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Win Rate vs Reward-to-Risk: Why Being Wrong 60% Can Still Pay
A trader wrong six times in ten can earn three times as much as one who is right seven times in ten. Expectancy is the figure that reconciles them, and it takes a minute to work out.
New traders ask about win rate the way new drivers ask about top speed. It is the figure that sounds like skill. Taken on its own it carries almost no information about whether a method makes money, and the pursuit of it does a quiet and considerable amount of damage to accounts that would otherwise have been perfectly sound.
A child who wins most hands at cards will tell you about it at every opportunity, and will not have noticed that the hands they lose are the expensive ones and the hands they win are cheap. Frequency of winning and amount won are separate measurements, and only one of them settles up at the end of the evening.
Two traders with opposite records
Trader A wins 40% of the time, with winners averaging +2.4R and losers −1R.
Trader B wins 70% of the time, with winners averaging +0.6R and losers −1R.
Which of them is making money? Give each a hundred trades and find out. A takes forty wins at 2.4R, which is +96R, against sixty losses at −1R, which is −60R. The net is +36R. B takes seventy wins at 0.6R, so +42R, against thirty losses, so −30R. The net is +12R.
A is wrong more often than right and earns three times as much. B holds a record that sounds excellent in conversation while the account grows slowly, and if B’s costs are anything above trivial it may not grow at all.
The figure that reconciles them
Expectancy is the average result per trade, measured in units of what was risked:
Expectancy = (Win rate × Average win) − (Loss rate × Average loss)
Win rate carries little information without the reward-to-risk ratio beside it, and the ratio carries little without the win rate. Together they collapse into a single number, and that number is the only honest description of whether a method makes money.
The same formula yields the win rate required merely to break even at a given reward-to-risk
ratio: 1 ÷ (1 + ratio).
| Reward-to-risk | Break-even win rate |
|---|---|
| 0.5 : 1 | 67% |
| 1 : 1 | 50% |
| 1.5 : 1 | 40% |
| 2 : 1 | 33% |
| 3 : 1 | 25% |
At 3:1 a trader may lose three trades in four and still break even. At 0.5:1 the same trader must win two in three simply to stand still, and that is before any costs have been taken out of it.
Why chasing win rate backfires
A high win rate is easy to manufacture. Take profits early. Give losing positions room to recover. The proportion of winning trades rises almost at once, and the same two habits shrink the winners and enlarge the losers, which is precisely the exchange that destroys expectancy. The record improves while the results deteriorate, and only one of those two things is visible without doing the sum.
The mechanism is largely emotional. A win feels good regardless of its size and a loss hurts regardless of its size, so small wins are taken gladly while small losses are postponed until they have grown into large ones. Win rate rewards that pattern. Expectancy punishes it. Track the wrong one for long enough and you will train yourself into habits that are difficult to unlearn.
Consider a trader whose stretch of early profit-taking pushes the win rate into the sixties. It would be natural to feel that something has finally clicked, and natural to add a little size on the strength of the feeling, and if the expectancy over the same stretch has fallen by half then the feeling is misleading and the size is the one thing that should not have moved. The only way to know is to compute it.
The trade-off without a right answer
Higher reward-to-risk generally means a lower win rate. A 4:1 method that works will still lose most of its trades, and long runs of small losses are wearing in a way that is difficult to appreciate until one is living through them. A 1:1 method with a 60% win rate feels far better day to day. It can be just as profitable.
There is no correct point on that curve. There is only the point a given trader can execute consistently through an ordinary run of losses, which makes the choice a question about temperament, and one worth answering honestly before a method is settled on, since a strategy abandoned in the third week of an ordinary drawdown has told its owner very little about the market and a great deal about the fit between the two of them.
Applying it
- Log every trade as an R multiple, so that results of different sizes can be compared.
- After fifty or so trades, compute win rate, average win, average loss and the expectancy. Judge the method on that figure alone.
- Before each entry, check the reward-to-risk against real chart structure with the risk/reward calculator, which also shows the break-even win rate for the ratio.
- If the expectancy is negative, stop and repair the method. Discipline cannot make a negative-expectancy strategy profitable; it only determines how slowly the account declines.
Once the sample is large enough, the expectancy and position sizing guide covers the error bars around that number, which are wider than almost anyone expects.