Your Reward-to-Risk Ratio Does Not Change Your Expectancy
- Per-trade expectancy reduces to EV/risk = edge - cost/risk. Reward:risk cancels out of it entirely.
- That means moving your take-profit from 1:1 to 3:1 changes the SHAPE of your results — fewer, larger wins — but not what a trade is worth on average.
- It leaves exactly two levers: how much better than chance your signal is, and how large your friction is relative to the risk you take.
- The second lever is why timeframe decides more than tuning does. On our own measurements 1h directional trading is structurally unwinnable — costs exceed the entire gross edge — while at 4h costs still eat 30-70% of it.
- It also means trading rarely is correct behaviour on a thin edge rather than a bug. More trades on a break-even process is just more fees.
Most advice about reward-to-risk is about picking the right number: 2:1, 3:1, never take a trade below 1.5:1. Work the expectancy equation through and the ratio cancels. It is not that the number is unimportant — it changes your win rate, your drawdown shape and whether you can psychologically sit through the strategy — but it does not change what a trade is worth on average. That is worth knowing before you spend another month tuning take-profits, because the two things that DO move expectancy are elsewhere.
Expectancy calculatorSweep the reward-to-risk ratio yourself and watch the expectancy stay put while the win rate moves.The identity
Put a target R times your risk away, with a stop one times risk away. On a driftless random walk, the probability of touching the target before the stop is 1/(1+R) — a 3:1 target gets hit 25% of the time by chance alone. Now define your edge as how much better than that you are, so your real hit rate is p = (1+edge)/(1+R). Substitute that into the expectancy of a single trade and everything involving R cancels.
EV = p x (R x risk) - (1-p) x risk - cost
p x R - (1-p)
= [ R(1+edge) - (R - edge) ] / (1+R)
= [ R + R.edge - R + edge ] / (1+R)
= edge(1+R) / (1+R)
= edge
=> EV = risk x edge - cost
=> EV / risk = edge - cost/risk <- R is goneCheck it rather than believe it
The algebra is short enough to distrust, so run the numbers. Take any edge you like, sweep the reward:risk ratio across it, and expectancy per unit of risk comes out identical every time. At an edge of 0.05, a 0.5:1 target and a 10:1 target both return exactly 0.05 per unit risked — the first wins 70% of the time and the second wins 9.55%, and those two facts are worth the same.
edge = 0.05, cost = 0
R hit rate EV/risk
0.5 70.00% 0.0500
1.0 52.50% 0.0500
2.0 35.00% 0.0500
3.0 26.25% 0.0500
5.0 17.50% 0.0500
10.0 9.55% 0.0500
Six different strategies. One expectancy.What this does not say
It does not say reward:risk is irrelevant, and it is worth being precise about the limits. This is a result about a model — a driftless walk with your edge defined relative to it — not a law of markets. Two things it deliberately holds fixed are the ones you should think about. First, changing your target may change your actual edge: a wider target gives price more time and more opportunity to reach your stop first, and whether your signal survives that is an empirical question, not an algebraic one. Second, R changes variance enormously. A 10:1 strategy losing nine times in ten has drawdowns a 1:1 strategy never sees, and the size you can hold through it is a real constraint. What the identity rules out is the idea that R is a free lever on profitability. It is a lever on experience.
So there are two levers, and only two
Edge — how much better than chance the signal is. And cost divided by risk — friction relative to the size of the risk you are taking. Every improvement worth making moves one of them, and it is a useful filter: if a proposed change moves neither, it is decoration. Most retail strategy work lives entirely in the space the identity just cancelled, which is why it feels like effort and produces nothing.
