Discuss the following:
Q: a) For the two hypothetical leagues represented below calculate the league standard deviation (s t) of the winning percentage (wti) for each year. {Where wti is the winning percentage of team i in year t; st is the standard deviation of the winning percentages in one of the leagues in year t; and w is calculated as the number of wins divided by the number of games played by a particular team in a particular year and it is stated as a decimal with 3 numbers to the right of the decimal (i.e. in thousandths).}
Compare the 5 values of s that you determined for each league. What does this suggest about competitive balance in the two leagues? Explain.
b) Peruse the two tables do you really believe your results in (a)? Explain why or why not.
c) Would the ratio of the actual to the ideal s yield a different result? Calculate this ratio for each year and each league.
WON-LOSS RECORD IN TWO HYPOTHETICAL LEAGUES BETWEEN 2001 AND 2005
LEAGUE 1
TEAMYEAR 2001 2002 2003 2004 2005
A 4-0 4-0 4-0 4-0 4-0
B 3-1 3-1 3-1 3-1 3-1
C 2-2 2-2 2-2 2-2 2-2
D 1-3 1-3 1-3 1-3 1-3
E 0-4 0-4 0-4 0-4 0-4
LEAGUE 2
TEAMYEAR 2001 2002 2003 2004 2005
F 4-0 3-1 2-2 1-3 0-4
G 3-1 2-2 1-3 0-4 4-0
H 2-2 1-3 0-4 4-0 3-1
I 1-3 0-4 4-0 3-1 2-2
J 0-4 4-0 3-1 2-2 1-3