Sort function with countif?

DerrellSC 

<< Is it possible to sort 2 columns based on the second when the second is using counif? >>

Yes, your second-column formula probably allows that.  You can (save your workbook and then) manually try that out.

<< I would like for the count to automatically sort when the winner column is updated. >>

Well, apparently you mean for both the players' names and counts to automatically sort.  The answer here is also yes, e.g., by using a "separate copy" of the data:

and a formula (in A13 in this example) that uses the SORT function:

=SORT(A3:B8,2,-1,FALSE)

(You do not have to put the Rankings data in the same columns as the Roster data; I just did that because it fits nicely.)

I have attached my workbook with that sample data (intentionally not creating entries for all the round-robin games).  Note what happens when you enter a winner for game 9.