Written lesson
Lesson transcript
A trader wins seventy percent of their trades.
Another trader wins only thirty percent.
Who makes more money?
The answer might surprise you.
Because the seventy percent winner is going broke, slowly but surely. While the thirty percent winner is building wealth, one calculated bet at a time.
This is the paradox that separates systematic traders from gamblers. And it all comes down to one mathematical concept that most traders never truly understand.
Expected value.
In our foundation series, we've covered how much you can lose with the one percent rule. We've explored how much you should bet with position sizing.
Today, we answer the most fundamental question in trading: Is this bet worth taking in the first place?
Expected value is the probability-weighted average of all possible outcomes. In trading terms, it's what you would earn or lose on average if you repeated the same decision infinitely.
The formula is straightforward.
Let's make this concrete with an example.
Imagine a trading strategy with a sixty percent win rate. When it wins, it averages two percent profit. When it loses, it averages one percent loss.
The calculation: zero point six times two percent, minus zero point four times one percent.
That gives us one point two percent, minus zero point four percent.
Equals plus zero point eight percent.
This zero point eight percent is the strategy's expectancy. It means that over many trades, each bet is theoretically worth zero point eight percent of your capital.
Not just the winning trades. Every single trade.
Even the losses.
This is where the mathematics become profound.
Have you ever won most of your trades, but then a few losses suddenly erased the progress? Our strategist will reply with a framework that helps you move forward with more clarity.
Now let's look at the math behind why this happens.
Now here's where most traders go wrong.
They chase win rate. They want to be right. They want to feel successful on every trade.
But win rate alone is meaningless.
Let me show you why.
Strategy A has a seventy percent win rate. Sounds great, right? But when it wins, it makes fifty dollars. When it loses, it loses two hundred.
The math: seventy percent times fifty, minus thirty percent times two hundred.
That's thirty-five dollars, minus sixty dollars.
Negative twenty-five dollars per trade.
This trader wins seventy percent of the time and still loses money.
Now consider Strategy B. Only thirty percent win rate. Three out of ten trades lose.
But when it wins, it makes three hundred dollars. When it loses, only one hundred.
The math: thirty percent times three hundred, minus seventy percent times one hundred.
That's ninety dollars, minus seventy dollars.
Plus twenty dollars per trade.
This trader is wrong seventy percent of the time, and makes consistent profits.
This is the win rate paradox. It explains why the greatest traders in history often have surprisingly low win rates.
Trend followers typically win only thirty-five to forty-five percent of their trades. Yet they've generated billions in profits over decades.
Because their winners are three, four, five times larger than their losers.
The question isn't how often you win. It's whether your system has positive expected value.
And if this brought clarity,
So how do you know the minimum win rate you need?
There's an elegant formula. Breakeven win rate equals one, divided by one plus your reward-to-risk ratio.
With a one-to-one reward-to-risk, you need fifty percent to break even. Simple.
With two-to-one, you only need thirty-three percent.
With three-to-one, just twenty-five percent.
With five-to-one, only seventeen percent.
This is why asymmetric setups are so powerful.
Design your trades so that wins are multiples of losses, and suddenly you don't need to be right very often.
Michael Burry's famous bet against subprime mortgages exemplifies this. He was wrong for years, paying premiums, looking foolish.
But when he was right, the payoff was enormous.
His win rate was low. His expected value was astronomical.
Van Tharp, one of the foremost researchers on trading performance, introduced a framework that makes expectancy actionable.
He calls it R-multiples. R equals your initial risk per trade, the distance from entry to stop loss in dollars.
Every outcome gets expressed as a multiple of R.
You risk one hundred dollars, you lose one hundred, that's negative one R.
You risk one hundred dollars, you make two hundred, that's positive two R.
You make five hundred? Positive five R.
This standardization is powerful.
It removes dollar distortion. A one thousand dollar win on a hundred thousand dollar account means something different than on a ten thousand dollar account.
But a two R win is a two R win, regardless of account size.
Van Tharp's research revealed something remarkable.
Position sizing explains ninety percent of performance variation among professional traders.
Not entry signals. Not market analysis. Not prediction accuracy.
How they size positions based on their edge.
But here's the key: position sizing amplifies edge. It doesn't create it.
Without positive expectancy, no position size is optimal. You will eventually lose everything.
Van Tharp went further. He developed a metric called the System Quality Number, or SQN.
The formula: square root of the number of trades, times expectancy, divided by the standard deviation of R-multiples.
What does this capture?
Three dimensions. Is the system profitable on average? How consistent are the results? And how many opportunities does it generate?
The rating scale is brutally honest.
Below one point five: probably very hard to trade.
Two to three: good system.
Three to five: excellent.
Above seven: Tharp calls it Holy Grail territory. Almost never found.
Most traders overestimate their system's quality. Calculate your SQN honestly.
If it's below one point five, you don't have a position sizing problem. You have an edge problem.
Now, there's a critical bridge between theory and reality.
The Law of Large Numbers.
It states that as sample size increases, the average converges to the expected value.
This is the bridge. It's how theoretical edge becomes realized profit.
But it requires patience.
Ten trades? High variance. Meaningless statistically.
Thirty trades? Patterns emerge.
One hundred trades? Reasonable confidence.
One thousand trades? High-confidence expectancy manifestation.
This is why casinos always win. Not on any single bet. But across millions of bets, their edge becomes certainty.
We want to be the casino. Trade with positive expectancy. Size appropriately. Let the law work over sufficient sample size.
The danger is abandoning a winning system during an inevitable losing streak.
Even a system with sixty percent win rate will have sequences of five, six, seven consecutive losses. That's not failure. That's variance.
This brings us to the most profound reframe in trading psychology.
The invisible payout.
Alexander Elder said: Losses are an inevitable cost of doing business.
But most traders see losses as failures. As setbacks that push success further away.
From an expectancy perspective, that's fundamentally wrong.
If your system has positive expectancy, every rule-following trade moves you closer to success. Wins and losses alike.
Remember our earlier example? Plus zero point eight percent expectancy per trade.
That means every trade you take earns you an invisible zero point eight percent. Whether it wins or loses.
The winning trade makes it visible. The losing trade keeps it invisible. But both bank the edge.
This is the mindset shift that separates professionals from amateurs.
You don't ask: Did I win this trade?
You ask: Did I follow my positive-expectancy system?
When your system is always working, regardless of individual outcomes, trading becomes what it should be.
A systematic extraction of edge from market inefficiency.
We've now completed the foundation.
Video one: The one percent rule. How much can I lose. Survival.
Video two: Position sizing. How much should I bet. Growth optimization.
Video three: Expected value. Is this bet worth taking. Edge validation.
These three pillars form the complete foundation for systematic trading mastery.
Without positive expectancy, no risk management saves you. You're rearranging deck chairs on the Titanic.
Without proper position sizing, even positive expectancy gets destroyed by variance. You blow up before the math works.
Without risk management, one bad trade ends everything. Survival is the prerequisite.
All three work together. Expectancy creates edge. Position sizing optimizes it. Risk management protects it.
So here's your action step.
Calculate your last thirty trades. Determine your win rate, your average win in R, your average loss.
Apply the formula.
Is your expectancy positive?
If yes, you have edge. Now optimize with position sizing.
If no, stop trading that system. No position size fixes negative expectancy.
Trading isn't about predicting the future. It's about finding positive expectancy and exploiting it systematically.
We're building a community of traders who think exactly this way — probability over ego, discipline over impulse. Join us at risk1reward3.com. It's free. Think in odds. Act with discipline. See you in the next one.