Two traders run the same number of trades over a year. One wins 65% of the time and ends down. The other wins 38% of the time and ends comfortably up. Most newer traders find that impossible. It is not — and the reason it is not is the single most important piece of arithmetic in trading: expectancy.

This article explains expectancy from the ground up, shows why win rate alone tells you almost nothing, and gives you a way to estimate the expectancy of your own decisions inside a simulator before any real money is involved. By the end you will be able to look at a record of decisions and answer the only question that matters over a large sample: does this approach make money on average, or does it just feel good?

What Expectancy Is

Expectancy is the average amount you can expect to win or lose per decision, across many decisions. It combines two things people usually keep separate: how often you win, and how much you win or lose when you do. The simplest form is:

Expectancy = (Win rate × Average win) − (Loss rate × Average loss)

If the number is positive, the approach makes money over a large enough sample. If it is negative, it loses money no matter how good any single result felt. That is the whole game. Everything else — entries, indicators, setups — only matters insofar as it moves this number.

Why Win Rate Alone Is Misleading

A high win rate is emotionally satisfying. Being right feels good, and a string of small wins feels like skill. But a high win rate paired with a few catastrophic losses is a classic way to lose money slowly and then all at once. The trader who wins 65% of the time but lets the 35% of losers run far larger than the winners has a negative expectancy hiding behind a comforting hit rate.

The reverse is equally true and far less intuitive. A trader who wins only 38% of the time but whose winners are, on average, three times the size of the losers has a strongly positive expectancy. Most of their decisions are small losses. A minority are large wins. The arithmetic still works.

The R-Multiple Frame

The cleanest way to think about size is in R-multiples, where 1R is the amount you decided to risk on a decision before entering. A trade that loses what you risked is −1R. A trade that makes twice what you risked is +2R. Measuring outcomes in R has a powerful effect: it separates the quality of the decision from the dollar amount, and it lets you compare decisions of different sizes on one scale.

In R terms, expectancy becomes the average R per trade. A strategy with a 38% win rate where winners average +3R and losers average −1R has an expectancy of: (0.38 × 3) − (0.62 × 1) = 1.14 − 0.62 = +0.52R per trade. Over a hundred decisions, that is roughly +52R. The 65%-win-rate strategy where winners average +1R and losers average −2R has: (0.65 × 1) − (0.35 × 2) = 0.65 − 0.70 = −0.05R. Negative. Over a hundred decisions, a slow bleed.

The Mental Model: A Biased Coin

Think of any repeatable trading approach as a biased coin you flip many times, where the payouts are uneven. You do not control any single flip. You control two things: the bias of the coin (how often it lands your way) and the payout structure (how much you collect on a win versus pay on a loss). Expectancy is just the long-run average payout of that specific coin. A casino does not win every hand; it wins because the expectancy of every game it offers is tilted, slightly, in its favor, and it plays enough hands for the average to dominate.

This frame has one uncomfortable implication: in the short run, a positive-expectancy approach can lose, and a negative-expectancy approach can win. The math only asserts itself over a meaningful sample. That is why a single good or bad result tells you almost nothing about whether your approach is sound.

Estimating Your Own Expectancy

Record decisions in R, not dollars. For each decision, note what you risked (1R) and what you made or lost as a multiple of it.
Collect a meaningful sample. Twenty decisions is noise. Aim for at least thirty to fifty before the average means anything.
Compute the average R. Sum the R-multiples and divide by the number of decisions. That single number is your expectancy.
Separate the two levers. Look at your win rate and your average winner-to-loser ratio independently. If expectancy is negative, one of those two is the problem — usually losers that are allowed to run larger than planned.

Common Mistakes

Chasing win rate. Tightening exits to bank more frequent small wins often shrinks the average winner faster than it shrinks the loss rate — lowering expectancy while feeling like improvement.
Letting losers exceed 1R. The entire R framework collapses if a −1R planned loss is allowed to become −3R because the exit was abandoned in the moment. One unmanaged loss can erase many disciplined wins.
Judging expectancy on a tiny sample. A run of five winners does not make an approach positive-expectancy. Variance is large at small samples; the average needs volume to stabilize.
Ignoring costs. Real expectancy is net of slippage and fees. A thin positive expectancy before costs can be negative after them.

Simulator Exercise

Open a Speed Run in Abu Terminal and, before each decision, write down the amount you are conceptually risking as your 1R. After the run, convert every result into an R-multiple relative to that risk. Then compute two numbers across the session: your win rate, and your average R per decision. Do this for three separate runs. Notice whether your expectancy is being driven by how often you are right or by how large your winners are relative to your losers. Most developing traders discover their problem is not their hit rate at all — it is that their losers are quietly larger than their winners.

Reflection Prompt

Write an answer to this: If I could only improve one of the two levers — my win rate or my average winner-to-loser ratio — which would move my expectancy more, and what specific behavior is currently holding that lever back?

Quick Check

A strategy wins 40% of the time, with winners averaging +2.5R and losers −1R. Is its expectancy positive or negative, and by how much per trade?
Why can a 65% win rate still produce a losing record?
Why is a sample of five trades a poor basis for judging whether an approach has positive expectancy?

Answers: (1) (0.40 × 2.5) − (0.60 × 1) = +0.40R per trade — positive. (2) If the average loss is larger than the average win by enough, the losses outweigh the more frequent wins. (3) Variance dominates small samples; the long-run average only emerges over many decisions.

Expectancy: The Math That Decides If You Survive