The standard deviation of win percentage for the 32 teams in the NBA in 2005-2006 was 0.134. The NBA plays an 82 game season. The standard deviation of win percentage for the 20 teams in the English Premier League in 2005-2006 was 0.158. The EPL plays a 38 game season. The idealized win percentages for the NBA and EPL are
A) 0.055 (NBA) and 0.081 (EPL)
B) 0.078 (NBA) and 0.115 (EPL)
C) 1.672 (NBA) and 1.580 (EPL)
D) 2.427 (NBA) and 1.948 (EPL)

Question

Quizplus · Accepted Answer

The idealized standard deviation of win percentage can be calculated using the formula for the standard deviation of a binomial distribution, which is sqrt[p(1-p)/n], where p is the win probability (assumed to be 0.5 for an idealized scenario), and n is the number of games. For the NBA, this gives sqrt[0.5*(1-0.5)/82] = sqrt[0.25/82] = sqrt[0.00305] ≈ 0.055. For the EPL, it's sqrt[0.5*(1-0.5)/38] = sqrt[0.25/38] = sqrt[0.00658] ≈ 0.081.

The Standard Deviation of Win Percentage for the 32 Teams