Many of my posts have turned out to be wrong on later examination. Looking back, the reason every time was that I tried to solve a hard problem, found a solution that looked new and interesting, and failed to examine it enough before posting.

The phrase "worse than random" in your post sounds misleading to me. Many questions have answers in the form of long sentences, not just yes/no. A random number generator has an astronomically low chance of generating a coherent sentence, never mind interesting or correct. So even if I'm wrong every time, I still like to think that I'm doing better than random: my faulty proofs can be patched, and my faulty explanations can still point toward the truth.