We were there this past New Year's. We noticed the crowds diminishing greatly by Friday. On Monday the crowds were non-existent. We went to IOA on Friday and noticed the crowds were less there than at WDW. We left on Wednesday, and enjoyed quite a few days of fun, crowd-free days. I didn't take notes this trip, so I am going from memory. So, I would say you could look for crowds to start tapering by Saturday and Sunday. People will probably take those days for travel days.