In the intricate world of trading, success is not just about winning more often than you lose. It’s about understanding the long-term potential of your trading strategy. This is where the concept of trading expectancy comes into play, and a Trading Expectancy Calculator becomes an essential tool in a trader’s arsenal.
Trading expectancy is a formula that helps predict the profitability of your trading strategy over time. It combines the probability of winning and losing with the average gain or loss from each trade. The formula to calculate trading expectancy is as follows:
Expectancy = (Win% x Avg Win) – (Loss% x Avg Loss)
Here’s a breakdown of the formula:
- Win% is your win rate, a percentage of trades that are profitable.
- Avg Win is the average amount gained from winning trades.
- Loss% is your loss rate, a percentage of trades that are not profitable.
- Avg Loss is the average amount lost on losing trades.
For instance, if you win 50% of the time with an average win of $200, and lose 50% of the time with an average loss of $100, your trading expectancy would be:
(0.50 x $200) – (0.50 x $100) = $100 – $50 = $50 per trade.
How to Use the Trading Expectancy Calculator
The Trading Expectancy Calculator is designed to be straightforward, allowing traders to input their trading scenario data with ease and receive an instant calculation of their strategy’s expectancy.
Here’s how to use it:
- Input Your Scenarios: Locate the white cells in the calculator. These are your input fields. Here, you’ll enter the win rate percentage, average win amount, loss rate percentage, and average loss amount, based on your historical or projected trading data.
- Hit Calculate: Once you’ve entered your scenarios, simply click the calculate button. The calculator will process the data using the trading expectancy formula and present you with a figure.
- Determine Expectancy: The resulting number is your trading expectancy. This figure is a prediction of the average amount you can expect to win (or lose) per trade over the long term, based on your current trading strategy.
For example, you input the following into the calculator:
- Win%: 55
- Avg Win: $150
- Loss%: 45
- Avg Loss: $100
Upon hitting calculate, you receive an expectancy of:
(0.55 x $150) – (0.45 x $100) = $82.50 – $45 = $37.50 per trade.
This means, on average, you can expect to make $37.50 per trade over the long haul with the given strategy.
Why Is Trading Expectancy Important?
Trading expectancy is not about the outcome of a single trade; it’s a metric that provides insight into the effectiveness of your trading strategy over many trades. A positive expectancy indicates a potentially profitable strategy, while a negative expectancy might signal that it’s time to reevaluate your approach.
The real power of trading expectancy lies in its ability to demonstrate the profitability of a trading strategy over a series of trades. It quantifies the edge of your trading strategy, serving as a litmus test for profitability in the long run. A positive expectancy value signals that your strategy is likely to yield profits over time, while a negative value warns of a strategy that may need reevaluation or adjustment.
Why is this important?
Trading is inherently fraught with a wide range of wins and losses, but the average outcome of these trades ultimately determines your financial fate. Expectancy provides a normalized measure, stripping away the emotions and allowing a factual assessment of your strategy’s performance. It tells you not just if you’re winning or losing, but more critically, by how much per trade.
Finally, trading expectancy is extremely useful when comparing different trading strategies. By distilling performance down to a single metric, it allows traders to objectively compare strategies (or different versions of the same strategy) against each other. This comparison is invaluable, whether you’re refining existing methods or considering a completely new approach.
In summary, the Trading Expectancy Calculator isn’t just another tool—it’s an essential companion for any serious trader. Use it to sharpen your trading edge and to make informed decisions backed by solid, statistical confidence.
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The expectancy calculator confirms that it is not the percentage of winning trades that determines the value of a rules based trading system but rather a combination of the percentage of winning trades and average win versus a combination of the percentage of losing trades and average loss.
Well stated Annette – thank you! This understanding makes a huge difference in our trading results (and psychology)
What counts is the average win when you win against the average lose when you loose.
Perfect – it is fascinating how what we are naturally driven towards as traders (high win rate) is actually not that important at all. We are only attracted to high win rates because it gives us the ability to be ‘right’ more often, which satisfies our ego… but not necessarily our wallet 😉
I learned you don’t need to be a trading savant with a 60%+ win rate and a 2:1 R:R to have an effective trading strategy, there are a variety of ways to have a positive expected return.
Fantastic insight Joe – well done! This takes the pressure off being right all the time and you can just let the maths work for you over many trades.
This formula is the next valuable asset in my trading journey.
Brilliant – thinking this way certainly makes it more clear how to make money trading doesn’t it!
Question: So this calculation has to be done at level of back testing or is based on your actual results over time? If it’s based on actual results over time, how time is statistically significant in this case?
Hi Ozemena,
It can be done on both of these levels. If you are doing it on your backtested results the trading software does this for you. The key is to just understand this concept so you know the relationship between winning percentage and size of wins / size of losses… when you are systematic and backtest your rules you don’t actually need to do this separately – it is just part of the backtesting statistics.
