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Well given that just amongst people I know, symptoms after vaccine have varied from none whatsoever (me, despite anticipating being really ill) , to totally knocked out for a day and a half with temperature, etc (my partner who is almost never ill and was expecting to be fine), to another friend who was really ill for a couple of days with corresponding drop in blood oxygen levels. Basically most people I know have been either properly ill with a temperature or absolutely fine. No correlation whatsoever between expectation of being ill and subsequent symptoms. Also seemingly little correlation between having had covid or not. So I'd say that's hugely unlikely to be placebo effect. Obviously all anecdotal, but I think very very different to your example of branded vs non branded painkillers.
Sorry, am confused by your point?