Why would a grad school make admission offers prior to the deadline? The University of Illinois physics PhD deadline is January 15th. When I submitted on January 1st I got an email confirming submission and it included the following:


  "Committee reviews will begin immediately after the application deadline, January 15 for Fall term. Admissions decisions are typically completed by March 15 for Fall admission. Decisions will be sent to you via e-mail."


However, the GradCafe results board shows that multiple applicants received offers within days of applying. 

The more I think about it, the more this doesn't make sense for the program to do. Aren't they missing out on potentially more qualified applicants who are busy and haven't applied yet (deadline isn't for another 5 days)? What if these offers they are sending out BEFORE the deadline are accepted? They are reducing the number of spots in their program.
Sending offers too late to a very good applicant also involves the risk that the applicant will accept a different offer, and the university will lose out. Very good applicants also tend to receive many offers, so this risk should not be underestimated.

Similarly to the case of hiring employees at a company, if a university wants to admit the best students, the optimal strategy would probably be to make sure to admit the very best applicants as quickly as possible, while delaying the decision for the "good but not best" applicants until the end of the deadline, in case someone better shows up. The difference between study programs and hiring processes is that universities have plenty of statistics from previous years that let them know what a "great" applicant is and what a "good" applicant is, so the could optimize this process much more if they wanted.

In the German system, some universities have this explicitly built into their admission procedure. For example, at the Technical University of Munich, great applicants are immediately admitted, and good applicants are invited to an interview:


  In the initial stages, the grades you obtained during your Bachelor's program, as well as your written documents, will be evaluated using a point system. Depending on the number of points accumulated, applicants are either immediately admitted, rejected or invited to a 20 minute admissions interview carried out by the department faculty.