1. Imagine over five seasons (1,2,3,4,5) the order of finish for five teams (A,B,C,D,E) in the Greenwich Village League (GVL) and the East Village League (EVL) are as follows.

GVL Season EVL Season

seasons seasons

1 2 3 4 5 1 2 3 4 5

finish E E E A A finish E B C D A

order D B D D D order A E E E E

C C C C C C C D A D

B D B B B B D B B B

A A A E E D A A C C

[For clarification: an example of finish order is in Season 1 of the GVL, Team E finishes first, Team D finishes second, Team C finishes third, Team B finishes fourth, and Team A finishes fifth].

(i) (2 points) Calculate the Herfindahl-Hirschman Index, and then use it to determine which league has better competitive balance across seasons.

(ii) (1.5 points) Imagine you were a fan of Team E. Which set of distributions would you prefer (GVL or EVL), and why?

(iii) (1.5 points) If we introduced a system of promotion and relegation into the leagues, would this affect the usefulness of the HHI? If so, explain why.