Win rate and reward-to-risk

The win rate is the proportion of trades that end in profit: 8 wins out of 10 is 80%. It answers how often a plan wins and says nothing about how much.

To know whether a plan makes money you need two more numbers, both after costs: the average win and the average loss. The total for a batch of trades is wins × average win − losses × average loss.

Nora's last ten trades on her Pebble practice account: 8 wins averaging 50 dollars and 2 losses averaging 250. Wins bring 8 × 50 = 400, losses take 2 × 250 = 500, so the total is −100, or −10 a trade. Two big losses erased eight small wins.

A high win rate feels like skill, which is why it is the number people show off. Before a win rate impresses you, find out the average win and the average loss.

A plan can lose most of its trades and still come out ahead, as long as its losses are small and its wins are big. The result is decided by the win rate and the size of wins and losses together.

Marc's ten trades: 3 wins averaging 300 dollars and 7 losses averaging 100, after costs. Wins: 3 × 300 = 900. Losses: 7 × 100 = 700. Total: +200, or 200 / 10 = +20 a trade, with a win rate of only 30%.

Small losses come from respecting a stop chosen before the trade (The stop: where it goes and why). Big wins come from letting a winning trade run to its planned target instead of grabbing the first profit.

The hard part is emotional, not arithmetic: seven losses in ten feel like failure. If a plan works this way, expect long strings of small losses and judge it by the total of many trades, not by how the last trade felt.

Three numbers describe how a plan wins and loses.

• Win rate: the proportion of trades that end in profit. It measures how often.
• Reward-to-risk: the gain a trade plans to make compared with the loss it plans to take at its stop. It is set before the trade.
• Payoff: the measured version, the average win divided by the average loss over real trades in a journal.

Marc plans 300 of gain for 100 of risk: a reward-to-risk of 3 to 1. Nora's real trades averaged a 50 win against a 250 loss: a payoff of 0.2 to 1.

Plans promise a reward-to-risk; journals show the payoff. When the payoff comes out far below the plan, something happened between the plan and the exit: profits taken early, stops moved, or costs bigger than expected. The win rate always goes together with one of the two size ratios; either alone tells half the story.

Reward-to-risk is worked out before the trade, from three prices: the entry, the stop and the target.

• Risk = the distance from the entry to the stop.
• Reward = the distance from the entry to the target.
• Reward-to-risk = reward ÷ risk.

Example on Pebble: buy NWF at 40.00, stop at 39.00, target at 43.00. The risk is 1.00 a unit, the reward is 3.00, so the plan is 3 to 1. The number of units doesn't change the ratio: with 100 units it is 300 against 100.

The stop comes first, at the price that proves the trade idea wrong (The stop: where it goes and why). The target is the weak spot: a far-away target picked to show a pretty 6 to 1 ratio is rarely reached, so the win rate drops. A ratio is only as honest as the target behind it, and costs (Where the money goes: spread, fees and slippage) shrink every reward and enlarge every loss.

Every pair of average win and average loss has a break-even win rate: the proportion of wins at which the plan makes exactly zero after costs.

break-even win rate = average loss ÷ (average win + average loss)

For Marc, with wins of 300 and losses of 100: 100 ÷ (300 + 100) = 25%. Check it on 100 trades: 25 × 300 = 7,500 gained, 75 × 100 = 7,500 lost. He actually wins 30%, so he sits 5 points above his line.

For Nora, with wins of 50 and losses of 250: 250 ÷ 300 = 83.3%. Her 80% looks great and is still below the line.

The formula turns a vague "is this plan any good?" into a check on paper before any money is at risk: estimate the averages, compute the line and compare it with the win rate you can realistically expect. A thin margin above the line is fragile, because a few extra dollars of costs per trade can push the plan under it.

Knowing the break-even line is half the check. The other half is the distance between the line and the plan's real win rate: that distance decides whether the plan earns or bleeds.

A BFE plan with an average win of 120 and an average loss of 120 (a 1 to 1 payoff) has its line at 120 ÷ 240 = 50%. If it wins 45%, then over 100 trades it gains 45 × 120 = 5,400 and loses 55 × 120 = 6,600: −1,200 in total, about −12 a trade. Five points below the line cost real money.

Plans with a low payoff need a high win rate and leave little room: a 1 to 1 plan winning 52% is only 2 points above its line, so a weaker month or slightly higher costs flip it into a loss. Plans with a high payoff tolerate a low win rate. Neither style is better in itself; what matters is a clear margin above the line, measured on enough trades.

The usual way to end up like Nora, winning 80% of trades and still losing money, is two habits that each feel sensible in the moment.

• Grabbing small wins early. Closing a winner at the first profit feels safe, but it shrinks the average win.
• Holding losers until they "come back". Moving the stop away or ignoring it feels hopeful, but it grows the average loss.

Together they produce a high win rate that loses money, because the break-even line climbs faster than the win rate. Take Marc's numbers: wins of 300 and losses of 100 put his line at 25%. If he closed winners at 150 instead, the line would rise to 100 ÷ 250 = 40%, above his 30%. If he also let losses drift to 150, it would be 150 ÷ 300 = 50%.

Extra costs work the same way, quietly: fees and the spread cut every win and add to every loss. The cure is dull: set the stop and the target before the trade, then let the trade reach one of them.

No single number says whether a plan works. A higher win rate does not mean more money: over ten trades Nora won 80% and lost 100 dollars, while Marc won 30% and made 200. What counts is the win rate measured against the break-even line that the average win and the average loss set.

One more condition: enough trades. Ten trades are far too few to judge either of them, because luck alone can produce eight wins or seven losses in ten. Treat a win rate or a payoff from fewer than 30 trades as "too few to tell", and prefer more. Also check that the numbers are after costs; a result before costs must be labelled that way.

How it fits together: the win rate says how often, the payoff says how much, and the break-even line joins them. The next lesson, Expectancy: the average trade, folds all three into one number: the average result of a trade after costs.