R-Multiples and Expectancy: The Math Backbone of Trading

What 1R actually is

R stands for risk, and 1R is simply the amount of money you planned to lose on a trade if it went wrong. It’s defined before you enter, not after. The recipe is: distance from entry to stop, multiplied by the number of shares. That’s it. If you don’t have a stop, you don’t have an R, and none of the math in this article can help you.

A full worked setup. Suppose a trader buys a stock at $130 and places a stop-loss at $122. The risk per share is $130 minus $122, which is $8. Say the trader’s account is $25,000 and their rule is to risk 1% per trade, or $250. Dividing $250 by $8 per share gives 31.25, which rounds down to 31 shares. The position costs 31 × $130 = $4,030, but that’s not the risk. The risk is 31 shares × $8 = $248. That $248 is this trade’s 1R.

Notice what just happened: position size was derived from the stop distance, not picked out of the air. A wider stop forces fewer shares, a tighter stop allows more, and either way the planned loss stays near $250. That’s the whole point of R — the thing you hold constant from trade to trade is the damage a single loss can do.

Measuring results in R instead of dollars

Once 1R is defined, every outcome becomes a multiple of it. In the example above, if the stock hits the stop at $122, the loss is $248, which is exactly −1R. If it instead runs to $146, that’s a gain of $16 per share, twice the $8 risked per share, so 31 × $16 = $496, which is +2R. An early exit at $134 would be +$4 per share, or $124, which is +0.5R. Same trade, three possible outcomes, all described on one scale.

Why bother, when dollars are what you actually spend? Because dollar results aren’t comparable and R results are. A $500 win means one thing in a $10,000 account and something very different in a $500,000 account. It also means something different on a trade where you risked $100 versus one where you risked $1,000. Saying a trade made +2R communicates the only thing that matters about the outcome: you made twice what you were willing to lose.

R-thinking also keeps a trading journal honest across time. As an account grows, dollar profits naturally get bigger even if the trader isn’t improving at all. A list of results like +2R, −1R, −1R, +3R, −0.5R strips out account size and position size and leaves only the quality of the decisions. Two traders with wildly different account sizes can compare notes in R and actually learn something from each other.

Expectancy: one number that describes your whole system

Expectancy answers the question: on average, what does one trade from this system earn, measured in R? In words, the formula is: (percentage of winners × average winner in R) minus (percentage of losers × average loser in R). It blends the two things people usually argue about separately — how often you win and how big you win — into a single per-trade number.

Worked system: suppose 40% of trades win and the average winner is +2R, while 60% lose and the average loser is −1R. Expectancy is (0.40 × 2R) − (0.60 × 1R) = 0.8R − 0.6R = +0.2R per trade. Over 100 trades, the 40 winners earn 40 × 2R = +80R and the 60 losers cost 60 × 1R = −60R, leaving +20R, which is indeed 0.2R per trade. If 1R is $248, that’s about $49.60 per trade and $4,960 across the 100 trades: $19,840 of wins minus $14,880 of losses.

Read that again, because it’s the most counterintuitive fact in trading math: this system loses more often than it wins — 60% of its trades are losers — and it still makes money. The reverse is also true. A system that wins 70% of the time but averages only +0.5R on winners and −1.5R on losers has an expectancy of (0.70 × 0.5R) − (0.30 × 1.5R) = 0.35R − 0.45R = −0.1R per trade. It feels great most days and slowly bleeds the account.

The break-even line is easy to compute. If winners average +2R and losers −1R, you break even at a 33.3% win rate, because one 2R win pays for two 1R losses. If winners and losers are both 1R, you need better than 50%. Win rate alone tells you nothing until you know the average sizes on each side.

Why cutting losers and letting winners run is the entire game

Look at the two levers inside the expectancy formula. Win rate is mostly set by your edge — how well you pick entries — and it’s hard to move. The average size of winners and losers, though, is largely a matter of behavior: whether you actually exit at −1R when the stop is hit, and whether you give winners room to reach +2R or +3R instead of grabbing +0.3R the moment a trade turns green.

The failure mode is nearly universal. Taking profits early feels safe, and moving a stop lower to avoid taking the loss feels hopeful. Do both and the numbers invert: winners shrink toward +0.5R while occasional disasters hit −2R or −3R because the stop was abandoned. Plug those into the formula with even a decent win rate and expectancy goes negative. The trader’s picks didn’t get worse; the R-multiples did.

This is why experienced traders talk about discipline in such absolute terms. Capping every loss at −1R puts a floor under the left side of the formula, and letting winners exceed +1R is the only force pushing the right side up. Everything else — indicators, screeners, news — feeds the win rate, which is the lever you control least. The R distribution is the lever you control most.

Sample-size honesty: 20 trades tell you almost nothing

Here’s the uncomfortable part. Take the genuinely profitable system from earlier: 40% winners at +2R, 60% losers at −1R, true expectancy +0.2R. Over just 20 trades, ordinary luck means you might see anywhere from about 5 winners to about 12 winners without anything being wrong. Five winners in 20 trades measures out to (0.25 × 2R) − (0.75 × 1R) = −0.25R per trade — a losing system, apparently. Twelve winners measures out to (0.60 × 2R) − (0.40 × 1R) = +0.8R per trade — four times its real edge. Same system, same trader, wildly different verdicts.

Losing streaks deserve the same honesty. A system that loses 60% of the time will regularly produce streaks of six, seven, or eight consecutive losses across a few hundred trades. That’s not the system breaking; that’s the system working as designed. A trader who abandons a +0.2R system after eight straight −1R losses — a stretch the math practically guarantees will happen eventually — never collects the edge.

The practical takeaway is to hold two ideas at once. Track every trade in R from day one, because the habit and the data are valuable. But treat any expectancy computed from fewer than 100 trades or so as a rough sketch, and even a few hundred trades as an estimate with real uncertainty, not a verdict. Systems earn trust slowly, in sample sizes, not in good weeks.

Where expectancy leads: Kelly and risk of ruin

Expectancy is the foundation that the more famous formulas sit on. The Kelly criterion, for example, takes exactly the numbers we’ve been using — win rate and the ratio of average win to average loss — and converts them into a suggested fraction of capital to risk. For the 40% / +2R / −1R system, Kelly works out to (2 × 0.40 − 0.60) / 2 = 0.10, or 10% of capital per trade at full Kelly. In practice that’s far too aggressive for most people, and many traders who use Kelly at all use a half or a quarter of it, but the point stands: without a measured expectancy, Kelly has nothing to chew on.

Risk-of-ruin math tells the other half of the story: given your expectancy, your R distribution, and how much you risk per trade, what is the probability of drawing the account down past the point of no return? Two facts fall out of it. First, a negative-expectancy system ruins you with certainty if you keep trading it — position sizing only changes how fast. Second, even a positive-expectancy system can ruin you if each trade risks too much, because the losing streaks we just discussed arrive before the edge has time to pay. Eight straight −1R losses at 1% risk per trade is a drawdown of under 8%; the same streak at 10% risk per trade cuts the account by more than half.

So the pieces fit together in a specific order: define 1R before every trade, record every result as an R-multiple, let a real sample accumulate, compute expectancy from it, and only then let Kelly-style sizing and risk-of-ruin estimates inform how much to risk. Skipping ahead — sizing aggressively on an expectancy you haven’t actually measured — is how good systems produce ruined accounts. None of this says what to trade; it’s the accounting layer that sits under whatever you trade.