Hats can tell you style preference, what group of people your specimen wishes to be attached to, and wealth range. Look at type of hat - does it say sports, trendy, melodramatic, or insipidly stupid? Does it scream “I WANT TO BE INDIE” or “LOOK AT ME I AM STEAMPUNK”? And is it in good condition and good quality (well-to-do and conscientious), or bad condition and good quality (either hand-me-down, or used to be well-to-do and now down on their luck), or just bad quality (stingy or poor)?
Or just insipidly stupid.