Suppose in a six-team league, the winning percentages were as follows at the end of the season. Team A: .750, Team B: 0.600, Team C: 0.500, Team D: 0.500, Team E: 0.400, Team F: 0.250.
(a)Compute the standard deviation of winning percentages within season (4 points). (Round to the third decimal.)
(b) Why do we use team-specific variation across seasons to measure competitive balance to complement the within season variation? (1 point)
Using the above, suppose each team plays a 50-game schedule. (Compute the "ideal" benchmark standard deviation based on equal playing strength, and the ratio of the actual to the ideal. (2 points)
Compute the same measures if they were to play a 90-game schedule (Round to the third decimal.) (2 points)
Which one has a higher "ideal" benchmark standard deviation and why? (1 point)