The Hidden Math Behind Every Winning Trade

From the outside, and among novice traders, there’s the widespread belief that trading is about predicting the future and being right. 

Call the top, buy the bottom, predict what happens next. 

Unfortunately, that mindset is why most traders have suboptimal results.

It rarely works out. Taking into account the edge institutional traders have, plus the transaction costs, psychology and emotions of it all, being highly tactical doesn’t generally lead to great results.

It’s far less glamorous: trading and making money in markets, more generally, is about math. And for the most part, simple math. 

Expected value, costs, probabilities. The math of a corner store, not a physics lab.

If you understand the hidden math behind every trade, you stop caring about being right once. 

You start caring about having some sort of edge over hundreds of trades. 

That’s the shift from taking a guess to running a business.

Key Takeaways – The Hidden Math Behind Every Winning Trade

• Treat every trade like a product with costs, margins, and returns.
• Always calculate expected value (EV) after all fees and slippage.
• Positive EV is meaningless if you size too big because losses happen and you can never allow unacceptable losses.
• Edge only shows up over many trades, not one lucky win.
• Diversify across strategies with low correlation to better smooth results over time.
• Correlations can spike in the left tails of distributions (i.e., crises). Stress test for worst cases.
• Track a small dashboard: EV, win/loss size ratio, drawdown, Sharpe, costs.
• Survival is the first KPI. Profit comes second.

Trading is a Business, Not a Bet

Think of every trade as a product on the shelf. You’re the shop owner.

That product has a cost to acquire, a margin, and a return rate.

Sometimes customers love it, sometimes they return it.

What matters is not whether one SKU flies off the shelf, but whether your store makes money across all SKUs over time.

In trading language:

• Acquisition cost = commissions, spreads, slippage, borrow fees.
• Average order value = the size of your average win.
• Return rate = how often the trade fails.
• Contribution margin = what’s left after costs.

That’s unit economics. Every trade is a unit. If your unit economics are positive, your trading business can survive and grow.

If they’re negative, no amount of hope or “conviction” will save it.

The Heartbeat: Expected Value

Here’s the single question every winning trader asks: What is the expected value of this trade? 

Expected value (EV) is the average outcome if you repeated this trade a thousand times.

The formula is simple:

EV = (probability of win × average win) − (probability of loss × average loss) − costs

Example: let’s say your strategy wins 45% of the time. When it wins, you make 2 times your risk (2R). When it loses, you lose 1R. Costs (fees, slippage, spread) equal 0.05R.

EV = (0.45 × 2R) − (0.55 × 1R) − 0.05R
EV = 0.90R − 0.55R − 0.05R
EV = +0.30R

That’s thirty cents of edge for every dollar of risk. In business terms, your store makes thirty cents of profit for every dollar of inventory you put on the shelf. That is the math that compounds.

Transaction Costs

Transaction costs are the silent tax on every trade. 

They include commissions, borrow fees, and slippage, but the bid-ask spread is often the biggest. 

If you buy at the ask and sell at the bid, you instantly lose the spread. 

For active traders, this cost adds up. 

A strategy that looks profitable on paper can turn negative once spreads are factored in. 

They’re especially important for day traders because the size of their wins tend to be small relative to the spread they pay because the timeframe is so short.

Wider spreads also mean worse liquidity; you pay more to get in and out. 

Smart traders always subtract transaction costs from expected value before deciding if a setup is worth taking.

Averages Hide the Ride

Expected value tells you if you have an edge. But it doesn’t tell you what the ride feels like. That’s where variance comes in.

Imagine two shops:

One sells coffee beans.

Customers come every morning, steady demand, steady profit.

The other sells fine art.

Sometimes a painting sells for $50,000. Sometimes nothing sells for months.

Both businesses could have the same average monthly profit. But one feels like a calm river, the other can have long dry periods.

Trading is the same. Two systems can have the same EV but very different swings.

A system with small wins and rare big losses might look good on paper, but it can crush you emotionally and financially if you size it wrong.

Variance matters. Survival matters.

Position Sizing: The Price Tag on Risk

Even with positive EV, you can blow up if you bet too big.

That’s why casinos don’t let a single player put the entire house at risk in one spin of the wheel. They cap bet sizes for prudent risk management purposes.

