Based on the information in your post I created a 3 table base setup that I think may work for your needs.
The first table tracks the number of Quizzes (I made them separate quizzes but you could make another table to track questions to associate to each quiz depending on what workflow would work best for you):
The second table tracks Teams and each of their scores(I’ll expand on the rollup field further down):
The third table is a joins table that tracks each Team’s score for each Quiz. So each time a team completes a quiz you could create a new record using this table to track the team, quiz, and their score for that quiz :
(As an aside the main “Unique Name” field is an identifier for that record, and is a formula tracking the team and Quiz with a Autonumber field)
With those three tables in place you can now use the Rollup field on the Team’s table to find out a team’s average score:
Then, depending on how you’d like to visualize the leaderboard, you could use the Chart App to visualize the score for each team:
I hope this helps, but please let me know if I can expand on any of the above!