The Only Number That Pays
EXPECTANCY
WHAT ONE MORE TRADE IS WORTH
In plain EnglishExpectancy is what one trade is worth on average once all the wins and losses are added up. If it is above zero, the strategy makes money over many trades. If it is below zero, nothing else can save it.
Expectancy is the average R a system earns per trade across a large sample. Positive, and every trade you take is worth something before it starts, even the ones that lose. Negative, and no amount of discipline, psychology or position sizing will save the account. It only decides how slowly it goes.
Expectancy = (win rate × average win in R) − (loss rate × average loss in R)
Notice what is not in the formula. Win rate alone is not there, and neither is the biggest winner you ever had. A system can win 40% of the time and make money if its wins are large enough, and a system can win 70% of the time and bleed if its losses are larger still. The two halves only mean something together.
Here is the published CAP book taken apart the same way, because a formula is easier to trust when you can watch it resolve on real figures. The four-book walk-forward test returned a 66.3% win rate on n=6,147. The average win across the 4,076 winners was +1.028R. The average loss across the 2,071 losers was −1.153R.
+0.682R in, −0.389R out, +0.293R kept. Every figure is from the published tables. Note the ugly one: the average loss is bigger than the average win. This edge does not come from big winners. It comes from winning often enough to beat a loss that is larger than the win. Backtested, not a live account.That last point is the one most trading education skips, so it is worth sitting on. A high win rate with a payoff below 1:1 is a legitimate edge, and so is a low win rate with a payoff of 3:1. They feel completely different to trade. The first wins most days and occasionally takes a loss that erases three wins. The second loses most days and occasionally pays for a month. Neither is better. What matters is that you know which one you are running, because the emotional failure mode of each is different.
Two more measures sit next to expectancy and are worth knowing by name. Profit factor is gross R won divided by gross R lost. The book's is 1.76. System quality, Van Tharp's SQN, is expectancy divided by the standard deviation of R, times the square root of the number of trades. It rewards a smooth edge over a lumpy one, which is exactly what a trader who has to live through the equity curve should want.