R-Multiples & Expectancy
R-multiples and expectancy are the core accounting tools for judging whether a trading system actually has an edge. R-multiples normalize every trade outcome against the risk taken on that trade, so wins and losses become comparable across different stocks, position sizes, and price levels. Expectancy then averages those normalized outcomes to answer one question: over a large number of trades, does this system make or lose money per dollar risked? The framework is most associated with Van K. Tharp.
R-multiples
R is the initial risk on a trade — the dollar distance between the entry and the protective stop, per share, times shares (equivalently, just the entry-to-stop distance if you measure per share). If you buy at $100 with a stop at $95, then 1R = $5 per share.
Every outcome is then expressed as a multiple of R. Exit at $110 and the $10 gain is +2R. Get stopped at $95 and the loss is −1R. A trade that runs to $120 is +4R; one cut early at $97 is −0.6R. Because R standardizes results, a +2R win on a $20 stock and a +2R win on a $400 stock are equal contributions to the system, regardless of share count or capital deployed. This is what lets you compare and combine trades that look nothing alike in raw dollars.
Expectancy
Expectancy is the mean R-multiple per trade — the average amount you expect to make (or lose), per unit of risk, over many trades:
Expectancy (R) = (Win% × average win in R) − (Loss% × average loss in R)
A positive expectancy means the system has an edge: each trade, on average, returns more than the risk taken, and the equity curve trends up over a large sample. A negative expectancy means the system loses over time no matter how good individual trades feel — high win rate cannot save it. Expectancy near zero is a coin flip that fees and slippage turn into a slow loss.
Worked example
Take a swing system with a 40% win rate, where winners average +2.5R and losers average −1.0R (clean stop-outs at the initial risk):
Expectancy = (0.40 × 2.5) − (0.60 × 1.0) = 1.00 − 0.60 = +0.40R per trade
So despite losing 6 trades out of every 10, the system earns on average 0.40 of one risk unit per trade. If you risk $500 per trade (1R = $500), that is about +$200 of expected value per trade before costs. Over 100 trades, expected gain ≈ +40R ≈ $20,000 — but only as a long-run average, not a guaranteed path.
How it's used in practice
The power of R is that it lets you compare systems regardless of price or size. A low-priced momentum system and a high-priced mean-reversion system can be ranked side by side purely on expectancy in R. It also exposes the win-rate vs. payoff tradeoff: a system can be highly profitable at a 40% win rate if its winners are large multiples of its losers, while a 70%-win-rate system bleeds out if its rare losses dwarf its frequent small wins. There is no "good" win rate in isolation — only the combination of frequency and payoff matters, and expectancy is what collapses both into a single number. Van Tharp also pairs expectancy with opportunity (how often the system trades): a smaller per-trade edge that fires often can beat a larger edge that rarely triggers.
Strengths & limitations
Expectancy's strength is that it reduces an edge to one comparable figure and forces honesty about the win-rate/payoff tradeoff. Its limitations are real and matter with real money:
- It is a long-run average that needs a large sample. With a handful of trades the estimate is noise; one outlier winner can make a losing system look profitable. Reliable estimates need dozens to hundreds of trades.
- It says nothing about variance or drawdown. Two systems can share the same expectancy yet have wildly different equity-curve paths — one smooth, one with 40% drawdowns that would force you (or a risk model) to stop trading. Expectancy describes the destination, not the bumpiness of the road.
- It assumes the future resembles the sample; regime change can invalidate a historically positive expectancy.
For these reasons expectancy is paired with variance-aware measures (e.g. Van Tharp's System Quality Number, which folds in standard deviation and the square root of the trade count) rather than used alone.
System relevance
For Augustus and Cairn, R-multiples are the natural common currency for scoring any candidate system. Each strategy's historical and forward trades should be logged in realized R (exit-vs-initial-risk), then summarized as mean R (expectancy), win%, and average win/loss R over a stated sample size. Augustus should rank competing setups by expectancy in R rather than raw dollar P&L, refuse to act on samples too small to be statistically meaningful, and flag the standard deviation of R alongside the mean so Cairn can gate position size and portfolio heat on variance — not just on the headline edge. A high-expectancy system with punishing R-variance should score lower in confidence than its average alone suggests.