Four With Ties

There are 4! = 24 ways to rank four objects. However, a friend told me that if ties are allowed, the number increases to 75.

I attempted to list all the possibilities by first listing the 24 orderings of four objects, then using brackets to group ties involving two players, then group ties involving three players, and finally the single case in which all four objects are tied. But something has gone wrong; my list includes just 69 possibilities, not 75.

What happened? Did I miss something, or was my friend mistaken?

This brainteaser was written by Derrick Niederman.