A high win rate is not an edge

Win rate is the most intuitive statistic a strategy produces and among the least informative. It is the probability of a positive outcome, and it says nothing about the magnitude of outcomes on either side. A strategy can be right ninety percent of the time and lose money steadily, and the fact that this is arithmetically obvious does not stop it being one of the most common ways research goes wrong.

The arithmetic, stated once

Expectancy is the probability of winning multiplied by the average win, less the probability of losing multiplied by the average loss. Win rate is one of four terms, and it is the only one most people quote.

A strategy winning ninety percent of the time with an average win of one unit and an average loss of twelve units has an expectancy of negative three tenths of a unit per trade. A strategy winning thirty percent of the time with an average win of five units and an average loss of one unit has an expectancy of positive one half. The second is the better business and will feel considerably worse to operate.

That asymmetry is not incidental. It is the central fact about the class of strategies that produce high win rates.

Why high win rate strategies concentrate their losses

A high win rate is usually manufactured, structurally, in one of three ways, and each carries the same tail.

Wide stops and narrow targets. Taking a small profit quickly and allowing losses room to recover raises win rate mechanically. Each individual decision is defensible and the aggregate is a strategy whose losses are, by construction, several times its wins.

Short optionality. Selling options, selling volatility, or any position that collects a premium in exchange for accepting a contingent liability produces frequent small gains and infrequent large losses. The win rate is high because most days nothing happens, which is what the premium was paid for.

Mean reversion without a regime filter. Fading moves works until it does not, and the occasion on which it does not is a trend. The distribution is many small reversions and occasional large runs against the position.

In all three the win rate is high because the loss distribution has been pushed into the tail, not because the strategy is more often correct in any useful sense. Reporting the win rate as evidence describes the shape of the payoff and presents it as a measure of skill.

The evaluation problem this creates

The consequence for research is severe and is a sample-size problem rather than an arithmetic one.

If losses arrive in one trade in twenty, then a hundred trades contain about five loss events. The average loss is estimated from five observations, and the variance of that estimate is enormous. The strategy's entire expectancy depends on a quantity known with almost no precision, while the win side, estimated from ninety-five observations, is known well.

The reported expectancy therefore looks stable while resting on the least stable input. In sample the strategy appears consistent, and remains so until a period arrives with three loss events instead of one. Nothing has changed except the realisation of a random variable that was never adequately measured.

This is the curvature argument from the firm's method in a concrete form. The likelihood surface for the average loss is nearly flat because so few observations inform it. A flat surface means the parameter was not identified, and an expectancy computed from an unidentified parameter carries the same uncertainty whether or not the point estimate looks reassuring.

The equity curve compounds the illusion

A high win rate produces a smooth ascending equity curve punctuated by discontinuities. Over any window not containing a discontinuity it appears excellent by every conventional measure: a high Sharpe ratio, a small maximum drawdown, a high proportion of profitable months.

Every one of those measures is estimated from the same sample that omits the tail. They are not independent confirmations. They are the same missing information reported five ways, and their agreement is guaranteed rather than evidence.

Live, the failure is characteristically sudden. The strategy performs to expectation for months and gives back a large multiple of its accumulated gains in a short period. The usual interpretation is that conditions changed. The more likely interpretation is that the distribution was always this shape and the sample had not yet included its tail.

What to report instead

Win rate is not useless. It is a description of trade frequency and psychological profile, and it should be reported alongside the things that determine whether the strategy makes money.

• Expectancy per trade, with a confidence interval from a bootstrap over trades rather than a standard error assuming independence.
• The payoff ratio, average win divided by average loss, which makes the asymmetry explicit and is the missing half of any win rate figure.
• The loss distribution, not its mean. Worst loss, the ninety-fifth percentile, and how many observations the tail estimate rests on. If that count is under twenty, say so, since it is the single most important number for interpreting everything else.
• Sensitivity to the tail. Recompute expectancy after removing the largest win, and after doubling the largest loss. A result that inverts under either is resting on a handful of observations regardless of how many trades were taken.
• Time to ruin under the estimated distribution, which converts an abstract tail into an operational question about whether the position can be held long enough for the expectancy to be realised.

The general form

The underlying error is not specific to win rate. It is reporting a statistic that is easy to estimate in place of one that is hard, because the easy one is stable and the hard one is not.

Frequency of being correct is easy to estimate and nearly irrelevant. Magnitude of being wrong is hard to estimate and decides everything. A research process that reports the first prominently and the second in a footnote has arranged its presentation in inverse order to the importance of its contents, and will keep producing strategies that work until they do not.