Hi TB,
This may provide the end result you are looking for. Rather than sorting your Ranking Table, it extracts a list, sorted by rank, of the 16 teams, and lists their "Standings Points" and Rank.
The method uses an added column to provide a points list with no duplicate values (required by LOOKUP). The 'distinct values' column, shown greyed, may be hidden.

The renamed "Point totals" table contains the formula below in the added column (G):
G2, and filled down: =E+ROW()/1000
The second table, "Team Ranking" contains a lookup formula in columns B and C to retrieve the values shown in those columns:
B2, and filled down: =LOOKUP(LARGE(Point totals :: $F,ROW()-1),Point totals :: $F,Point totals :: $A)
C2, and filled down: =LOOKUP(LARGE(Point totals :: $F,ROW()-1),Point totals :: $F,Point totals :: $E)
Note that these differ only in the return-values column address.
Column A uses the RANK function and the actual Standings points values in column C to determine the RANK of each team, according to it's Standings points total.
A2, and filled down: =RANK(C,$C,0)
For a list sorted in descending order, replace LARGE with SMALL.
If the smallest point total means the team is in first place, replace =RANK(C,$C,) with =RANK(C,$C,1)
Regards,
Barry