Expectancy, Sharpe and Sortino: the metrics beyond win rate

Win rate tells you how often you are right. It tells you nothing about whether you are making money. These three numbers close that gap — one answers "does this strategy work?", the other two answer "was the return worth the risk?"

Expectancy: does this strategy make money at all?

Expectancy is the average amount you expect to win or lose per trade, over many trades. In its usable form:

Expectancy = (Win% × Average win) − (Loss% × Average loss)

A worked example. Say 100 trades: you win 40 of them for an average of $300, and lose 60 for an average of $150.

• Wins: 0.40 × $300 = $120
• Losses: 0.60 × $150 = $90
• Expectancy = $30 per trade

A 40% win rate, and the strategy makes $30 every time you press the button. That is the whole reason win rate in isolation is misleading: it ignores the size of the wins relative to the losses, which is the part that decides your account balance.

Flip it around and the point lands harder. Win 70% of the time at $100 a win, lose 30% at $250 a loss: expectancy is $70 − $75 = −$5. You are right more than twice as often as you are wrong, and you are still going broke.

Positive expectancy is the minimum bar a strategy has to clear. Everything else — position sizing, psychology, execution — only matters if that number is above zero, because size multiplies expectancy and multiplying a negative gets you there faster.

Why isn't expectancy enough?

Because it says nothing about the path. Two strategies can both return 20% a year while feeling completely different: one grinds upward, the other gains 60%, gives back 40%, and gains it again. Same destination, and only one of them is survivable — you can respect a drawdown on a spreadsheet and still abandon the plan in the middle of it.

Risk-adjusted metrics exist to put a number on that difference.

Sharpe ratio: return per unit of volatility

The Sharpe ratio divides your return (above a risk-free rate) by its standard deviation — how much your results bounce around. Higher is better: more return for the same turbulence, or the same return with less.

Its useful function is comparison. A strategy returning 15% with a Sharpe of 1.5 is a better piece of work than one returning 20% with a Sharpe of 0.5, because the second is taking far more risk to get there and is far more likely to have got there by luck.

Its flaw is straightforward: standard deviation treats upside and downside as the same thing. A month where you unexpectedly gain 15% hurts your Sharpe exactly as much as one where you lose 15%. As a measure of "risk", punishing good surprises is odd.

Sortino ratio: the same idea, downside only

The Sortino fixes precisely that. It uses the same structure but divides only by downside deviation — the volatility of losing periods.

For a trader that is usually the more honest number, because what actually threatens you is not variability, it is loss. A strategy with occasional large gains and small controlled losses can look mediocre by Sharpe and excellent by Sortino, and the Sortino is describing your experience better.

How do you use them without fooling yourself?

Three cautions, and they matter more than the formulas:

• Sample size first. All three metrics are estimates. Computed on 20 trades they are noise; you need a real sample before the number means anything, and a backtest that only covers one market regime is not a real sample.
• Expectancy before ratios. If expectancy is negative, no Sharpe will save you. Get that number positive, then optimise how smoothly you earn it.
• Track them from your own trade log, not from a backtest. Backtested metrics measure your rules. Live metrics measure you following them, and the gap between those two is where most strategies actually fail.

The takeaway

Win rate is the metric that feels best and tells you least. Expectancy tells you whether the edge exists; Sharpe and Sortino tell you what it cost you to collect it. Get expectancy above zero first — the rest is refinement on top of something that already works.