Interesting question. Let's see.
First, we have to assume that the 2 systems must signal completely independently of each other or the numbers will vary with the amount of dependence. For example, if I had 2 systems, both based off of Moving averages, and just varied the periods slightly, then the signals would tend to have more confluence and also would tend to signal in the same direction, no matter how successful or unsuccessful those signals proved to be.
Let's say we have 100 signals from A. 40% win, 60% lose. The same applies to B.
So, let's wait for 100 confluent signals (A and B both signal and that signal is in the same direction).
So we've got 100 signals from A (with B confluence), and equivalently we have 100 Signals from B (with A confluence). In theory, each system is only 40% accurate. The question is whether this 60% inaccuracy rate is reinforced or not. In other words, is the accuracy of the subset of signals with confluence the same as the inaccuracy of the unfiltered set of signals from each system?
If there is no reinforcement, then the winners would remain at 40%. If there is reinforcement (successful filtering), then the winners would be 40% of 40%, which comes to 16% winners. Either way, using a losing system to try to filter another losing system looks like a bad idea. On the other hand, if the risk/reward is one to one, then trade the reverse of these signals and your success rates should (in theory) be somewhere in the 60-84% range, depending on the success level of filtering.
The math would get more interesting if we knew what the % signals was where confluence occurred. If only 1 signal in 1000 has confluence, then even a great system built this way would have very few trades (unless this is a system giving a very large number of signals per day). If half the signals have confluence, then one system can act as a filter for the other while leaving a reasonable number of trades. Of course, in general, it's better to start with 2 systems which have over 50% successful trades.
