Assume most people are smarter than you.
To assume you're below average is to admit you're a beginner. It puts you in student mind. It keeps your focus on present practice and future possibilities, and away from any past accomplishments.
Most people are so worried about looking good that they never do anything great. Most people are so worried about doing something great that they never do anything at all.
You destroy that thinking when you think of yourself as such a beginner that just doing anything is an accomplishment.
On the contrary it is also important to know you are (or at least have the potential to be) above average. It's an issue of confidence -- you can get a lot more done when you know that your ideas are good enough to be heard by others. This isn't arrogance, but rather a way to combat insecurity and low self-esteem.