Adrian
It shows that you don’t need a high win rate to make money. The 20% win rate was the best system of the 4 provided.
Well done David. Win rate isn’t nearly as important as most traders think.
Have learnt this before but good for the refresher:
being “right”(high win rate) does not necessarily mean you are profitable.
Also being “wrong”(low win rate) doesnt mean you arent profitable.
Having high win rate definitely helps your psychology but you need to be mindful of the expectancy of these systems that they could still result in an overall loss.
Brilliant, nicely stated Tim!
Valuable calculator, shows that I can lose a decent percentage of time as long as I keep the losses small and the winnings high I can still make money. If I have a proven method that has a reliable handle on the winning/losing percentages and amounts, I can plan more effectively for the future and lessen the emotional stress of trading.
Excellent learnings and realizations Ron – It is amazing how powerful one simple formula is and how effectively it can guide our thinking towards good trading!
The quality and effectiveness of the trade rather than the high quantity of trades will limiting loss and retaining capital is the objective.
Spot on – nicely stated. The obsession many have with high win rate is not that helpful when it comes to profitable trading. The expectancy formula shows that getting the balance right between size of wins / losses and the percentage winners is much more important.
This tells me: Let your winners run, and cut your losses short. You want a strategy with a high Reward:Risk, even if it has a low winrate, you’re taking many small bets but staying in the game for the outsized winners.
Perfect – Fantastic learning Noah!
You can be wrong more often than right and still be profitable.
Brilliant insight Neil – Well done! It is very liberating once this is really understood. I love the fact that we can make money even if we are wrong on many trades. The expectancy calculation is key, not being right!
The win rate is not the most important factor in rating the success of a strategy. It’s the size of the average win vs the size of the average loss, combined with the win rate, that determines the profitability of the strategy. A higher win rate is great emotionally, but the lower win rate just might be the better strategy to take to make the largest profit over the long run.
Fantastic insight Jennifer – well done! Knowing this is a game changer because it takes the pressure off finding a strategy that has a high win rate. Most of the time when you have a high win rate strategy there is hidden tail risk that will get you or the system is very fragile and prone to break quickly.
This exercise demonstrates the importance of the formula. If you set equal to zeor and rearrange it, you can find the breakeven point is when the ration of the %wins : %losses equals the ratio of the average losses : average wins. Thus if the second ratio exceeds the first, don’t do the trade. Similarly, the more the first ratio exceeds the second, the greater the expectancy (which I assume suggests a greater expected profitability of the trade).
Thanks for your comment Brindha – you want to think about this more at the ‘system’ level than the individual ‘trade’ level. Over time a system will have winning and losing trades, but the outcome over many trades is what is important. I encourage you to think about your trading results at the system level as it takes the pressure off each individual trade to perform, and you can just let the system statistics work in your favour over time.
Adrian
Why not simply consider the profit (Total Gain – Total Loss)? If it is positive, I’m winning.
I must be overlooking something (as I approach this from an investor mindset) or you are preparing us for something else.
Yes if you do that San you will know if you are winning… the expectancy formula gives you additional information about WHY you are winning. The profile of wins and losses and the percent winners helps you understand why you are profitable (or not) and which part of the system you need to adjust to improve things.
Great way to emphasize the fact that the risk/reward ratio is more important than the win percentage. I often get caught up in how many trades are “wins” vs. how much I have made from my trades. Need to make sure we can determine when a trade is going the wrong direction and get out of it quickly. As an engineer, I love the equation and black and white analysis that a high win percentage is NOT the only factor in a winning strategy!
Fantastic realisations Jenn – Great work! Yes I love the fact that there is more to it than winning percentage. I get some sort of perverse pleasure from making money despite being wrong on many of my trades 😉
The ratio of average win to average loss appear to weigh more than that of rate of percentage win or loss.
Question: 1. How do you factor in losses due commissions into this expectancy rule
2. Can this be determined at the level of back testing or does it have to be data from actually traded account?
Great realisation Ozemena. For commissions you would include these in the size of the average winner and average loser so the expectancy includes commission impact. The expectancy and the other statistics are generated by the backtest so once you understand it you don’t have to do it manually. Of course you should also track your actual trades to ensure they are in line with what the backtest is generating as well.
Yes, expectancy is what takes you there. Can you live with only 20% winners? A portfolio of strategies makes it so much easier.
Nice – well said Ola!
It doesn’t matter that you lose more often than you win as long as your risk to reward
ratios are correct. That said it can be difficult psychologically to accept more losses than wins.
Both great observations Vlado – well done!
The calculator clearly demonstrates that a low percentage win rate with an average high dollar gain is still profitable even if a large number of losses is incurred providing the average loss in dollar terms is small. eg. 20% win rate versus a loss rate of 80% in the example above.