WOW,....I didn't mean to spark such anger on this board. Just trying to engage in a HEALTHY discussion about Probability win rate and Expectancy and stats about a trading system.
I have taken a look at the issues brought up above. That is where someone (I believe neke said it..but not sure) made reference to expectancy as a ratio of wins to losses. What I think he was actually trying to compare was PROFIT FACTOR. So I did a MC Sim on the same 2 systems with EQUAL Profit Factor. I ran the exact same sims with $100,000 acct and used the following formula.
Profit Factor = (Total Profit of Wins)/(Total Profit of Losses)
I assumed a WINNING system for both with a PF of 2.
So for the 10% system we would have a 1 win of 18 R and 9 R losses. (18/9 = 2)
For the 90% system we would have 9 wins each of only 0.222R and 1 R loss. You could do the same calc. with 9 wins at 1R but your loss would need to be 4.5R. Since I hardly think a 4.5R loss is realistic or fair to compare to a system that loses 1R on average I chose this calc. instead. {(9*0.222) = 2...therefore 2/1 = 2}
The results can be interpreted in different ways. First one would say that the 10% system made more money. This is true with equal PF systems. However, this was NOT the point I was trying to make earlier. The point is that there is wildly different levels of equity in the lower probability win rate system when compared to the 90% system. Notice that even with a 10% system and ONLY 0.1% risk of capital there is a possible net -$7100 LOSS!!!. There is also a $50,000 net MAX Profit. Again,....this proves exactly what I said earlier. Probability win rate effects volatility swings in ones account equity and MAX DRAW DOWN!! Notice how much worse this swing gets with 1% at risk (see following posts).
You could say well volatility is also high with 90% systems and I would say this is true but it is FAR less than the 10% systems AND the 90% systems have FAR less draw down. See that the 0.1% risk model on 90% system has MIN P/L of $933....again ZERO chance of a losing year!!! Notice that as the risk increases to 1% you now have a small possible loss (ONLY $500) for the year which I would say is MORE THAN acceptable level of risk of loss given that the MAX gain is $39,833....~40% return!!!
As for the person (may have been neke too...) that said you should look at a fixed risk ratio because as you lose moiney you will risk less I can only say this. This particular MC Sim file does not allow one to make this analysis but I have another MC Sim that came with a spreadsheet program I use to keep track of my trades. That spreadsheet is here...
http://tradingspreadsheets.com/default.aspx
This file is not available for free but it DOES allow fixed risk ratio MC Sim. I have done the same data on this system and it shows very similar results only that you bleed slightly slower with a fixed risk ratio than what I have presented here. So it will take longer to lose money but the effect is the same. You will just have to take my word on that as I have provided enough data to prove my point.
SO,...there you have it. All you nay sayers that say probability win rate means shit are sadly mistaken. I have shown that with equal Expectancy and even equal Profit Factor that 2 systems that vary in ONLY probability will have less draw down and MORE ability to withstand higher risk capital per trade. This was shown with lower losses with a 90% system.
Remember the old adage of protecting capital to live to fight (trade) another day. That is what this discussion was all about. A higher probability system gives you a better chance at this. A "Holy Grail" system would have HIGH Probability, HIGH Expectancy, HIGH Profit Factor, and LOW Standard Deviation. EACH OF THESE 4 IS IMPORTANT IN THEIR OWN WAY. NONE ARE IRRELEVANT JUST SOME MORE RELEVANT THAN OTHERS!!
The idea is to use a proper MC sim to find the IDEAL RISK capital per trade that meets YOUR definition of ruin and staying WELL within those limits. Every system is different, but to say probability is irrelevant or useless is simply speaking without know the facts!!
Instead of opining on what you have heard or read before why dont you provide solid DATA and stats to prove what you believe to be true. If you can not do that then you are bound to make the mistakes of all of the others before you.
For those that would like this MC sim in Excel,...here is the link. I have modified this file slightly to suit my needs.
http://www.box.net/shared/9ogdzi1epn
Good Luck.
First pic is 10% system with PF = 2 and only 0.1% risk