One Column --- I want to rank the Most Frequent

[land80land]

So I have one column, a list of names
John
James
Aaron
Aaron
Sarah
John
Harry
Aaron
James
Harry
Carmen
Mike
Carmen
John
Mike
etc...
Goal: I want a new column that will display them in order from most frequent to least frequent.
This is what I tried: I tried with INDEX, MATCH and LARGE but I ran into a problem when lets say 2 names (Carmen and Mike') both appear on the list the same number of times, it will only display the name higher up on the list.
*The parameter here is: It must be done with formulas only and no macros. As many helper columns necessary are fine. *
Thank you & really appreciate the help reddit.

 

[FDibbins]

Try 1 of these...
Rank without missing numbers...=RANK($H5,$H$5:$H$25,1)+COUNTIF($H$5:H5,H5)-1
rank with missing numbers........=SUMPRODUCT((A2>A$2:A$7)/COUNTIF(A$2:A$7,A$2:A$7))+1