Quick question about Effective Nuclear Charge.

What is the trend for Zeff as you go DOWN a group?
I would normally think that it would decrease since there are more shells and more core electrons to shield the valence electrons, but my teacher and textbook both say that it increases and don't say why. I get why it increases as you go right down a period, it's because the protons are increasing and creating a greater charge that the added valence electrons can't shield from since electrons in the same shell don't shield. Any help would be appreciated. Thanks