it says $70 a trade — but the R version is the one that keeps working after you change your size.

The long form, if you prefer it broken out: (win rate × average win in R) − (loss rate × average loss in R). It is the same number. What the long form makes obvious is that win rate appears in it as one factor among three, which is where the next section starts.

Win rate is not edge, and asking about it first is the tell

The record above wins 35% of the time and makes money comfortably. A method winning 80% of the time loses money if the two losses in every ten are big enough. Win rate is one input to expectancy and is useless on its own — which is why it is the first thing every beginner asks about.

The average hides the shape, and the shape is what you have to live through

This is why expectancy alone is not a complete description. Two methods with the same average produce very different experiences, and the one that is harder to sit through is the one you are more likely to abandon at exactly the wrong moment. See does your trading system fit you for what to do about that.

The second lever nobody optimises

Expectancy tells you what a trade is worth. Multiply it by how many trades you get, and you have the year.

Tharp calls this expectunity. The practical consequence is that the honest way to compare two methods is per year, not per trade — and that a very selective method with a big edge can lose to a duller one simply by not showing up often enough. It also cuts the other way: raising frequency by taking marginal setups lowers expectancy, usually faster than it raises the count.

How to actually get these numbers

1. 1Before each entry, write the stop and the size. That fixes 1R, and it has to be written before — a stop reconstructed afterwards is a story, not a measurement.
2. 2On exit, record the result divided by 1R. One column, one number.
3. 3After 30 trades, take the mean. That is your expectancy. Fewer than 30 and you are reading noise.
4. 4Also record the largest losing run and the largest winning run. Those two numbers are what tell you whether you can live with the method.
5. 5Recompute quarterly. Expectancy is a property of a method in a market, and markets change without telling you.

Two places the book claims more than the maths supports

• The marble-bag analogy assumes independence. Drawing R-multiples from a bag treats every trade as a fresh independent draw. Real trades cluster: the conditions that produced three losses often persist into the fourth. That makes real loss runs longer than the bag predicts.
• The System Quality Number is presented with more precision than it has. Dividing expectancy by the standard deviation of R and scaling by the trade count is a reasonable summary statistic. The published bands that grade a system from "poor" to "holy grail" are not derived from anything; treat them as labels, not measurements.

Neither of these damages the core. R and expectancy are bookkeeping conventions that make trades comparable, and they would be worth adopting even if every other chapter were wrong.