These 2 backtest analysis metrics terms sound similar but are very different. And one is far more useful than the other.
Expectancy
This metric is included in the Metrics Report/Extended ScoreCard > Risk/Reward Ratio.
For illustrative purposes I chose the sample strategy Dynamic Breakout System, all default settings, daily data till 11/18/22. See pics 1 & 2.
A few points:
1. Its value is *always* identical to Avg Profit (the developers can check this on *any* strategy, *any* time frame).
2. The description says its the expected profit per dollar risked per trade; if so, then this value should be divided by the avg dollar invested per trade so it can be normalized allowing for meaningful comparisons (otherwise, all else being equal, a strategy with a larger position size would have a larger Expectancy even though it may theoretically be an inferior system).
So... (a) either the description should be modified to state its just the avg profit per trade or (b) it can be removed from the Extended ScoreCard and Avg Profit (under Basic ScoreCard > Positions) can be renamed to Avg Profit (Expectancy).
Choice (b) is probably better because it keeps the name Expectancy just in case someone looks for that and, more importantly, its place under Risk/Reward Ratio can be taken by Expectancy Ratio - a far more useful metric.
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Expectancy Ratio
https://www.learningmarkets.com/determining-expectancy-in-your-trading/
https://improve-your.trade/blog/what-is-expectancy-ratio/
where
Reward-to-Risk Ratio = Avg Profit / Avg Loss
Win Ratio = % Profitable trades
Loss Ratio = 100 - Win Ratio
Using values from pic 1 above:
Reward-to-Risk Ratio = 244.85 / 162.59 = 1.51 (rounded)
Win Ratio = 46.67
Loss Ratio = 100 - 46.67 = 53.33 (same as % Unprofitable trades)
Thus, Expectancy Ratio = (1.51 x 46.67) / 53.33 = 70.47 / 53.33 = 1.32
Even though less than half the trades were winners yet the Expectancy Ratio is positive b/c the avg profit was significantly larger than the avg loss.
The Expectancy Ratio is a robust metric, is independent of position size and makes direct comparisons possible across ALL trading strategies. It's also great for comparing strategy modifications.
Summary:
I urge the developers to replace Expectancy with Expectancy Ratio and to include it under Metrics Report (in the same location where Expectancy is currently located) as well as under Optimizations and Rankings.
Expectancy
This metric is included in the Metrics Report/Extended ScoreCard > Risk/Reward Ratio.
For illustrative purposes I chose the sample strategy Dynamic Breakout System, all default settings, daily data till 11/18/22. See pics 1 & 2.
A few points:
1. Its value is *always* identical to Avg Profit (the developers can check this on *any* strategy, *any* time frame).
2. The description says its the expected profit per dollar risked per trade; if so, then this value should be divided by the avg dollar invested per trade so it can be normalized allowing for meaningful comparisons (otherwise, all else being equal, a strategy with a larger position size would have a larger Expectancy even though it may theoretically be an inferior system).
So... (a) either the description should be modified to state its just the avg profit per trade or (b) it can be removed from the Extended ScoreCard and Avg Profit (under Basic ScoreCard > Positions) can be renamed to Avg Profit (Expectancy).
Choice (b) is probably better because it keeps the name Expectancy just in case someone looks for that and, more importantly, its place under Risk/Reward Ratio can be taken by Expectancy Ratio - a far more useful metric.
------------------------------------
Expectancy Ratio
https://www.learningmarkets.com/determining-expectancy-in-your-trading/
https://improve-your.trade/blog/what-is-expectancy-ratio/
CODE:
Expectancy Ratio = (Reward-to-Risk Ratio x Win Ratio) – Loss Ratio
where
Reward-to-Risk Ratio = Avg Profit / Avg Loss
Win Ratio = % Profitable trades
Loss Ratio = 100 - Win Ratio
Using values from pic 1 above:
Reward-to-Risk Ratio = 244.85 / 162.59 = 1.51 (rounded)
Win Ratio = 46.67
Loss Ratio = 100 - 46.67 = 53.33 (same as % Unprofitable trades)
Thus, Expectancy Ratio = (1.51 x 46.67) / 53.33 = 70.47 / 53.33 = 1.32
Even though less than half the trades were winners yet the Expectancy Ratio is positive b/c the avg profit was significantly larger than the avg loss.
The Expectancy Ratio is a robust metric, is independent of position size and makes direct comparisons possible across ALL trading strategies. It's also great for comparing strategy modifications.
Summary:
I urge the developers to replace Expectancy with Expectancy Ratio and to include it under Metrics Report (in the same location where Expectancy is currently located) as well as under Optimizations and Rankings.
Rename
Thanks for the detailed info here, I think we should make your recommended change for the next release cycle.
"Expectancy (traditional)" is there for a purpose, being the simplified formula from 1st edition of Van K. Tharp's book "TYWTFF". The formula is:
(Probability of Win * Average Win) - (Probability of Loss * Average Loss) / Average Risk
We should investigate why its value is always equal to the Avg Profit. Thanks for pointing this out.
