All the evidence I've seen shows that positive thinking and confidence improves performance. In anything.
Give someone an easy math problem, watch them get it right and then they'll do better on the ensuing standardized test than someone who just failed a difficult practice test.
No, positive thinking doesn't allow you to do anything, but it's been shown over and over again that it improves performance over negative thinking.
Key question then: why do smart people engage in negative thinking? Are they actually stupid?
The reason, I think, is that negative thinking feels good. In its own way, we believe that negative thinking works. Negative thinking feels realistic, or soothes our pain, or eases our embarrassment. Negative thinking protects us and lowers expectations.
In many ways, negative thinking is a lot more fun than positive thinking. So we do it.
If positive thinking was easy, we'd do it all the time. Compounding this difficulty is our belief that the easy thing (negative thinking) is actually appropriate, it actually works for us. The data is irrelevant. We're the exception, so we say.
Positive thinking is hard. Worth it, though.