What Expectancy Tells You That Win Rate Does Not

A record of nine small wins and one large loss can be a losing record. A record of three wins and seven losses can be a winning one. Win rate alone cannot distinguish between the two, because it discards the size of every outcome.

This is not an edge case. Strategies naturally cluster at opposite ends: some take frequent small gains and occasional large losses, others take frequent small losses and occasional large gains. Both can work and both can fail, and win rate ranks them in an order that has no relationship to which is which.

Expectancy is the win rate multiplied by the average win, minus the loss rate multiplied by the average loss. The result is the average amount a trade returns, taken over many trades.

Expressed in R - where one R is the amount risked on a trade - the formula becomes independent of position size, which is what makes results comparable across accounts and across time. An expectancy of 0.2R means the average trade returns a fifth of what it risked.

A positive expectancy is the minimum condition for a strategy to be worth trading. It is not a guarantee of anything over any particular sequence of trades, because expectancy is an average and averages say nothing about the path.

Commissions, spreads, financing and slippage are subtracted from every trade regardless of its outcome. An expectancy calculated from theoretical entry and exit prices describes a strategy nobody is actually trading.

For short-hold, high-frequency approaches these costs can consume the entire edge. The correct method is to compute expectancy from realised prices and realised fees, which is the number that describes what actually happened to the account.

Expectancy estimated from a handful of trades is dominated by whichever few outcomes happened to occur. A single large win in a sample of twenty can make a negative strategy look positive.

The problem is worse for approaches with a low win rate and large winners, because the outcomes that carry the entire result are rare by construction. A sample that contains none of them describes a losing strategy that is actually profitable.

This is the practical argument for keeping a journal with consistent record-keeping. Expectancy is a statistic, and a statistic needs a sample that was recorded the same way throughout - not a reconstruction assembled from memory after the fact.