worst case in MAX-HEAPIFY: "the worst case occurs when the bottom level of the tree is exactly half full"

In CLRS, third Edition, on page 155, it is given that in MAX-HEAPIFY,

"the worst case occurs when the bottom level of the tree is exactly half full"  

I guess the reason is that in this case, Max-Heapify has to "float down" through the left subtree.
But the thing I couldn't get is "why half full" ?
Max-Heapify can also float down if left subtree has only one leaf. So why not consider this as the worst case ?