Risk Reward Ratio and Win Rate: The Maths Behind Every Trade

The risk reward ratio compares what a trade can lose (the distance to your stop) with what it aims to make (the distance to your target). On its own it tells you very little: a 1:3 ratio still loses money if you hit the target less than 25% of the time, before costs. What decides your result is the ratio and the win rate together, called expectancy. Below: the formula, a break-even table, costs and how to measure yours.

What is the risk reward ratio?

It is the distance to your stop compared with the distance to your target, both measured from the entry. Say you buy NQ at 21,600.00 with a stop at 21,590.00 and a target at 21,620.00:

• Risk: 10 points, 40 ticks, 200 dollars per contract.
• Reward: 20 points, 80 ticks, 400 dollars per contract.
• Ratio: 1:2. You risk one unit to make two.

That unit of risk is called R. Here 1R is 200 dollars, so the target is +2R and a stop-out is -1R. Thinking in R lets you compare trades of different sizes and instruments.

One warning on notation: some traders write the same trade as "2:1", reward first. This article always puts risk first, so 1:3 means risking one to make three. Check which way round a source writes it before you copy a rule.

The trading expectancy formula, explained with numbers

Expectancy is the average amount you make or lose per trade over many trades:

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

In R, with W as the win rate and a reward of R per winner, it becomes W × R − (1 − W). Three traders, before costs:

1. Trader A: 40% wins at 1:2. 0.40 × 2 − 0.60 = +0.20R per trade. Risking 200 dollars, that is +40 dollars per trade, or +4,000 over 100 trades.
2. Trader B: 60% wins at 1:0.5. 0.60 × 0.5 − 0.40 = -0.10R per trade. Right most of the time, losing overall.
3. Trader C: 30% wins at 1:3. 0.30 × 3 − 0.70 = +0.20R per trade. The same expectancy as A, with a very different experience.

Trader C wins only three trades in ten. The chance of any ten trades in a row all being losers is 0.7 to the power of 10, about 2.8%. That sounds rare, but over several hundred trades a streak like that becomes likely, and most people abandon a strategy during one. For Trader A, ten losses in a row has a probability of 0.6 to the power of 10, about 0.6%. Same maths, different nerves.

Expectancy is also the input to sizing formulas such as the Kelly criterion, published in 1956. Beginners should not size from it at full strength, because their estimate of their own edge is almost always too optimistic.

Break-even win rate for each risk reward ratio

Set expectancy to zero and solve for W: break-even win rate = 1 ÷ (1 + reward). Below that win rate you lose money over time; above it you make money, before costs.

Read the last column as the room for error. At 1:2 each winner pays for two losers; at 1:0.5 one loser wipes out two winners. Sizing is a separate decision: the ratio says nothing about how many contracts to trade, which comes from the stop and your account, as covered in risk management for beginners.

How spread and commission move the break-even point

The table assumes trading is free. It is not. Every round trip pays the spread or some slippage and a commission. Assume a total of 2 ticks per round trip on NQ: about 1 tick of spread or slippage, plus commission and fees close to one more tick (around 5 dollars, an assumption; check your broker's all-in rate). Costs make every winner 2 ticks smaller and every loser 2 ticks bigger:

• 1:2 with a 40-tick stop and an 80-tick target. Net win 78 ticks, net loss 42. Break-even: 42 ÷ (78 + 42) = 35.0%, up from 33.3%.
• 1:3 with a 16-tick stop and a 48-tick target. Net win 46, net loss 18. Break-even: 18 ÷ 64 = 28.1%, up from 25%.
• 1:1 scalp with 8 ticks each way. Net win 6, net loss 10. Break-even: 10 ÷ 16 = 62.5%, up from 50%.

The pattern is clear: costs are fixed in ticks, so the smaller the stop and target, the bigger the share costs eat. On the scalp, two ticks are a quarter of the target. That is the core of why the maths of scalping works against you: a tight scalper needs a much higher hit rate than the textbook table suggests.

Costs are also part of why the large-sample data is so harsh: in the study of Taiwanese day traders by Barber, Lee, Liu and Odean, less than 1% earned reliably positive abnormal returns net of fees. The guide on whether trading is profitable looks at what the data says.

What is the best risk reward ratio for day trading?

There is no best ratio in isolation, only the best ratio for a given setup. Pushing the target further out does three things at once:

• The hit rate falls, because price has to travel further before the stop is hit.
• Trades last longer, so they sit through more news, more noise and more temptation to close early.
• Losing streaks get longer, which is where discipline usually breaks.

Hypothetical example: the same pullback setup tested over 200 trades with three targets. At 1:1 the target is hit 58% of the time; at 1:2, 38%; at 1:3, 24%. Expectancy before costs:

• 1:1: 0.58 × 1 − 0.42 = +0.16R
• 1:2: 0.38 × 2 − 0.62 = +0.14R
• 1:3: 0.24 × 3 − 0.76 = -0.04R

The 1:3 version looks best on a social media chart and is the only one that loses. In practice, the target should sit at the next real level, where price is likely to react, and the ratio is whatever that level gives you. If the nearest level offers less than about 1:1 after costs, skip the trade instead of stretching the target.

How to measure your real risk reward ratio from a journal

The bracket you place is your planned ratio. What you actually get is different: you exit early, you slip, you move stops. Your journal gives you the real number in five steps:

1. For each trade, log the initial risk (entry to original stop, times size) and the net result after costs.
2. Divide result by initial risk to get the R multiple of each trade.
3. Average the R of your winners and, separately, of your losers.
4. Realised ratio = average win ÷ average loss. Win rate = winners ÷ all trades.
5. Compare your win rate with the break-even for your realised ratio, not for your planned one.

Worked example: 60 trades, all planned at 1:2. 24 winners averaging +1.4R, 36 losers averaging -1.1R. Win rate: 40%. Realised ratio: 1.4 ÷ 1.1 = 1.27. Break-even at that ratio is 1.1 ÷ (1.4 + 1.1) = 44%. Expectancy: 0.40 × 1.4 − 0.60 × 1.1 = -0.10R. This trader planned a winning system (40% at 1:2 is +0.20R) and turned it into a losing one with two leaks: winners cut at +1.4R instead of +2R, and losers at -1.1R from slippage or moved stops. If you do not log this yet, the trading journal template has the R column ready, and the guide on where to place a stop loss deals with the second leak.

Frequently asked questions

BullHero is a trading game with play money and a price tape generated by a mathematical model, not a broker. This article is for educational purposes and does not constitute financial advice.