No more than any other horizontal line drawn randomly on a chart, and a good deal less than some non-randomly drawn ones indicating previous support and resistance.
At least tens of thousands of people believe in them (albeit not as many as believe in astrology), but I’ve never seen anything other than anecdotal, cherry-picked evidence that they “work” at all.
Of course, people tend to notice preferentially the times that they do appear to work and to interpret them that way (just as they do with their horoscopes), and that typically strengthens their beliefs. Michael Shermer explains why in great detail and describes a lot of research findings in detail, on related subjects of belief patterns, in his excellent book [I]Why People Believe Weird Things[/I] (very highly recommended - seriously).
All the independent, objective, academic studies I’ve ever seen on the specific subject of pivot points (and that’s actually quite a few, because I used to study these things in detail, at one time) have shown that they don’t “work” any better or mean any more than random lines.
But I’m not naive enough to imagine for a moment that my mentioning that is going to shake the confidence or beliefs that anyone else has about them. (In fact, if anything, according to Shermer and other authors who have studied this phenomenon, it’s probably even going to [I]strengthen[/I] their beliefs, so there’s that to be thankful for. ).