Who can spot the blunder in the example in the table by the Van Tharp Institute? http://www.iitm.com/sm-Expectancy.htm

He did not account for the difference in position sizes. The R multiple expectancy formula will only work if all positions risk the same dollar amount.

Expectancy is just a jargon to impress beginners because its components probability and average win-loss ratio simply means your best guess in target distance & a historical variable which changes. This statistical number may look good until it encounters a black swan situation.

I will play devils advocate here and say that it is more than that. I realize that expectancy being > 0 means a profitable system over the number of trades in the data set. You do not need a fancy number to tell you that if your profit is greater than losses....simple...I get it. That is always the arguement as to why its useless. However, Expectancy is not (in my mind) used to tell if I have a profit as I just look at profit for that. I use it to help determine appropriate risk to take on a trade to reach my goal. If I have a 0.5R Expectancy then the unwary person may think if they risk their entire account they would make 50%. You need to think of it in terms of risk and draw down for that reward. Expectancy just allows you to look at your trade stats to analyze your reward in terms of risk....how much risk did you take to get that reward? So looking at Expectancy (or profit) in isolation means very little...it needs to be examined in the setting of the amount of risk taken to achieve that reward. Just my $0.02

I don't see an error. For each trade, you risk a different amount. Whatever that amount is, you will, on overage, earn twice that risk amount. The chart extracts out the nominal dollar values and compares only the risk:reward ratio.

As I mentioned, risk to reward ratio is the probability component of expectancy,which is just a best guess,individual perception of profit to loss target distance, differs from person to person.It means even less than the (statistical avg profit) component of expectancy which is at least a historical record not a subjective projection.

I think one cannot average different Rs. This is the error IMO, very basic algebra. These are basically R1, R2, R3 and R4. They have different values. Does anyone else see it? I think it is the kind of error that would get you an F in a high school test.

This doesn't make any sense to me. I can't see any connection to the other table. There they average the R multiples, something that I think is not correct. In your table, you divide the net P/L by the sum of the fixed dollar risk you arbitrarily defined.