Placebo is such a curious thing. If you can prove to yourself that your effects are placebo-effects, then those effects should disappear, because you no longer believe in them.
So if it's working for you, you probabaly should NOT start a study to find out if it works or not. It might stop working (for you). What good would that do?
I am hoping my level of self-delusion would be strong enough. When I was a kid and wanted to play sick to get out of school, I'd always quickly develop an actual low-grade fever and begin feeling legitimately sick. Even after I noticed the pattern, it still happened.
I'm hoping I can use this power of deception against myself with L-Theanine if I were to run this kind of study (but, maybe fortunately, have no motivation to do so at this point).
It may have something to do with what we say to ourselves inside our heads. If we say something to ourselves it is kind of believing. We believe what we think, we believe what we say. We can of course change our thoughts later. Like when you started feeling sick but when there was no more need for the symptoms, you could say "I'm no longer sick at all" :-)
So if it's working for you, you probabaly should NOT start a study to find out if it works or not. It might stop working (for you). What good would that do?