Why do roots of polynomials tend to have absolute value close to 1? I know very little about the math going on in the background but a colleague demystified this for me by saying that basically it is a special feature of the basis you have chosen, namely the monomials. If you choose a different basis or even just weight each monomial by a factor, the roots will tend to congregate on a different set. Basically although a) any polynomial can arise and b) you chose them randomly... They aren't as generic as as you think; they've in fact been chosen in a special way.