Payoff ratio

This is a statistic of a specified trade ledger. It is different from a trade's planned reward-to-risk ratio: a profit target and a stop level describe intended exits; the payoff ratio describes the outcomes actually recorded in the chosen sample.

Average the two groups separately

Let $x_i$ be net P&L for completed trade $i$, expressed in one currency. Let $n_w$ count trades with $x_i>0$ and $n_l$ count trades with $x_i<0$. When both groups are nonempty, define

Consider four synthetic completed round trips. Each row is the full position from flat to flat, with all fills grouped together. P&L is in USD, after the specified execution costs, commissions, fees and any financing or borrow charges; no further cost deduction is due.

The average winner is $(10+20)/2=15$ USD. The average loss magnitude is $(5+15)/2=10$ USD. Thus $R=15/10=1.5$: the average winner is one and a half times the average loser in magnitude.

Counts still decide the money

For a different synthetic ledger, $+15,-10,-10$ USD, the payoff ratio is still $1.5$, but profit factor is $15/20=0.75$ and total P&L is $-5$ USD. Bigger average winners do not compensate for every possible frequency of losses.

For the four-trade ledger, this gives $0.5(15)-0.5(10)=2.50$ USD per trade, matching total net P&L of $10$ USD divided by four. It does not establish that the next trade has positive expected P&L. Future frequencies, payoff sizes and trading costs can change; a small historical sample can miss rare large losses.

Under a stipulated future win/loss model with no zero outcomes, constant conditional mean win $W>0$ and loss magnitude $L>0$, expected P&L is positive only when the win probability $p$ satisfies $p>1/(1+W/L)$. A model payoff ratio of $1.5$ therefore needs a win probability above $40\%$. Substituting a backtest ratio does not prove that this model describes future trades.

Fix the measurement before comparing strategies

• Define one trade. Group partial entries and exits consistently, specify how offsetting fills are matched, and use the same reporting window. QuantConnect's trade-statistics documentation makes grouping and matching configurable. Splitting a position into several rows can change the conditional averages even if total P&L stays the same.
• Declare the basis. Currency P&L, percentage return and P&L per unit of initial risk answer different questions. Use one basis for both groups. Large positions can dominate currency averages; a dimensionless ratio does not remove position-sizing differences.
• Use consistent costs. Classify winners and losers after the chosen deductions. A small gross gain can become a net loss. Actual fill prices already contain their execution-price effects: do not subtract the same spread or slippage a second time. For more on constructing cost-aware results, see Realistic Backtesting: Transaction Costs, Borrow, and Survivorship Bias (membership required for the full lesson; public preview available).
• Keep zeros explicit. An exactly zero net outcome belongs to neither conditional average. Here it remains in the denominator for hit rate and mean P&L. Adding a zero to the four-trade ledger leaves $R=1.5$ but changes hit rate to $2/5=40\%$ and mean P&L to $2$ USD.
• Report unavailable ratios honestly. With no winners, the average win is undefined; with no losers, the average loss is undefined. In either case this definition has no payoff-ratio estimate. An all-zero or empty ledger is also undefined. A report's placeholder of zero or infinity is not evidence of a measured conditional ratio.

Sources

• NinjaTrader — Trade Performance: Statistics Definitions: average winning and losing trades, their ratio, and the distinct profit-factor statistic. Check the platform's units and trade-classification rules when reconciling reports.
• QuantConnect — Trade Statistics: how fills are grouped and matched into completed trades.
• Ernest P. Chan, Quantitative Trading: How to Build Your Own Algorithmic Trading Business, Wiley, first edition, copyright 2009, Chapter 2, pp. 22–23: transaction costs in strategy evaluation. The ledgers and calculations above are original synthetic examples.