Why timeframe beats tuning
The second lever is where timeframe enters, and it is brutal. Costs are roughly fixed per trade while the move you are trying to capture scales with the horizon, so cost/risk falls as you slow down. On our own measurements, 1-hour directional trading is not badly tuned — it is structurally unwinnable, because costs exceed the entire gross edge before any view is expressed. Donchian and Bollinger variants at 1h measured net R between -0.07 and -0.01, and the fast intraday engine ran a 37% win rate at a 0.61 profit factor for an expectancy of -1.09% per trade. Move to 4h and the same friction is 30-70% of gross edge: survivable, still the dominant term. Our cross-sectional study put the same point in absolute figures — a 0.600% round trip against a median 16-hour move of 2.25% is 27% of a typical move, spent before you are right about anything.
EV/risk = edge - cost/risk 1h cost/risk exceeds any edge measured -> structurally negative 4h cost is 30-70% of gross edge -> survivable, still dominant Measured, same window: Donchian / Bollinger 1h net R -0.07 to -0.01 fast intraday engine 37% WR, PF 0.61, expectancy -1.09%
The two things that actually reduce cost/risk
Widen the stop, and trade less. Both sound like retreats and both are the arithmetic. Cost-in-R falls as stops widen, because the friction is fixed while the R it is measured against grows — the tight stop that feels disciplined is often just paying the spread more often for the same view. And on a thin edge, trading rarely is correct behaviour rather than a bug. More trades on a break-even process is more fees, full stop. The third lever is the venue: maker fills instead of taker, and a better fee tier, change cost/risk directly and are usually worth more than any parameter you could tune.
What we stopped doing because of it
Three things, each because it moved neither lever. We stopped trying to make 1-hour directional technical analysis profitable — three separate measurements said no, and the identity explains why no amount of tuning was going to rescue it. We stopped treating more trades as progress. And we stopped treating model confidence as edge: a confidence score is not backtestable as a return, and its only defensible use is as a veto on a mechanical signal rather than as a reason to size up.
Summary
Expectancy per unit of risk is edge minus cost-over-risk, and reward:risk cancels out of it. Tuning take-profits rearranges your win rate and your drawdown shape without changing what a trade is worth — a 0.5:1 and a 10:1 version of the same edge return exactly the same expectancy. What is left is two levers: be more right than chance, or pay less friction for the risk you take. On our own numbers the second one is where the losses were: 1h directional trading is structurally negative because costs exceed gross edge outright, and even at 4h friction is 30-70% of it. Widen stops, trade less, pay maker fees. None of that is exciting, and all of it is in the equation.
Frequently Asked Questions
What is the best risk-to-reward ratio for crypto trading?
There is no best one on expectancy grounds, because reward:risk cancels out of the expectancy equation — EV per unit of risk is your edge minus your cost-over-risk, with R nowhere in it. At an edge of 0.05, a 0.5:1 target winning 70% of the time and a 10:1 target winning 9.55% return the same 0.05 per unit risked. Choose R for the drawdown shape you can actually sit through, and for whether your signal still works over the longer horizon a wider target needs.
If reward:risk cancels, why does everyone tune it?
Because it visibly changes the win rate, which feels like it changes profitability. It does not — it moves the same expectancy between a few large wins and many small ones. It does genuinely change two real things: variance, which decides the drawdown you must survive, and possibly your realised edge, since a wider target gives price more time to hit your stop first. Neither of those shows up in the algebra, and both matter.
Why can't a 1-hour strategy be made profitable with better settings?
On our measurements the problem is not the settings. Costs are roughly fixed per trade while the move available scales with the horizon, so at 1h the friction term exceeds the entire gross edge — the strategy is structurally negative before any parameter is chosen. Donchian and Bollinger variants measured net R between -0.07 and -0.01 there, and the fast intraday engine ran an expectancy of -1.09% per trade. At 4h the same costs are 30-70% of gross edge: survivable, but still the largest term in the equation.
Does a tighter stop reduce my risk?
It reduces the loss on a single trade and increases the friction you pay per unit of risk, because the cost is fixed while the R it is measured against shrinks. Cost-in-R falls as stops widen. A stop placed inside normal noise for the asset also converts ordinary volatility into realised losses, which is the mechanism by which a strategy with a real edge still bleeds out on fees.
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