Weekly Rating System

I am trying to do the following.

A2:A11 are a ten point system.
A2 is first place - ten points, A3 is second place - nine points.. and so on

A1:E1 are the five weeks I need rated.

B2:E11 are different names. We can use sports teams. They vary every week.

At F2 I would like to be able to find a said sports team, and accumulate it points and rank it.
So if the Giants are in first place every week, except the last week, they should have 49 points (4 first place ten points, 1 second place 9 point)
I would like for them to show up first in the rankings list with their total points.

Can someone guide the way please?

Ranking.xlsx

I gave it a shot, although I am sure there is a more consolidated and sophisticated way to write these formulas.