Why a 30% win rate can beat a 90% win rate: understanding expected value

A trader posts a strategy with a 90% win rate and calls it proven. A few weeks later, one unmanaged loss on the tenth trade wipes out every gain the other nine produced. The strategy did not get unlucky. It was never measured on the number that determines whether it is profitable.

Win rate answers how often a rule is right. It says nothing about how much is won or lost when it is right or wrong. This post sets out how expected value combines the two into a single figure, what that figure does and does not capture, and where a report has to show it alongside win rate rather than in place of it.

The problem

A win rate is a count. It treats a trade that returns a small amount the same as a trade that returns a large one, as long as both are wins. Ten trades with nine wins and one loss produces a 90% win rate whether the wins are tiny and the loss is enormous, or the reverse.

That is precisely the gap a trader chasing a high win rate falls into. Strategies that win often tend to do so by taking small, frequent gains and capping risk loosely, or not at all, on the rare trade that goes wrong. The result looks reliable on a scorecard that only counts outcomes, right up to the trade where the uncapped loss arrives.

The reverse is also true, and less intuitive. A rule that is wrong most of the time can still be profitable, if what it wins when it is right comfortably outweighs what it loses when it is wrong, in proportion to how often each happens. Judging a strategy by win rate alone throws away exactly the information needed to tell these two cases apart.

How it works

Expected value is the average outcome per trade, calculated from four inputs: how often a trade wins, how much it wins on average, how often it loses, and how much it loses on average.

The formula

$$\text{EV} = (p_w \times \bar{W}) - (p_l \times \bar{L})$$

Here $p_w$ is the win rate, $\bar{W}$ is the average win, $p_l$ is the loss rate, and $\bar{L}$ is the average loss. Because a trade can only win or lose, $p_l = 1 - p_w$. The formula weighs each side by how often it occurs, then nets one against the other.

A worked example

Take a rule that wins 30% of the time. Its exits are asymmetric by design: a winning trade returns $300, a losing trade is cut at $100.

$$\text{EV} = (0.30 \times \$300) - (0.70 \times \$100) = \$90 - \$70 = \$20$$

The rule is wrong on seven trades out of ten, and the average outcome per trade is still positive. Nothing about that result depends on predicting which seven trades will lose. It depends only on the ratio between how big the wins are and how big the losses are being allowed to get, relative to how often each occurs.

Flip the asymmetry and the same win rate turns negative. A 30% win rate paying $100 a time against a $300 loss the other 70$(0.30 \times $100) - (0.70 \times $300) = -$180$. Same win rate, opposite sign, because the sizes moved.

What it means for a backtest

A report that states win rate without also stating average win and average loss has stated a number that cannot be interpreted on its own. The table below is the worked example above, shown the way these figures need to sit together.

Illustrative figures, used to demonstrate the calculation, not a backtested result.

Read on its own, the 30% figure in the first row looks like a weak strategy. Read against the other four rows, it is the strategy that is actually worth funding. A report that prints win rate in isolation, or highlights it as the headline number, invites the reader to draw the first conclusion instead of the second.

What it does not tell you

Expected value is an average. It says what a trade is worth over a large number of repetitions, not what happens on any particular run of ten or fifty trades. A rule with a positive expected value can still produce a losing streak long enough to breach a drawdown limit or exhaust an account, because the calculation says nothing about how outcomes are sequenced.

It also assumes the win rate, average win and average loss observed in the past continue to hold. If the market regime that produced them changes, the inputs to the formula change with it, and a figure computed from history stops describing what comes next. Expected value is a statement about a set of trades that already happened, not a forecast.

Finally, the formula treats every trade as the same size. It says nothing about position sizing, so two strategies with an identical expected value per trade can carry very different risk of ruin once the size of each bet is accounted for.

How this shows up in a Taurus report

The headline metrics block in a Taurus report lists win rate next to average win, average loss and profit factor on the same line, so none of them can be read in isolation from the others. The plain-English read at the end of the report states directly whether the combination nets to a positive or negative average outcome, rather than leaving a reader to react to whichever figure is printed largest.

If a report you already have shows a win rate with no average win or average loss beside it, that is the figure to ask for before treating the win rate as meaningful on its own.