Calculating Trade Expectancy from Wins and Losses
Summary
The document discusses how to calculate expectancy from a short record of trades. It presents a formula that combines the proportion of winning and losing trades with the respective total winning and losing amounts, then divides by the number of trades. In its example, the outcomes are recast as net wins or losses before calculating the win rate and amounts. This illustrates that the amount initially risked is not itself the formula’s direct input; position size can affect the net outcomes being evaluated.
A second response instead describes expectancy as average win divided by average loss and applies that ratio to the same trades. The two definitions produce different interpretations, and the document does not reconcile them or establish which measure should be preferred. Readers should distinguish an average net profit per trade from a win-to-loss size ratio, and define whether amounts are gross or net before comparing trade records.
Key ideas
- Expectancy can be calculated from win frequency, loss frequency, and the amounts won and lost.
- The example converts each trade into a net win or loss before calculating the statistics.
- One response divides the weighted win and loss amounts by the number of trades.
- Another response uses average win divided by average loss, a different measure that the document does not reconcile.
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Full text
# How do I calculate expectancy from a past series of trades in my trading account?
# How do I calculate expectancy from a past series of trades in my trading account?
Expectancy is defined as "How much money gained for every $1 risked".
What is the expectancy for this particular series of trades?
- Risked €1, won €2
- Risked €2, won €1
- Risked €3, won €6
- Risked €3, won €6
## Answer by rajah9 (score 1, accepted)
https://quant.stackexchange.com/a/2093
Van Tharp addresses expectancy in his book, Trade Your Way to Financial Freedom. Here is his definition of expectancy.
$\frac{winPct * winAmt - losePct * loseAmt}{trades}$
I would recast your trades as follows:
- Won €1
- Lost €1
- Won €3
- Won €3
Your winning percentage is 75%. Your losing percentage is 25%. Your winning amount is €7. Your losing amount is €1.
So your expectancy would be $\frac{.75* €7 - .25 * €1}{4}$
Your expectancy, by Tharp's reckoning, would be €1,25. Tharp does not directly use the amount at risk. Rather, his definition takes into account that the trader or quant may choose a larger bet size when the odds are in his favor.
## Answer by Contango (score 0)
https://quant.stackexchange.com/a/2091
Lets see if I have this right:
Expectancy = average win / average loss.
Thus:
- Risked €1, won €2 means total wins are now €1 for 1 trade.
- Risked €2, won €2 means total losses are now €1 in 1 trade.
- Risked €3, won €6 means total wins now rise to €4 over 2 trades.
- Risked €3, won €6 means total wins now rise to €7 over 3 trades.
Thus, average win = €7 / 2 = €3.50, average loss €1 / 1 = €1, so expectancy is 3.50 for this series of trades?Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.