First, he didn't account for commission, slippage, or spread in the Risk side of things. This is a nice sales technique as it makes the noob feel like it's going to be an easy game, but it's not accurate. Secondly, he calculated his reward based on what HAPPENED. "For example, if you make a profit of $2,000 (2 x $1000 or $20/share), then you have a 2R profit." The whole point of calculating a Risk/Reward ratio is to choose trades that have at least a certain RRR BEFORE the trade is even placed. If your reward is calculated in hindsight, the whole purpose of an RRR is lost. Third, what Bill said. It's like your high school teacher trying to calculate a "weighted" grade by using a simple average. If one assignment was worth 10 pts and you got a 3 or 30%, and another assignment was worth 90 pts and you got a 90 or 100%, your overall score is 93 of 100 (3/10 plus 90/90). What this guy did was like the teacher trying to average your grade by taking 100% plus 30% and dividing by 2 to give you a 65% grade.
Ever notice how convenient it is to assign a proper, even scientific label to shitty trading strategies ?
I've stopped counting the number of 'experts' who have written books that cover expectancy (among other things) that fail to accurately account for varying position sizes, eg pyramiding as price moves in your favour.
They simply can't account for all these things, you are right. IMO positive expectancy is a fancy, useless really way of saying that one is making money. More importantly, as it is shown in the blog link below, the formula for expectancy is equivalent to the formula for the average trade. They are exactly the same thing. In other words, Expectancy = w x avg win - (1-w) x avg loss = (Sum winners - sum losers)/No of trades which I will go one step further than the author of the blog and declare expectancy equal to Net profit/No of trades Funny, eh? So simple! So much for the fancy expectany concept. Useless really. As far as R:R, you do not need expectancy to get that. You can just divide the Net Profit by the number of trades times the average stop-loss. Simple, eh? http://www.priceactionlab.com/Blog/2010/12/what-is-a-trading-edge-part-ii/
It is more of a serious limitation of the concept, not a blunder per se. For the averaging to work, the risk per trade must be a constant value. This is in general not true or even applicable. Many traders adjust risk based on volatility. So yes, this analysis is flawed in general. Someone should invite V. Tharp here to explain this. I don't have his email address.
Everything in the markets is just a best guess, individual perception which differs from person to person. Also, in the markets historical records are of dubious value. What's the alternative to expectancy? There isn't one. Not calculating it isn't an option, because if you don't have a clue how a trade might perform, you have no justification for making it. So, unfortunately, you have to make your best guess and hope it's not too far out. The fact is that all trades rely on educated guesswork, there is no getting away from that.
All the more it seems like saying expectancy is a form of measurement of fallacy... "I guessed 10 out of 15 times correctly, therefore I can project and expect a certain performance in my guessing system for the future" Not calculating it could help you avoid a false sense of 'Great Expectations'.
+ Calculating expectancy is equivalent to saying "hey, I made money". You don't need any calculations for that. Just look at your PnL. Besides, I don't understand why people keep calling expectancy somehting that in all books of probability is called expectation. Enough with this expectancy BS.