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Module 14 · Proving it · lesson 1 of 14 · stage 2 of 3 · intermediate

Expectancy, not win rate

7 minintermediatesample lesson
A grid of forty trades with sixteen filled in, a forty percent win rate that the size of its winners can make the stronger of two methods.
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
Expectancy per trade
+0.60R
Payoff ratio
3.00:1
Break-even win rate
25.0%
One run of 100 trades
+52R
break even
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 A70% winners at 0.4R, losers 1R → 0.70 × 0.4 − 0.30 × 1 = −0.02R per trade
Method B40% winners at 3R, losers 1R → 0.40 × 3 − 0.60 × 1 = +0.60R per trade
What A feels likeRight seven times out of ten. Pleasant, and losing.
What B feels likeWrong 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
2. 70% winners at 0.4R against 1R losers gives an expectancy of
3. At a 3:1 payoff, the break-even win rate is
4. Records are kept in R rather than dollars because
5. A method that wins 40% of the time
Answer every question to check.
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