Expectancy, not win rate

7 minintermediatesample lesson

Objective

Compute expectancy from a win rate and a payoff ratio, and say why a win rate alone cannot tell you whether a method makes money.

A win rate is the first number everyone reaches for and the least informative one available. Sixty percent winners sounds like a good method and describes a losing one whenever the winners are small and the losers are not. The number that settles it is expectancy: the average R a trade returns across a record. Win rate times average win, less loss rate times average loss.

Expectancy from a win rate and a payoff

Interactive · your numbers

Win rate40%Average win3.0RAverage loss1.0R

Expectancy per trade

+0.60R

Payoff ratio

3.00:1

Break-even win rate

25.0%

One run of 100 trades

+52R

At 40% winners paying 3.0R against losers costing 1.0R, this method needs a 25.0% win rate to break even, so it is above the line. It loses more often than it wins and still makes money.

Expectancy is the average R a trade returns: the win rate times the average win, less the loss rate times the average loss. It is the only one of these three numbers that determines whether a method makes money, and a win rate on its own never does. The drawn path is one hundred trades drawn at this win rate from a fixed seed — one possible run of these assumptions, not a forecast.

Two methods, same year

Method A	70% winners at 0.4R, losers 1R → 0.70 × 0.4 − 0.30 × 1 = −0.02R per trade
Method B	40% winners at 3R, losers 1R → 0.40 × 3 − 0.60 × 1 = +0.60R per trade
What A feels like	Right seven times out of ten. Pleasant, and losing.
What B feels like	Wrong six times out of ten. Unpleasant, and the only one of the two that works.

Two things follow. The first is that a method's break-even win rate is set by its payoff ratio, not by any general rule — at 3:1 the break-even is twenty-five percent, at 1:2 it is sixty-seven. The second is that expectancy is expressed in R because R is the only unit that survives a change in account size or position size. A record kept in dollars tells you how big your positions were; a record kept in R tells you whether the method works.

NOTE

The platform reports expectancy this way for records that carry a stop, rather than a win rate on its own — lib/expectancy.js returns the win rate as one of expectancy's inputs precisely so it cannot be mistaken for the answer. There is also a chooser: when most records have no stop, they are directional calls rather than trades, and forcing an R multiple on them would be inventing one.

Key takeaway

Expectancy decides; win rate is one of its inputs. A method that is wrong most of the time can be the better of two.

Common mistakes

Judging a method by its win rate.
Keeping the record in dollars, so a change in position size looks like a change in skill.

Test your knowledge · 5 questions

1. Expectancy is

The largest win divided by the largest lossThe win rate over the last fifty tradesThe average R a trade returnsThe total profit over the year

2. 70% winners at 0.4R against 1R losers gives an expectancy of

−0.02R+0.40R+0.28R+0.70R

3. At a 3:1 payoff, the break-even win rate is

33%25%75%50%

4. Records are kept in R rather than dollars because

R is what every broker reports on statementsDollars are taxed and R is not, so it is cleanerR is more precise than dollars to the centR survives a change in account or position size

5. A method that wins 40% of the time

Needs a win rate above 50% to workCannot be measured in R at allCan be the better of two methodsIs losing money, since it loses more often

Answer every question to check.

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The three sample lessons

Stage 1 · beginnerWhat BUY means Stage 2 · intermediateExpectancy, not win rate Stage 3 · advancedAverage return and compound return

Proving it

1Expectancy, not win rate2How many trades before it means anything3Drawdown, streaks and ruin4When returns arrive: overnight and the session5Why a big week often gives some back6The 52-week high as an anchor7Lottery stocks: the one-day spike8What a journal catches9Reading your own account statement10Your real trades, measured in R11Reading your own equity curve12The ledger and the gate's own receipt13The ratios a record is judged by14Alpha, benchmarks and attribution15Why backtests lie16Judging a record someone else shows you17What the research actually supports18Reading a report written by someone with a position19Sharing a record: what a link shows, and to whom20A shared card: one dated close, the same for every reader

The other lessons in this module open with membership.

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