I believe (no sauce) that there have been studies on the placebo effect that have indicated it is quite powerful - and in the study they made the point that it was as powerful as the actual medication they were testing. "Placebo effect" has become a pejorative, like "conspiracy theory," that is designed to manipulate you into thinking that it has no value.

But I have a personal story, regarding homeopathy, that counters the placebo claim. When my eldest daughter was born, she did not sleep well, and constantly cried. We tried several things to soothe her, that all failed, and a friend recommended trying a homeopathic remedy, and mentioned two possible remedies. (small pill in water, administered with a dropper). We tried the first, no effect - A few minutes later we tried the second. Her crying stopped within seconds! She was able to sleep through the night. When this re-occurred (rarely), the treatment had the same effect (as it did with our second daughter) We have also mentioned this to friends who had the same problem, and they had similar results.