You never know. I've got great cabins at a fair price late AND I've have no choice because I waited too long. Just depends.
My BIL just booked a 12 day European late and was burned somewhat. $6K for a balcony, but he wanted on that cruise. In the past he got a flash sale for a bargain rate for 1/3 of that. It just depends on timing, wait list, etc.