Trading Expectancy: Why Win Rate Isn't Enough

Step 5 of 6 in Trading Foundations.

Win rate is the number traders quote and the number that means least on its own. A 90% win rate loses money if the 10% of losses are large enough. Expectancy is the number that settles it: what one trade is worth, on average, over a large sample.

The formula

Expectancy = (win rate × average win) − (loss rate × average loss)

Expressed in R multiples — where 1R is the amount risked per trade — the average loss is 1R by construction, and the formula simplifies to:

Expectancy (R) = (win rate × average win in R) − loss rate

A strategy winning 45% of the time with an average win of 2R:

(0.45 × 2) − 0.55 = 0.90 − 0.55 = +0.35R

Every trade is worth 0.35R on average. Risking $100 per trade, that is $35 per trade — $3,500 over 100 trades, whatever order the wins and losses arrive in.

Very different strategies, similar expectancy

The scalping row is the cautionary one. A 70% win rate sounds excellent and produces a barely positive 0.05R — an edge thin enough that commission and slippage can erase it entirely. Meanwhile the trend-following row loses 7 trades in 10 and makes four times as much per trade.

What expectancy has to clear

Positive is not the bar. Costs are.

Every trade pays spread, commission and slippage. On liquid instruments that is often 0.02–0.05R; on wider markets or with a tight stop it can exceed 0.2R. Subtract it:

Net expectancy = gross expectancy − cost per trade

The 0.05R scalping strategy above, paying 0.04R in costs, nets 0.01R — which after a bad week of slippage is zero. The 0.35R swing strategy loses barely a tenth of its edge to the same costs. A thin edge is fragile in proportion to how thin it is.

This is also why increasing frequency is not automatically good. Doubling the trade count doubles the gross edge and doubles the costs.

How many trades before you believe the number

Expectancy computed over 20 trades is noise. A strategy with a genuine +0.2R edge routinely produces stretches of 20 trades that look negative, and a strategy with no edge produces stretches that look brilliant.

As a working guide:

• Under 30 trades — no information. Do not adjust anything.
• 30–100 trades — a direction, not a number. Useful for spotting the obviously broken.
• 100–300 trades — a usable estimate, still with a wide error band.
• 300+ — trustworthy, provided market conditions have not changed underneath the sample.

Lower win rates need bigger samples. A 30% win-rate strategy takes far more trades to distinguish from noise than a 70% one, because the wins that carry it are rarer.

From expectancy to position size

Once expectancy is positive and measured, the Kelly criterion gives the mathematically growth-optimal fraction of capital to risk:

Kelly % = (win rate × (payoff + 1) − 1) ÷ payoff

At a 55% win rate with a 2:1 payoff, Kelly returns 32.5% — a number no sane trader should use. Full Kelly assumes your win rate and payoff are known exactly, and produces drawdowns over 50% even when they are. Most practitioners run a quarter to a tenth of Kelly, which lands back in the familiar 0.5%–2% range.

Kelly's real value here is as a warning system. Feed it a 30% win rate with a 2:1 payoff and it returns a negative number — the arithmetic telling you the strategy has no edge to size.

Tracking it honestly

Expectancy is only as good as the log behind it. Three habits keep it real:

1. Record the planned R at entry, before the outcome is known. Working backwards from results is how strategies get flattered.
2. Include every trade — the ones closed early, the ones you should not have taken, the ones where the platform froze. Excluding "unrepresentative" trades is how a losing system looks profitable on paper.
3. Segment before you conclude. Expectancy by setup type, by session, by day of week. A flat overall number often hides one profitable setup subsidising two that lose.