Quote from nonlinear5:
Yes, everything else being equal, the system with 1000 trades will have the PI about 3 times higher than the system with 100 trades: sqrt(1000) / sqrt(100) ~ 3
That's built in the PI to reflect that higher number of trades gives higher statistical significance to the system performance. I am not a statistician, so I can't say if that sqrt(trades) term is too dominant. It seems to replicate the "standard error", which is inversely proportional to the square root of the sample size: http://en.wikipedia.org/wiki/Standard_error_(statistics)
The PI formula closely resembles Van Tharp's System Quality Number (SQN): http://www.ninjatrader.com/support/forum/showthread.php?t=4320
I did see a reference somewhere about Van Tharp's recommendation to cap the sqrt(trades) term when the number of trades is too large.
I see your point about statistical significance and the number of trades, but I do think that Van Tharp's idea of cutting it off at some point makes sense. I personally do track this metric for my own trading, but just multiply ratio of average to std dev by 10 to get a number. As long as it's over 1.65, I'm relatively satisfied my results aren't due to chance.
I had a big go-around with some people here a few weeks ago on this metric after I suggested someone calculate it for their method to test statistical significance. Was even accused of being Van Tharp. I don't know that I'd go so far as to say it's better than any other metric, as I like profit factor and Kelly (in either the discrete or continuous formulations), although those don't do a good job of capturing the number of opportunities to trade, just how well each trade performs. Obviously, there is no perfect metric.