My guess is not much? Because we are doing rolling applications, so we are somehow trying to judge how many good applicants in total we are going to get (classical secretary problem). Applying early means we might let you in with a lower bar if we end up getting a lot of great applications later and raise our bar. Applying later might be better if we realize we were overly conservative in the beginning and are disappointed in the later applications.

Thinking about it, my guess is we will probably let promising people who applied early know that they are on some kind of waitlist and extend an invite to them if we end up disappointed with the later applications, so if you are flexible, I think that makes early strictly easier. I don't expect the effect to be that large though.