You are right, the number does very a lot. I never really paid too much attention to the number of landings a student would have, but I do remember that my (and most other CFIs at my school) students would have anywhere from 12ish to around 20 hours. The number of landings would probably be less at airports with runways long enough to do touch and goes considering you could get more TOLs in any given lesson.

I also noticed that the younger students would pick it up quicker than students in thei later years.

What helped my students was when I said something along the lines of "get the mains just a few feet above the runway and prevent them from touching for as long as possible". This is of course if you are teaching in a tricycle.

Howany landings are your students averaging?