# Expectancy versus average P/L



## Gringotts Bank (7 December 2010)

expectancy versus average profit/loss.

Aren't they the same thing?

I was calculating my expectancy and found that it was the same as the average profit/loss in AB backtest report.


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## the phantom (7 December 2010)

Hi GG, hope this helps,

https://www.aussiestockforums.com/forums/showthread.php?t=2398&highlight=Expectancy


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## Synergy (7 December 2010)

Pretty sure they are the same thing...

What's the number you're getting?


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## tech/a (7 December 2010)

No not the same.

Expectancy is return / $ invested.
P/L is Profit returned over X periods.


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## Gringotts Bank (7 December 2010)

Thanks both.

Synnergy:  2.4% of position size.  Don't read anything into that though.

I don't see why people emphasize expectancy, when there's nothing you can expect (into the future) unless you have a smooth, even equity curve (ie. low std deviation).  I guess both together give meaning to the test.


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## Gringotts Bank (7 December 2010)

tech/a said:


> No not the same.
> 
> Expectancy is return / $ invested.
> P/L is Profit returned over X periods.




But they were the same figure when I calculated them.


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## the phantom (7 December 2010)

I haven't reviewed these calcs in a while (also suppose to be studying for an exam but thought I would take a break), but I believe both assume a large enough sample size, the bigger the better.

But for simplicity,

if we had 4 trades, +$10, +$10, +$10, -$30, 

average P/L  ((10+10+10)/3)/((30)/1), which is 10/30, so 1/3.

however Expectancy would be 0.75*10-0.25*30 = 0;


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## Gringotts Bank (7 December 2010)

Hmm.

gah, edit my stupid maths....
sorry, best I go back to my stats and do it again.  Your example makes perfect sense, thanks.


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## Gringotts Bank (7 December 2010)

ok did that... now a new problem.  AB has this formula for average P/L.

Avg. Profit/Loss: (Profit of winners + Loss of losers)/(number of trades)

which would work out to zero also, same as expectancy!

So now I'm wondering if your ave P/L formula is correct Phantom?  How could the average trade be >0 if by the end of the trading period you end up with 0 balance?


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## the phantom (7 December 2010)

Hi G/B,

Software or people are allowed to have their own definitions (however yes does make things confusing), 

my basic definition of Avg P/L , is similar to 

http://www.investopedia.com/terms/p/profit_loss_ratio.asp




However let's look at the formula you have given above.

Avg. Profit/Loss: (Profit of winners + Loss of losers)/(number of trades)

I'll try the maths on a slightly different example,

+10,+10,+10,-35


Expectancy = 0.75*10 - 0.25*35 = 7.5 - 8.75 = -1.25.

using the formula,

Avg. Profit/Loss: (Profit of winners + Loss of losers)/(number of trades)

equals: (30-35)/4 = -1.25 

(to be honest I have not seen Avg. Profit/Loss, formulated the above way as you mentioned.)

YES, same values !!!! Using your mentioned calculation in AB.

I also use AB, looking at standard reports the closest I see is Profit Factor.

But reviewing the maths on a simple level,

(3*10/4) - (35/4) = X

((10+10+10)-35)/4 = X

AB, seems to be showing Average P/L as the same as expectancy. So you are not going crazy !


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## Wysiwyg (8 December 2010)

Gringotts Bank said:


> *I don't see why people emphasize expectancy*, when there's nothing you can expect (into the future) unless you have a smooth, even equity curve (ie. low std deviation).  I guess both together give meaning to the test.




The dollar figure that the AB Expectancy formula calculates is the same as Avg. Profit/Loss. It should be as Tharp calculates Expectancy as in R (risk) per trade terms and the resultant profit/loss ratio against the initial R (risk). That is 0.5R, 1R or 2.7R for example. If you know the formula to do this it would be helpful. Thanks.


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## Wysiwyg (8 December 2010)

From 176 trades I risk $1400 per trade and the resulting Average Profit/Loss equals $112, then if I divide the Avg. P/L by the dollars risked per trade, i.e. 112 / 1400, this equals 0.08 which is the expectancy. 0.08R per $1400 risked equals  Expectancy. Yes???


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## tech/a (8 December 2010)

Wysiwyg said:


> From 176 trades I risk $1400 per trade and the resulting Average Profit/Loss equals $112, then if I divide the Avg. P/L by the dollars risked per trade, i.e. 112 / 1400, this equals 0.08 which is the expectancy. 0.08R per $1400 risked equals  Expectancy. Yes???




Yes for every $ invested you would "expect" to make 8c


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## skc (8 December 2010)

Geez louise.

There is a difference between Avg P/L and Avg P / Avg L.

Which one are you talking about?!


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## the phantom (8 December 2010)

SKC, are you referring to Profit Factor ?

PF = Gross Profit / Gross Loss

What do you mean by Avg P/L, if it does not equal Avg P/Avg L ?


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## skc (8 December 2010)

the phantom said:


> But for simplicity,
> 
> if we had 4 trades, +$10, +$10, +$10, -$30,
> 
> ...




In the above you are working on Average P / Average L. This tell you what is your average win compared to average loss.

Average P/L is the average profit or loss per trade. Which is simply how much you make per trade. Divide that by the position size you get average % return per trade. This is the same as expectancy (which by definition is what you expect per trade).



the phantom said:


> SKC, are you referring to Profit Factor ?
> 
> PF = Gross Profit / Gross Loss
> 
> What do you mean by Avg P/L, if it does not equal Avg P/Avg L ?




Profit fact is like you said gross P / gross L, which is how many steps forward you take for each step backwards. Tells you something different entirely again.


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