Why being right isn't the same as winning

You can be right three times out of ten and make money consistently. You can be right nine times out of ten and go broke. The hit rate alone says nothing, because the other half of the equation is missing: how much you make when you're right and how much you lose when you're wrong.

Why the hit rate deceives

Because it describes frequency, not magnitude. Knowing how often something works is useless without knowing how much it works when it does.

The example, with round numbers

Someone makes ten trades and gets only three right. Sounds bad.

• Three wins, making €300 each → +€900
• Seven losses, losing €100 each → −€700
• Result: +€200

A 30% hit rate and a profit. The reason is the reward-to-risk ratio: each win was worth three times what each loss cost.

Why this isn't a numbers trick

It's exactly how many real strategies work, and how things outside markets work too. A pharmaceutical company researching twenty compounds where only one reaches market isn't failing: the one that arrives pays for the nineteen that didn't.

What decides the result isn't how often you're right, but the size of the wins compared to the size of the losses. And that size can largely be decided in advance, which the hit rate can't.

The practical consequence

When someone boasts about a hit rate without stating their reward-to-risk ratio, they've given half the figure. And usually the half that's easier to achieve.

A system that closes gains very early and lets losses run can have an extremely high hit rate and lose money steadily. We'll see it in two sections.

What expected value is and how to calculate it

Expected value combines both halves into one number: what you'd make on average per trade if you repeated the same decision very many times.

The formula

Expected value = (probability of winning × average gain) − (probability of losing × average loss)

With the earlier example: (0.3 × €300) − (0.7 × €100) = €90 − €70 = +€20 per trade.

That number is the only thing that says whether a way of trading makes sense. If it's positive, repeating it many times tends to add up. If it's negative, repeating it many times tends to subtract, however well some of them go.

Mathematical expectancyEuros per trade

WIN0.3LOSE0.7

Probability of winning × average gain

0.3 × €300€90

Probability of losing × average loss

0.7 × €100€70

Repeating the same decision very many times

Expectancy

+€20

per trade

(0.3 × €300) − (0.7 × €100) = €90 − €70 = +€20 per trade

What expected value isn't

It isn't a promise about the next trade. With an expected value of +€20 per trade, the next one can lose €100. Expected value describes the average of a large set, not an individual case.

And it doesn't work on small samples. Calculating expected value across ten trades doesn't give you the real expected value: it gives you the result of those ten. How different those two things are is the subject of this chapter's final session, on drawdowns, streaks, and sample size, and the difference is enormous.

The same idea, put in reverse

A casino has a slightly positive expected value on each roulette bet. Slightly: a few cents per euro.

It needs no more. With enough spins, that minimal edge becomes a predictable business. The casino doesn't win by being right often — it loses constantly against individual players — but because its expected value is positive and it plays an enormous number of times.

That's the whole logic: a small edge repeated many times is worth more than a large edge used once. And to repeat you need to still have money, which is what the next session, on how much to risk on any single trade, is about.

And if you aren't going to trade, is any of this useful?

Worth answering, because most people reading this course won't be opening and closing positions weekly. It is useful, in two specific places.

In every individual decision you do make. Buying a particular stock because you think something is going to happen is a bet with an expected value, whether you calculate it or not. The question "how much can I gain if I'm right and how much can I lose if I'm wrong?" applies equally whether you make two trades a year or two hundred.

And in understanding why the boring thing works. Buying an index fund and not touching it for twenty years is accepting a small positive expected value and repeating it an enormous number of times without interruption. It's exactly what compounding does to your money over time, with the investor playing the house.

Seen that way, the difference between long-term investing and short-term trading isn't philosophical: it's about how many times you repeat and how much each repetition costs. Chapter 3 already put numbers on the second part, in what every trade really costs.

The inverse case: right often and losing money

It's the most common one among individual investors and the most painful, because it feels like doing well.

The example

Someone makes ten trades and gets nine right.

• Nine wins, making €50 each → +€450
• One loss, losing €600 → −€600
• Result: −€150

A 90% hit rate and a loss. Expected value is −€15 per trade: repeating that a thousand times ruins anyone, with the constant feeling of being right nearly always.

Why this pattern is so frequent

Because it's exactly what default human behaviour produces, without anyone designing it.

When a position is doing well, the temptation is to close it and lock in the gain, which feels excellent. When it's doing badly, the temptation is to wait for a recovery, because closing it means admitting the mistake.

The result, repeated, is a collection of small gains and a few enormous losses. The hit rate rises and the account falls.

That impulse has a name — the disposition effect — and its own chapter later, in the biases that cost the most, because it's among the best-documented biases and one of the costliest.

How to detect it

With a one-minute check on your own history: compare your average gain against your average loss.

If your average loss is bigger than your average gain, you need a very high hit rate just to break even. And the bigger that gap, the higher that rate has to be, up to levels nobody sustains.

It's a calculation almost nobody does, and it requires nothing but recorded trades. Which is, incidentally, the other problem: without a record there's no calculation possible.

Why judging a decision by its outcome teaches the opposite

This is the idea holding up the whole chapter, and the hardest to apply. A decision can be well made and turn out badly. It can be badly made and turn out well. Judging it by the outcome teaches, half the time, exactly the wrong lesson.

The four combinations

	Good outcome	Bad outcome
Good decision	Ideal. Nothing to correct	Bad luck. Also nothing to correct
Bad decision	The dangerous one. Reinforces a bad habit	What it looks like, and the only one that teaches on its own

The emotionally painful box is top right. But the genuinely damaging one is bottom left: making a bad decision that works out.

Why that box is the dangerous one

Because the brain records "this worked" and repeats the behaviour.

Buying a stock without looking at anything, on a stranger's recommendation online, and having it rise 20% is a bad decision with a good outcome. It doesn't teach that it was a coincidence: it teaches that the method works. And next time the bet will be bigger.

It's exactly the mechanism the previous chapter described with the hindsight bias of looking at a chart knowing the ending, applied to your own decisions rather than to charts.

The example that makes it obvious outside markets

Crossing a street on a red light without looking and reaching the other side intact doesn't make that decision sound. Outcome bias consists precisely of concluding that it does, because it worked out.

Nobody has trouble seeing this with the street. With money it's enormously harder, because the outcome arrives attached to a figure that looks objective.

What to do about it

Separating them requires having written down, beforehand, why you made the decision and what would have to happen for you to be wrong.

With that written, afterwards you can answer two different questions: was the reasoning correct given the information available? and how did it end? Without it written, you can only answer the second, and the second alone teaches the wrong lessons half the time.

It's the same discipline that appeared closing the earnings chapter, in how to read a full event, and that will appear again, this time as a concrete tool, in the method chapter's logbook. It appears three times because it's the same thing viewed from three places.

What to remember

• The hit rate is half the figure: without knowing how much you make when right and lose when wrong, it says nothing.
• Expected value combines both halves, and it's the only number that says whether a way of trading makes sense repeated.
• Being right 90% of the time and losing money is the most common pattern among individuals, because closing gains early and holding losses comes naturally.
• A bad decision with a good outcome is more dangerous than a good decision with a bad outcome, because it reinforces the wrong habit.

Related: what "risk" really means · how to read a full event · what each indicator measures and how people fool themselves