Profit/loss ratio or payoff ratio (pay off ratio) is the portfolio average profit per trade divided by the average loss per trade. If we have higher values – the portfolio performance is better. This is important term when we talk about money management (visit our article about money management and expert advisors).

Payoff ratio is not the same as sharpe ratio (Sharpe ratio is a measure of excess portfolio return over the risk-free rate relative to its standard deviation.)

## Formula :

Average win = Total Gain / number of winning trades

Average loss = Total Loss / number of losing trades

**Pay off ratio = Average win / Average loss = (Total Gain / number of winning trades ) / (Total Loss / number of losing trades)**

## Example how we can calculate payoff ratio for system or portfolio:

Our system or portfolio has :

300 winning trades

200 losing trades

Total gain is $9000

Total loss is $8000

than :

Average Win = Total Gain / number of winning trades = $9000 / 300 = 30

Average loss = Total Loss / number of losing trades = $8000 / 200 = 40

**Pay off ratio = Average win / Average loss = 30/40 = 0,75 **

**About payoff ratio formula and other formulas **

In Literature payoff ratio we use when we want to calculate winning rate or win rate.

**Win rate = Profit factor / (profit factor + payoff ratio)**

Very similar term is Expected Payoff where

Expected Payoff = Total Net Profit / Total Number of Trades

## What payoff ratio can tell us about our portfolio ?

It can tell us only about risk reward strategy but **it can not give** us nice explanation about our portfolio profitability.

Except this value we need to calculate average profitability per trade (APPT) or in math language Expectancy.

Average profitability per trade = (Probability of Win * Average Win) – (Probability of Loss * Average Loss).

So let we calculate Average profitability per trade for our case :

300 winning trades means that from 500 trades 300 are winning. Probability of Win = 300/500 = 60%

200 losing trades means that from 500 trades 200 are losing. Probability of loss = 200/500 = 40%

Total gain is $9000

Total loss is $8000

Average Win = Total Gain / number of winning trades = $9000 / 300 = 30

Average loss = Total Loss / number of losing trades = $8000 / 200 = 40

Average profitability per trade = (Probability of Win * Average Win) – (Probability of Loss * Average Loss) = 0.6*30 – 0.4*40 = $18 – $16 = $2

## Payoff ratio vs. Profit factor

Profit factor is better signal than payoff ratio. Payoff ratio can be very low and system can be profitable. Payoff ratio without win rate can not be used as measure.

So if we know that :

Profit factor is ratio when we divide profit from winning trades by the loss of losers.

Win rate is the percentage of winning trades based on the number of total trades.

Payoff ratio is the average winning trade divided by the average losing trade.

There is rule about Profit factor and payoff ratio :

**Profit factor will stay constant if we lower the payoff ratio only if we develop strategy with higher win rate. **