6.43 z scores and comparisons of sports teams: A common quandary faces sports fans who live in the same city but avidly follow different sports. How does one determine whose team did better with respect to its league division? In 2012, the Atlanta Braves baseball team and the Atlanta Falcons football team both did well. The Braves won 94 games and the Falcons won 13. Which team was better in 2012? The question, then, is: Were the Braves better, as compared to the other teams in Major League Baseball (MLB), than the Falcons, as compared to the other teams in the National Football League (NFL)? Some of us could debate this for hours, but it’s better to examine some statistics. Let’s operationalize performance over the season as the number of wins during regular season play.

a. In 2012, the mean number of wins for MLB teams was 81.00, with a standard deviation of 11.733. Because all teams were included, these are population parameters. What is the Braves’ z score?

b. In 2012, the mean number of wins for all NFL teams was 7.969, with a standard deviation of 3.036. What is the Falcons’ z score?

c. Which team did better, according to these data?

d. How many games would the team with the lower z score have had to win to beat the team with the higher z score?

e. List at least one other way we could have operationalized the outcome variable (i.e., team performance).