2nd Nth Indexed Value

Column D contains team names. Column E contains team rating values.

Column G contains the following formula beginning at G2 to sort the values in Column E high to low -
=LARGE($E$2:$E$245,ROW()-1)

Column F contains the team names from Column D that correspond to the appropriate ordered ratings in Column G with the following formula beginning at F2 -
=INDEX($D$2:$E$245,MATCH(G2,$E$2:$E$245,0),1)

In the instance that a rating is duplicated, the first alphabetic name of a team with that rating is listed twice. Is there a simple way to list the last team name alphabetically instead? Can it be done within the existing Column F formula such that if G34 contains a rating identical to G33 -
=IF(G34=G33,...,INDEX($D$2:$E$245,MATCH(G34,$E$2:$E$245,0),1)) ?

Also, I have heard that ROW() empty can cause problems. What is the solution to avoid such?

See the attached worksheet.

Again, G is listed using Large, high to low. F is the team Indexed from Column D with the rating from G.

As can be seen here, Green appears twice. The occurrence of two identical ratings in my data is unlikely but a concern since the values are indexed and each team must be represented. I've seen a number of methods that can be used to list all teams. However, I would prefer to set up IF statement criteria if it can be done.

Again, I would like to utilize a formula so that in the example above, the formula in F5 would be -
=IF(G5=G4,...,INDEX($D$2:$E$7,MATCH(G5,$E$2:$E$7,0),1))
with the IF criteria causing the last team alphabetically with a rating of 26 to be listed because it matches whatever criteria is required. In this example, Purple follows Green alphabetically so it would meet the criteria.

I hope that's clearer.

Entered just as shown as an array formula I get a #NAME? error.

That did it.

Thanks for the help, Sixthsense!