Damn Interesting has an article about the "Above Average Effect": "When asked, most individuals will describe themselves as better-than-average in areas such as leadership, social skills, written expression, or just about any flavor of savvy where the individual has an interest." Since, by definition, the majority of people are average, there's obviously something going on here. He continues: "It seems that the reason for this phenomenon is obvious: The more incompetent someone is in a particular area, the less qualified that person is to assess anyone's skill in that space, including their own. When one fails to recognize that he or she has performed poorly, the individual is left assuming that they have performed well. As a result, the incompetent will tend to grossly overestimate their skills and abilities."
Makes sense to me. But this logic focuses on below-average people. What about average people? So here's my take: If the average person is incompetent at something, then the above logic holds. I.e. anyone who perceives themselves to be competent at something (even if they're not) will then consider themselves to be above-average (since mere competence places you in that desirable category). The error therefore comes in assessing one's own competence. If the average person is competent at something, however, then the error is more likely to be that the individual simply believes that not to be the case. That is, they assume (incorrectly) that most people are incompetent, and that they are competent (whether that's true or not), and therefore they are above average.
There's also a stigma associated with "average" - "above-average" sounds so much better, even if average is really good! In a highly competitive environment, this is very likely to be the case - the "average" applicant to Harvard is most likely anything but! As a relevant aside, the Talmud says that it's better to be the follower of a pack of lions than the head of a pack of foxes - i.e. better to be below-average in a talented group than above-average in a mediocre group.
To sum up, if you want to know how competitive you are, you have make sure you know what your competition is, and be able to entertain the notion that you may not be the best. Sounds good to me. But then again, since I'm better than everyone else, I already knew that ;-)