It’s a very good idea to cap yours too.

The cleanest framework is called Kelly sizing. In short, it tells you what fraction of your bankroll to bet for maximum growth, based on your edge and variance.

The formula is:

Kelly Percentage = bp – q / b

Where:

• p is the probability of a winning bet,
• q is the probability of losing (q = 1 − p),
• b is the odds received on the bet (not the probability), defined as the potential winnings divided by the amount wagered.

The catch is that full Kelly is way too aggressive.

For example, let’s say you’re 60/40 (right/wrong) on 50/50 pricing ($1 if right/$1 if wrong).

Step 1: Write out the Kelly calculation

Kelly = (b × p – q) ÷ b

Here, b = 1, p = 0.6, q = 0.4.

Step 2: Plug in the numbers

Kelly = (1 × 0.6 – 0.4) ÷ 1
Kelly = (0.6 – 0.4) ÷ 1
Kelly = 0.2

Step 3: Interpret the result

That means the Kelly formula says bet 20% of your bankroll each round.

That’s a lot, and we’d argue too much.

It maximizes long-term growth but also guarantees some terrible drawdowns that you don’t want.

That’s why most professional traders are aware of the concept – i.e., bet more when you have more conviction relative to what’s discounted in the price. 

But essentially use fractional Kelly. Half Kelly, quarter Kelly, or even single-digit percent Kelly.

It’s like stocking half your warehouse with your best-selling SKU. Enough to benefit, not enough to sink you if demand shifts (e.g., you’re selling jackets but the weather warms up faster than expected and you’re stuck paying fees to store inventory that can’t be moved).

Think of sizing like inventory management. Even if a product prints great margins, you don’t buy so much that one bad season bankrupts the store.

Edge Shrinks With Size

Here’s the boring truth: the bigger you trade, the thinner your edge becomes.

Your costs rise, fills worsen, borrow fees creep up, and your orders start moving the market.

It’s not generally something you have to think about right away, but it can still occur at even millions of dollars in portfolio size, depending on your markets.

It’s not unlike ad spending in business.

Your first $1,000 in ads might bring in customers at a great return if your product/service makes sense. Your next $100,000? Diminishing returns kick in.

If your system makes +0.30R per trade at small size, maybe that drops to +0.20R or +0.12R when you scale. That’s capacity limits kicking in. Every business has it.

The Law of Large Numbers

A winning business shouldn’t live or die on one customer or one sales channel.

Edge plays out only through repetition.

If your system has a Sharpe ratio of 1 (i.e., risk-adjusted return), you might need hundreds of trades – or simply time – to confidently see your edge in the numbers. That’s the math of sample size. Small samples won’t generally give you great results. Big samples reveal what the results genuinely are.

A rule of thumb: the number of trades or the amount of time you need grows with the square of volatility relative to return. Translation: the noisier your system, the more trades you need before you can trust your results.

For example, let’s say you simply index to the S&P 500. The earnings yield plus growth is likely to be a single-digit percentage over time – i.e., the long-term return – while the volatility of the index tends to average around 15-16% long-term.

You will generally need at least a year, if not more, to draw reasonable conclusions.

Diversification: Multiple Shelves, Same Store

You wouldn’t open a store that only sells umbrellas. Great margins when it rains, but dead silent when it’s sunny.

Smart shop owners diversify product lines. The same principle makes a trading business resilient.

The magic happens when you combine uncorrelated edges.

Suppose you run two strategies, each with the same EV.

If they move in sync, your portfolio is just a bigger version of one. If they move differently, your swings smooth out without killing returns.

Portfolio volatility depends not just on the variance of each strategy, but also their correlation.

If two systems are highly correlated, the portfolio still swings hard. If they’re weakly correlated, the swings shrink even though the EV adds up.

Example

Say you have two strategies with equal risk.

We have two strategies. Each has the same volatility. We give them equal weight, fifty percent each.

The formula for the combined portfolio volatility compared to one strategy alone works out to:

Portfolio volatility ÷ single-strategy volatility = square root of (1 + correlation) ÷ 2

Now let’s plug in numbers.

If correlation = 0.8

• Take 1 plus 0.8 = 1.8
• Divide 1.8 by 2 = 0.9
• Take the square root of 0.9 = 0.95

So the portfolio volatility is about 95% of one strategy alone.

