Assume that we use an AVL tree to store about 20 million records.
We end up with a very deep binary tree with lots of different disk accesses; log220,000,000 is about 24, so this takes about 0.2 seconds.
We know we can’t improve on the log2n lower bound on search for a binary tree.
But, the solution is to use more branches and thus reduce the height of the tree!.
As branching increases, depth decreases.