The trader's equation: win rate, risk, and reward

The equation

Here it is:

If the result is positive, the trade makes money over many repetitions. If it is negative, the trade loses money over many repetitions, no matter how good any single trade feels. That is the trader's equation. Everything in trading is downstream of it.

Notice the words "over many repetitions." The equation says nothing about the next trade. The next trade is a coin flip weighted by your edge. The equation only pays off across a sample. This is why one trade proves nothing and a hundred trades start to prove something.

You only control two and a half of the numbers

You control your risk. Your stop defines it. You mostly control your reward. Your target defines it, although the market decides whether the target gets hit. You do not control your probability. The market sets it, and you can only estimate it.

Beginners get this backwards. They obsess over probability, hunting for the setup that "always works." There is no such setup. Professionals obsess over the relationship between the three numbers, because that relationship is the only thing they can engineer.

The arithmetic nobody does

Fix your reward-to-risk ratio and the equation tells you the win rate you need to break even:

• Risk 1 to make 1: you need to win more than 50 percent.
• Risk 1 to make 2: you need to win more than 33 percent.
• Risk 1 to make 3: you need to win more than 25 percent.
• Risk 2 to make 1: you need to win more than 67 percent.
• Risk 3 to make 1: you need to win more than 75 percent.

Look at the last line. A trader using a wide stop and a tight target needs to win three trades out of four just to break even. Many beginners trade exactly this shape without knowing it. They take quick profits and let losers run to a distant stop. Their win rate is high, they feel skillful, and the account bleeds. The equation knew from the start.

There is no good and bad among these shapes. A 40 percent win rate with 2-to-1 reward is a positive equation. A 70 percent win rate with 1-to-2 reward is a negative one. The win rate alone tells you nothing. See statistical tools for the longer version of that warning.

Costs sit inside the equation

The equation above is the gross version. The market trades the net version. Fees, spread, slippage, and funding subtract from every win and add to every loss. So the honest equation is:

Costs hit small-target trades hardest. If your average win is 0.4 percent and your round-trip cost is 0.1 percent, costs took a quarter of every win before you started. This is why scalping fails for retail traders and why trade frequency is a cost, not an achievement. See trading styles.

The equation is why strategies exist

A discretionary trader estimates the three numbers by feel, trade by trade. Feel is unreliable, and it gets worse under stress. A systematic strategy is nothing more than a machine for taking the same bet repeatedly, so the equation can be measured instead of guessed.

That is what a backtest is for. It estimates your probability, your average win, and your average loss from history, with costs included. The single number that summarizes the result is expectancy: average profit per trade after costs. Expectancy is the trader's equation, measured.

If a backtest's expectancy does not comfortably clear zero, the strategy has no reason to exist. And measure it honestly. An equation estimated on the same data that was used to find the strategy is optimistic by construction. That problem has its own article. See overfitting.

What to do with this

Before any trade or any strategy, write down the three numbers you believe. If you cannot write them down, you do not have a trade. You have a feeling.

Never evaluate a win rate without its reward-to-risk ratio. Never evaluate a reward-to-risk ratio without its win rate.

Subtract costs first. The gross equation is fiction.

Judge over samples, never over single trades. A good trade can lose. A bad trade can win. The equation does not care about either one.

How Edgecraft handles this

Every Edgecraft backtest reports the parts of the trader's equation directly: win rate, average win, average loss, and expectancy after full costs. The numbers are computed with fees, spread, slippage, and funding already inside them, so the equation you read is the net one. If the equation is negative, the report says so, and no amount of equity-curve squinting will say otherwise.