Because of rolling admissions, submitting a complete application early in the cycle has distinct advantages at many schools.That doesn't mean you should submit suboptimal written materials; it means you should start early enough (now, at the latest!) that you are offering your best work.
Rolling admissions means that a school takes applications in the order in which they are received and makes decisions about interviews and then acceptances, accordingly. So, as times goes by, there are fewer interview and admissions offers remaining to be made.
If your application is not complete, your candidacy may not be evaluated early when there are more opportunities for interviews and admissions. So, if you have not already, get started immediately. It could make a huge difference in your available opportunities.
