Expectancy thinking

The Risk Management course teaches how to compute expectancy. This lesson is about what it does to your head once you actually believe it.

The number

Expectancy is the average result per trade in R, over a large sample:

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

A system that wins 45% of the time with an average win of +1.8R and an average loss of −1R has an expectancy of (0.45 × 1.8) − (0.55 × 1.0) = 0.81 − 0.55 = +0.26R per trade. Over 200 trades that is about +52R. With 1R at 0.5% of the account, that is roughly 26% before compounding, before costs, and before any tilt.

That arithmetic is not the interesting part. The interesting part is that a trader who genuinely holds this number in mind experiences trading completely differently from one who does not.

What it does to a single trade

If your expectancy is +0.26R, then the trade you are about to take is worth +0.26R to you, on average, before it happens. Not the +1.8R you hope for. Not the −1R you fear. Twenty-six hundredths of an R.

This reframes everything.

The loss is already priced in. A −1R loss is not a mistake or a setback. It is one of the 55 losses in every hundred that the expectancy already includes. You have not fallen behind; you are exactly where the average says you should be. There is nothing to get back.

The win is not a reward for being right. A +1.8R win is one of the 45. It does not mean you saw something, and it does not mean the next one is more likely to win. It is the system paying out on schedule.

Skipping a valid trade costs +0.26R. Not nothing, but small. Taking an invalid one, off-plan and oversized, has an expectancy that is negative and potentially large. The asymmetry is the whole argument for circuit breakers: missing a trade is cheap, forcing one is expensive.

Size is a multiplier on expectancy, not a way to change it. Doubling size on a trade doubles both the expected gain and the variance. It does not make the trade better. A tilted trader who sizes up to "make it back" is doubling a +0.26R bet and calling it a plan.

Key idea: Your next trade is worth its expectancy, not its best case or its worst case. A loss is a scheduled cost of collecting the expectancy, and there is nothing to get back from it.

Mark Douglas and the twenty-trade sample

Douglas's most practical exercise, from Trading in the Zone, is to take a defined setup and commit to executing the next twenty occurrences of it at fixed size with no discretion at all, and to evaluate nothing until all twenty are done. The purpose is not to test the setup. It is to teach the trader, physically, that individual outcomes are random within a distribution and only the sample matters.

Traders who do this honestly report the same thing: somewhere around trade six or seven, the emotional charge of a single loss drops sharply, because the loss is obviously one of twenty and not an event in itself. That is what expectancy thinking feels like from the inside. It is not indifference; it is a shift in what counts as one unit of experience, from the trade to the sample.

Thinking in samples

An old poker line is that you do not play a hand, you play ten thousand hands. Translating that to trading:

• The unit of evaluation is not the trade. It is not the day. It is a block of trades large enough for the expectancy to show through the noise, and for most systems that is somewhere between 50 and 100 trades.
• Within a block, the only questions are execution questions (last lesson). Outcome questions are asked at the end of the block.
• A good block with a negative result is possible. A bad block with a positive result is possible. Neither tells you much on its own; it takes several blocks to see whether the system is what you think it is.

This is why the Risk Management course insists on 40 trades minimum before any sizing change. Below that, you are reacting to noise.

The dangerous half-belief

Many traders say they think in expectancy and do not. The test is what happens after a loss. A trader who half-believes will nod at the arithmetic and then take the next trade slightly larger. Their behaviour reveals that the loss registered as an event to be corrected, not as a scheduled cost.

Full belief is behavioural: the size on the ticket after a loss is identical to the size before it, and the trader does not have to force this. If you have to force it, you are still in half-belief, and the circuit breakers from Module 3 are there to hold the line until the belief catches up. That usually takes a few hundred trades of watching the sample behave as the arithmetic predicted.

Try it: Compute your A-trade expectancy from the last lesson's exercise. Write it on a card as "This trade is worth +0.__R." Put the card next to the order ticket. Before each entry, read it. After each loss, read it again and then read the size on the next ticket aloud. Do this for twenty trades and note in the journal at which trade the loss stopped feeling like an event.

Recap

• Expectancy is the average R per trade; a 45% win rate with +1.8R average win and −1R average loss gives about +0.26R per trade.
• A single trade is worth its expectancy, so losses are scheduled costs already included in the number, and there is nothing to get back.
• Skipping a valid trade costs one small expectancy; forcing an invalid trade costs a large negative one, which is why circuit breakers are cheap.
• Douglas's twenty-trade exercise teaches the sample as the unit of experience; most traders feel the shift around trade six or seven.
• The test of real expectancy belief is behavioural: identical size after a loss without forcing it.