The "Expectancy" what you probably expected to find is based on the average risk amount. It was part of a WL6 extension but hasn't been re-implemented yet because WL7 did not have a RiskStopLevel successor. Fortunately, Dion has brought the dynamic Max Risk Stop feature in WL8 B11 which I should be able to leverage to add the Expectancy formula's actual revision to the Extended Scorecard.
(Probability of Win * Average Win) - (Probability of Loss * Average Loss) / Average Risk
We should investigate why its value is always equal to the Avg Profit. Thanks for pointing this out.
The "Expectancy" what you probably expected to find is based on the average risk amount. It was part of a WL6 extension but hasn't been re-implemented yet because WL7 did not have a RiskStopLevel successor. Fortunately, Dion has brought the dynamic Max Risk Stop feature in WL8 B11 which I should be able to leverage to add the Expectancy formula's actual revision to the Extended Scorecard.
Tharp always insisted on placing a stop for every trade. But many traders don't use stops so RiskStopLevel cannot be used and the Average Risk is unknown. So for practical purposes Average Risk can be replaced by Average Loss and the formula can be rewritten as (using WL8's metric names):
(% Profitable trades * Average Win) - (% Unprofitable trades * Average Loss) / Average Loss
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With that said, having both Expectancy and Expectancy Ratio in the metrics may create confusion. Expectancy Ratio appears to be the more robust metric and is the one that should probably be kept.
My 2 cents.
(% Profitable trades * Average Win) - (% Unprofitable trades * Average Loss) / Average Loss
--------------------
With that said, having both Expectancy and Expectancy Ratio in the metrics may create confusion. Expectancy Ratio appears to be the more robust metric and is the one that should probably be kept.
My 2 cents.
Yes I will also call out to Please include Expectancy Ratio in the report, as it is a good way to compare and analyze strategies
QUOTE:
1. Its value is *always* identical to Avg Profit (the developers can check this on *any* strategy, *any* time frame).
This is a bug. Found and fixed for PowerPack B14.
QUOTE:
Expectancy Ratio - a far more useful metric
There is also special significance to "Expectancy Ratio" as defined above:
If you use a classic exit combination of Profit Target+Stop Loss+Timeout,
by choosing various value for (say) Profit Target, you can get a wide range of "Percentage of winning Trades", "Average profit of winning trades", and so on.
The only metric which stays constant is "Expectancy Ratio".
So this is a more fundamental metric which judges the quality of your entry rules, no matter how you choose the exact "standard" exit rules.
We decided to add Expectancy Ratio to PowerPack B14, too.
@Sammy_G
Are you sure your calculation is correct? The formula has substraction but there's division instead of it in your example.
QUOTE:
Expectancy Ratio = (Reward-to-Risk Ratio x Win Ratio) – Loss Ratio
...
Thus, Expectancy Ratio = (1.51 x 46.67) / 53.33 = 70.47 / 53.33 = 1.32
Are you sure your calculation is correct? The formula has substraction but there's division instead of it in your example.
Good catch, Eugene.
Reworking the example (using values from pic 1 above):
Reward-to-Risk Ratio = 244.85 / 162.59 = 1.51 (rounded)
Win Ratio = 46.67% = 0.47 (in decimals, rounded)
Loss Ratio (same as % Unprofitable trades) = 100 - 46.67% = 53.33% = 0.53 (in decimals, rounded)
Thus, Expectancy Ratio = (1.51 x 0.47) - 0.53 = 0.71 - 0.53 = 0.18 (rounded)
I apologize for my bungling. :(
Reworking the example (using values from pic 1 above):
Reward-to-Risk Ratio = 244.85 / 162.59 = 1.51 (rounded)
Win Ratio = 46.67% = 0.47 (in decimals, rounded)
Loss Ratio (same as % Unprofitable trades) = 100 - 46.67% = 53.33% = 0.53 (in decimals, rounded)
Thus, Expectancy Ratio = (1.51 x 0.47) - 0.53 = 0.71 - 0.53 = 0.18 (rounded)
I apologize for my bungling. :(
Using WL8 B23, PP B14.
Thanks for implementing the very useful and robust Expectancy Ratio!
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I've noticed discrepancy between the purpose of Expectancy and Expectancy Ratio and their descriptions.
Currently:
Expectancy is expected profit per dollar risked per trade...
Expectancy Ratio helps determine the expected profit or loss of a trade...
Should be:
Expectancy is the expected profit or loss per trade and as such depends on the position size...
Expectancy Ratio helps determine the expected profit or loss per dollar risked per trade...
------------------------
Note: The erroneous phrases and the suggested corrections are in italics.
Hope this gets fixed.
Thanks for implementing the very useful and robust Expectancy Ratio!
---------------------------
---------------------------
I've noticed discrepancy between the purpose of Expectancy and Expectancy Ratio and their descriptions.
Currently:
Expectancy is expected profit per dollar risked per trade...
Expectancy Ratio helps determine the expected profit or loss of a trade...
Should be:
Expectancy is the expected profit or loss per trade and as such depends on the position size...
Expectancy Ratio helps determine the expected profit or loss per dollar risked per trade...
------------------------
Note: The erroneous phrases and the suggested corrections are in italics.
Hope this gets fixed.
Thanks, this is resolved for PowerPack's B15.
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