If correlation = 0.2

• Take 1 plus 0.2 = 1.2
• Divide 1.2 by 2 = 0.6
• Take the square root of 0.6 ≈ 0.775

Accordingly, the portfolio volatility is about 77.5% of one strategy.

If correlation = 0.0

• Take 1 plus 0.0 = 1
• Divide 1 by 2 = 0.5
• Take the square root of 0.5 ≈ 0.707

So the portfolio volatility is about 70.7% of one strategy alone.

Of course, it gets better the more uncorrelated the returns streams and the more you’re able to put into a portfolio.

When Correlation Lies

Correlations aren’t fixed.

They’re essentially fleeting byproducts of how assets interact in their particular environment.

They stretch and snap, especially in stress. Two strategies that looked independent can suddenly sink together when liquidity dries up.

It’s like thinking sunscreen sales and umbrella sales are uncorrelated. Then a shipping bottleneck delays both containers. Or a drop in the broader economy causes both sales to slump since many view these items as discretionary. Suddenly, both lines are down at once.

That’s why you stress test. Check how your portfolio behaves if correlations spike in a crisis. Better to find out in your pre-deployment testing than in your P&L in real markets.

Unit Economics for Traders

Before scaling a strategy, you need the same checklist a startup uses:

• Acquisition cost: spreads, fees, slippage
• Average basket: average win size
• Gross margin: EV before fixed costs
• Contribution margin: EV after borrow and financing
• Inventory turns: how many trades per year
• Payback period: how many trades/how much time to recover a drawdown
• Churn: edge decay, signal half-life
• Capacity: size where EV flips negative

That’s your trading P&L. If those numbers work and you can execute it, you have a business.

If they don’t, or don’t know for sure, keep testing.

Survival First

The first KPI of any trading business is survival. Profit comes second.

That means managing drawdowns, capping risk per trade, and cutting size when things go south.

If something in your portfolio were to go to zero, is that still a manageable drawdown? 

Regimes: Seasons in Your Business

Markets move in regimes, just like businesses move in seasons. Summer tourists, winter slowdowns.

In trading, it might be trending markets, range-bound chop, or high-volatility shocks.

A strategy that thrives in one regime can bleed in another. Different assets act differently.

We’ve talked in other articles about how stocks do well in times of growth and managable/low inflation, safe government bonds do well in times of deflation, gold tends to do well when real rates fall, cash does best when money and credit are tight.

If your strategy is built for calm seas, there’s a period when it won’t work and you have to plan accordingly.

Businesses adjust to seasons. Traders should too.

Measurement That Matters

Focus on the few numbers that actually guide decisions:

• EV per trade (Even for indexers, this is the earnings/income generated by the underlying asset mix over a certain period of time.)
• Hit rate
• Win-to-loss size ratio
• Average holding time
• Trades per year
• Cost per trade
• Sharpe ratio
• Max drawdown
• Correlation between strategies/assets

A Mini Case Study

Take a breakout system. It wins 38% of the time. Average win is 2.6R. Average loss is 1R. Costs are 0.1R.

EV = (0.38 × 2.6R) − (0.62 × 1R) − 0.1R
EV = 0.988R − 0.62R − 0.1R
EV = +0.268R

Now pair it with a mean-reversion system. It wins 58% of the time.

Average win is 1.2R. Average loss is 1R. Costs are 0.08R.

EV = (0.58 × 1.2R) − (0.42 × 1R) − 0.08R
EV = 0.696R − 0.42R − 0.08R
EV = +0.196R

Each has positive EV. They work in different regimes. They’re weakly correlated.

Combined, they not only lift average EV, they smooth the ride.

That way, it can be easier to have the business you want: resilient, scalable, repeatable.

The Playbook

Here’s the math boiled down:

1. Compute expected value after all costs.
2. Size positions well below Kelly. Live to fight another day.
3. Track variance and drawdowns. Survive the ride with realistic expectations.
4. Diversify with low-correlation strategies.
5. Stress test correlations in crisis.
6. Measure unit economics like a business.
7. Keep a one-page dashboard. Cut noise, focus on edge.

That’s it. Not prediction, just basic math and discipline. The same math that keeps corner stores alive is not all unlike the math that builds trading businesses.