The trading expectancy formula
Expectancy = (Win % × Average Win) − (Loss % × Average Loss)
Loss % is 100 minus win %, and the average loss goes in as a positive number. A positive expectancy means the strategy pays you on average, even though any single trade can still lose. A negative expectancy means the opposite: you can string together winning weeks on variance alone before the maths catches up.
R-multiple calculator: expectancy in R
R is the amount you risk on a trade, so a 2R win is twice that risk and a 1R loss is exactly the risk. Win 40% of the time, make 2R on a win and lose 1R on a loss:
0.4 × 2R − 0.6 × 1R = +0.2R per trade
That is +20R over 100 trades. Losing six trades in ten, the strategy still makes money because the wins are twice the size of the losses. R-multiples let you compare strategies and contract sizes on one scale, and they are what the risk-reward calculator gives you from an entry, stop and target.
Expectancy example in dollars (futures)
Say you trade MES, a contract worth $5.00 a point. You win 45% of trades, average 6 points ($30.00) on a winner and 4 points ($20.00) on a loser:
0.45 × $30.00 − 0.55 × $20.00 = $2.50 per trade
That is $250.00 per 100 trades, before costs. A round trip on MES costs $2.12 with the verified exchange, clearing and NFA fees plus a $0.50 a side example commission. Take that off every trade and expectancy falls to $0.38, so 85% of the edge went to fees. Put the figures in the calculator above; it works in dollars, so enter net averages to get net expectancy.
Profit factor formula
Profit factor = Gross profit ÷ Gross loss
Gross profit is the sum of every winning trade and gross loss is the sum of every losing trade, as a positive number. A profit factor of 1.0 is break-even, above 1.0 the strategy made money and below 1.0 it lost. From averages, it is (win % × average win) ÷ (loss % × average loss). In the MES example that is 0.45 × $30.00 ÷ (0.55 × $20.00) = 1.23: 1.23 dollars won for every dollar lost. The calculator above shows it as n/a when there are no losses to divide by.
Profit factor is easy to inflate. A handful of outsized wins, or too few trades, can push it high without any real edge, so read it next to expectancy and the trade count. Many traders look for roughly 1.5 or more after costs, a rule of thumb rather than a standard.
What is a good expectancy?
Anything above zero after costs makes money on average. Beyond that there is no official threshold, and a number means little without its sample. As a rule of thumb, many traders look for roughly +0.2R per trade or better, because a thin edge is easily erased by fees and slippage. Two cautions come with that:
- Sample size. Expectancy from 20 trades is mostly noise. Wait for 100 or more before you trust it; see how many trades before you can trust your win rate for the reasoning.
- Net, not gross. A strategy at +0.2R gross can sit near zero once costs are counted, which is what the dollar example above shows.
Expectancy vs profit factor vs win rate
The three numbers answer different questions. Here they are for the MES example above: