Expressing every trade in common risk units so results from different instruments and account sizes can be compared.
Normalisation is what makes a track record legible. A $180 gain in gold and a $180 gain in a small-cap are the same number and completely different trades; expressed as r-multiples - +0.6R and +1.8R - they can finally be added together.
In practice you normalise twice. Size is normalised on the way in, so each trade risks a comparable fraction of equity (unit-sizing or fixed-fractional-sizing). Results are normalised on the way out, by dividing every profit and loss by that trade's initial risk to build an r-distribution.
Without it, portfolio statistics are noise: expectancy is dominated by whichever instrument you happened to trade biggest, and a single oversized winner makes a losing system look profitable.
Original diagrams for the ideas on this page. Illustrative, not real market data.
Expectancy: the average trade. Forty trades sorted by outcome: 24 small losses and 16 larger wins. Weighting each side by how often it happens gives the average result per trade, marked here by the dashed line at +$120.Working out a position size. Three numbers decide how big a trade is: the account, the share of it put at risk, and the distance from entry to stop. One percent of $25,000 is a $250 budget, and a $0.50 stop divides into that 500 times.
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