Expectancy: why win rate alone tells you little

What is trading expectancy?

Expectancy is the average result of one trade, measured over many trades. It answers a plain question: if these rules keep behaving the way they did, what does one more trade add or take away, on average?

It needs three numbers, each measured after fees and slippage:

• Win rate: the share of trades that made money.
• Average win: the average profit on the winning trades.
• Average loss: the average loss on the losing trades, written as a positive number.

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

The loss rate is simply one minus the win rate.

Worked example: Strategy A and Strategy B

Step by step for Strategy A: 35% of trades pay $500, which is worth $175 per trade on average. The other 65% lose $150, which costs $97.50 per trade. The difference, +$77.50, is what one trade is worth on average.

Strategy B wins almost two trades in three and still loses money: −$5.00 per trade. Each loss is twice the size of each win, so it needs to win more than 66.7% of the time just to break even. The break-even win rate is the average loss divided by the sum of the average win and the average loss.

Expectancy in R: the same idea without the dollars

Many systematic traders state results in R, where 1R is the amount a trader plans to risk on one trade. Trading educator Van Tharp, who made the idea popular, defines expectancy as "the average R-multiple that your system will give you per trade" [1].

In Strategy A, 1R is $150. The average win is $500 ÷ $150 = 3.33R, and the expectancy is $77.50 ÷ $150 = +0.52R. In plain words, each trade has added about half of what it put at risk, on average. R makes strategies with different trade sizes comparable.

The casino comparison, and where it stops

A European roulette wheel has 37 pockets. On a bet on red, the player wins on average 18 times in 37 and loses 19, so the house keeps about 2.7 cents of every dollar bet [2]. The casino has no idea where the next spin lands. It relies on a small, known edge repeated many times.

The comparison stops in one place: a casino knows its edge exactly, because the edge is built into the wheel. A trader only has an estimate from past trades, and that estimate can be wrong. The rest of this article is about how wrong.

How many trades does it take to trust the number?

For a large edge, it takes fewer trades than many traders expect; for a thin edge, it takes far more.

Every trade in Strategy A ends at +$500 or −$150. That spread is large next to the $77.50 average. In this two-outcome model, the typical swing of one trade is about $310. Averaging many trades shrinks that noise, but slowly: after 20 trades the measured average typically sits within about $69 of the true value, after 100 within $31, and after 500 within $14. Statisticians call the typical spread of these measured averages around the true value the standard error.

A simulation shows how this plays out: it runs Strategy A 10,000 times, 500 trades each, with every number held fixed.

Even a strategy with a real +$77.50 edge shows a net loss after 10 trades 26.2% of the time, and after 20 trades 11.8% of the time. After 100 trades that falls to 0.7%.

The win rate is uncertain too

A measured win rate is itself an estimate from a sample. A widely cited statistics paper recommends the Wilson interval for proportions like this, because the common textbook formula behaves badly on small samples [3]. For a strategy that won 35% of its trades:

• over 20 trades, the true win rate could plausibly be anywhere from 18.1% to 56.7%;
• over 100 trades, from 26.4% to 44.7%;
• over 500 trades, from 30.9% to 39.3%.

Strategy A breaks even at 23.1%. After 20 trades, the plausible range still includes losing versions of the same strategy. After 100, holding the average win and loss fixed, it no longer does.

Trades needed depends on the size of the edge

A flat rule such as "100 trades is enough" leaves out the main factor: how big the edge is next to the noise. Halve the edge and it takes roughly four times as many trades to see it. Keep Strategy A's $500 average win and $150 average loss, and change only the win rate:

The table estimates how many trades are needed for the true edge to equal about two or three standard errors; a measured average still varies from sample to sample. A t-statistic counts how many estimated standard errors a measured average sits above zero, and about two is the usual 95% yardstick for a large sample. In research on newly discovered stock-return factors, Harvey, Liu and Zhu argue for a t-statistic above 3.0, because many factors have already been tested on the same data [4].

A big edge shows itself quickly, while a thin one can need thousands of trades. A strategy tested many ways before one version was picked also faces a stricter bar, which is the subject of the next volume.

Professional allocators use the same logic for track records. Bailey and López de Prado define a "minimum track record length" needed before a measured edge can be trusted, and note that it fits "practitioners' standard practice of requiring similar lengths during the due diligence process" [5].

How long can a losing streak get when nothing is wrong?

Longer than intuition suggests, even when the rules and the market behave exactly as they did in testing.

Strategy A loses 65% of the time. Over 100 trades, the median longest losing streak is 9 trades, and a streak of 10 or more happens in 36.8% of cases. Over 500 trades, the median longest streak is 12. A streak of 10 or more shows up in 91.3% of cases, and a streak of 15 or more in 23.6%. These are exact probabilities for independent trades, computed for this article.

Mathematician Mark Schilling gives a quick estimate of the longest run from just two inputs: the number of trades and the chance of a loss [6]. With 500 trades and a 65% loss rate, it gives about 12. He also notes that the longest run is "much more likely" to be well above that estimate than well below it [6].

Drawdowns follow the same pattern. Across the 10,000 simulated runs, all with the same +$77.50 edge, the median deepest fall over 500 trades was $2,250, or 15 average losses, and one run in 20 fell $3,550 or more.

Experienced practitioners plan for this kind of variation in advance. Writing in 2026 about a strategy with a long record, quant trader Kris Longmore notes that it "can easily be underwater for two years or more without anything being 'broken'", and that "you just can't know if it's stopped working from a year or two of lousy P&L". His remedy is to "set expectations in advance" [7].

What the research says

• Expectancy is the average R per trade. Van Tharp defines it that way and shows a system that is right only 30% of the time earning 3.8R per trade on his example numbers [1].
• Small samples need better intervals. Brown, Cai and DasGupta (2001) show that the standard textbook interval for a proportion has "chaotic coverage properties" and recommend the Wilson interval for small samples [3].
• Testing many ideas raises the bar. Harvey, Liu and Zhu (2016) argue that newly discovered stock-return factors need a t-statistic above 3.0 after extensive multiple testing [4].
• Track records need a minimum length. Bailey and López de Prado (2012) show that the required length grows as the measured edge shrinks, as unusually large losses become more prominent, or as extreme outcomes become more common, with other inputs held fixed [5].

Common mistakes

• Reading win rate alone. Strategy B wins 65% of its trades and loses $5.00 per trade. Win rate means little without the size of wins and losses.
• Leaving out costs. Expectancy before fees and slippage describes results no trader could actually get. Thin edges are the most exposed.
• Judging after a handful of trades. After 20 trades, a real +$77.50 edge can look like anything from −$52.50 to +$207.50 per trade.
• Treating a long losing streak as proof of failure. For Strategy A, a run of 12 losses over 500 trades is the median outcome when nothing has changed, so on its own it says little.
• Quoting an unsourced benchmark. Popular rules such as "0.25R is good" or "100 trades is enough" ignore the size of the edge next to the noise.