Win Rate vs Risk-Reward: Reading the PF Formula

The short answer: neither win rate nor risk-reward decides anything on its own

Here is the conclusion up front. Profit factor (PF) is determined almost entirely by two things: win rate and risk-reward (average profit ÷ average loss, hereafter RR).

PF = win rate ÷ (1 − win rate) × RR

As the formula shows, there are infinitely many combinations of win rate and RR that produce the same PF. A high win rate may simply be the flip side of a small RR, and a low win rate may be the price of a large RR. This formula is the reason we tell people choosing an EA not to judge by win rate alone.

Where the formula comes from

PF is "gross profit ÷ gross loss." Let N be the number of trades and W the win rate. Then:

• Gross profit = N × W × average profit
• Gross loss = N × (1 − W) × average loss

When you divide, N cancels out and you are left with W/(1 − W) × (average profit / average loss). The second term is the RR. In other words, PF is just the product of "the ratio of wins to losses" and "the ratio of profit to loss per trade."

Combinations that produce the same PF of 1.5

Every row has the same PF of 1.5. Yet each one feels completely different to trade.

Breakeven win rate

Set PF to 1.0 and rearrange, and you get breakeven win rate = 1 ÷ (1 + RR). With an RR of 1, you need a 50% win rate. With an RR of 2, about 33%. With an RR of 0.5, you need to exceed about 67% to be profitable on paper (before costs).

Looking at our own EAs

The DONCHIAN ENGINE backtest shows a PF of 1.5 and a win rate of 34.5%. The win rate is low, but the design relies on the size of its winning moves to support the PF. In exchange, the maximum losing streak was 11 trades.

The GOLD TRIPWIRE backtest shows a PF of 2.72 and a win rate of 58.6%. It doesn't lean toward either win rate or RR; it builds its PF from both.

The GOLD KING v6 backtest shows a PF of 4.66 and a win rate of 83.1%. Because the win rate is high, each loss weighs more heavily, and the maximum losing streak was 10 trades. Even a high win rate does not eliminate losing streaks.

All figures are results from historical data and do not guarantee future performance.

Checklist: how to read an EA's results

When I look at an EA's performance report, I go through it in this order.

1. Put win rate and PF side by side: Once you know these two, you can work backward from the formula to the average RR.
2. Check the gap from the breakeven win rate: How far the actual win rate sits above the breakeven win rate is your safety margin. The smaller the gap, the sooner a slight deterioration turns the system unprofitable.
3. Check the maximum losing streak: Low-win-rate EAs tend to have long losing streaks by design. Ask whether your capital and your nerves can withstand that streak.
4. Factor in costs: Spreads and commissions reduce average profit and increase average loss. High-win-rate systems with a small RR are the most sensitive to this.
5. Check the number of trades: With few trades, both win rate and RR can swing by chance.

You can compare the win rate and PF of each EA side by side in the measured ranking.

Limits of the formula and cautions

Here are the inconvenient points, too.

• It only looks at averages: The formula uses only average profit and average loss. PF can't tell you about rare, huge losses, or whether profits are concentrated in a handful of big wins.
• It ignores order: With the same win rate and the same RR, drawdown can be completely different depending on whether losses arrive in clusters or spread out.
• Past win rates change: When market conditions change, both win rate and RR change. There is no guarantee that a backtest's combination will continue as is.
• The high-win-rate trap: Placing the stop-loss far away makes it easy to raise the win rate. The higher an EA's win rate looks, the more you need to check its RR and maximum loss.

We don't have a universal answer for which combination is best. We believe the fit depends on whether you can better tolerate long losing streaks or one large loss. We also cover how to read these metrics in our knowledge base.

Summary

• PF = win rate / (1 − win rate) × RR. PF is the product of win rate and RR
• There are infinitely many win rate and RR combinations that give the same PF
• Breakeven win rate = 1 / (1 + RR). The gap from the actual win rate is your safety margin
• With low-win-rate systems, watch for losing streaks; with high-win-rate systems, watch for a single large loss and for costs
• Because it is a formula built on averages, check loss concentration and the order of losses separately
• Rather than picking one combination, first decide what kind of losing you can endure